By using  Schauder fixed point theorem and Banach compression mapping principle, we studied a class of conformable fractional impulsive differential equation boundary value problems with delay, and established the existence and uniqueness theorems of the solutions. Based on this, we obtained the conclusions of Ulam-Hyers stability and Ulam-Hyers-Rassias stability. Finally, we provided an  example  to verify the theoretical results.

Aiming at the flight path planning problem of emergency communication unmanned aerial vehicle (UAV) in complex mountainous environment, by  comprehensively considering the constraints such as obstacles, UAV load and UAV battery capacity, in order to reduce the flight time and extend the flight distance of UAV, based on the framework of Harris hawk algorithm, we designed a three-dimensional path planning method of UAV based on improved Harris hawk algorithm. Firstly, we  improved the initial position of Harris hawk population, position update equation and escape energy of prey. Secondly, the path was smoothed by using cubic spline curve interpolation method to ensure safe, reliable and smooth operation of the UAV during flight. Finally, the emergency UAV was tested in mountainous areas with different obstacles, and the results were compared with the standard Harris hawk, ant colony algorithm and artificial bee colony algorithm. The analysis results show that the path generated by the three-dimensional path planning method planned by this algorithm is shorter and can find the optimal path faster.

Firstly, aiming at the problem of traditional single-stage remote sensing image fusion task that required a large number of supervised samples and poor retention of image feature information, we proposed a two-stage panchromatic sharpening method for remote sensing images. The method achieved the fusion of remote sensing images by decomposing the task into two tasks of feature fusion and super-resolution. In the first stage,  the adversarial network feature fusion was generated, and in the second stage,  the super-resolution network generated clearer spatial features,  achieving the goal of high quality remote sensing image fusion. Secondly, the  multiple experiments were conducted by using GaoFen-2 and WorldView-3 satellite datasets to verify the effectiveness of the proposed method, and the fusion results were evaluated by using reference image quality indexes and non-reference image quality indexes, respectively. The experimental results show that the method can better retain the spectral feature information and spatial feature details compared to the traditional methods, and effectively improving the visual effect of the fused image.

Aiming at the limitations of extracting retinal features from single-mode retinal images, we proposed a multi-modal retinal disease diagnosis model based on multi-level and multi-scale attention fusion network. Firstly, the multi-level attention network and multi-scale attention network were designed for color retinal images  and retinal optical coherence tomography respectively, and the fusion features were obtained by merging at the feature layer. Secondly, the weighted loss function of the two modes and the loss function of the fusion features were added to extract the unique and complementary information of the two modes in order to  improve the accuracy of retinal disease diagnosis. The results of evaluation experiments  on the MMC-AMD dataset and GAMMA dataset show that the proposed model outperforms  the current mainstream models and has superior diagnostic effect.

Using the theory of stochastic differential equations, we discussed  an Ebola infectious disease model with isolated compartments and animal compartments. We gave the threshold between extinction and persistence of infected animals within the animal subsystem of the model, as well as the conditions for persistence of the disease in the overall animal-human system, and proved the existence of  ergodic stationary distribution in the system. Finally, numerical simulations were conducted to validate the theoretical results. The  results show that it can form endemic diseases when the disturbance intensity is small, and it can lead to the extinction of disease when the disturbance intensity is large enough.

Aiming at  the problem of poor effect of the style transfer of existing image ink painting, we proposed a new data enhanced cycle generative adversarial network (GAN) for the style transfer of ink painting of unpaired natural landscape photos. Firstly, the binary synthesizer and discriminator structure was designed to effectively improve the mapping constraints of one-way GAN models. Secondly, we used multiple loss functions to optimize the model, introduced total variational loss and identity mapping loss, and designed a new cyclic consistency loss function combined with multi-scale structural similarity to better capture the characteristics of traditional ink painting. Finally, data enhancement techniques were used to increase the amount and variety of real and generated data to improve generator performance. The comparative experimental results show that this method can effectively transfer natural landscape images to traditional ink painting style images.

We considered a class of Gierer-Meinhardt models without  diffusion term. Firstly, we studied the existence,  the stability of equilibrium points and the various bifurcation phenomena of the model. Secondly, by choosing proper bifurcation parameters, we proved that the system had saddle-node bifurcation, Hopf bifurcation and Bogdanov-Takens bifurcation of codimensions 2. Finally, the theoretical results were demonstrated by numerical simulations. The results show that the rate μ influences the instability of system.

By using sliding mode synchronization theory and sliding mode dynamic methods, we studied sliding mode synchronization 
of fractional-order Rikitake uncertain chaotic systems and drew the attractor phase diagrams of Rikitake chaotic systems. According to fractional-order calculus, we constructed three sliding mode functions, gave three synchronization schemes, and compared and analyzed three synchronization schemes. The results show that fractional-order Rikitake uncertain chaotic system can achieve sliding mode synchronization under certain conditions.

Aiming at the problems of oversized models, slow detection speeds, and high complexity in existing unmanned aerial vehicle (UAN)  target detection algorithms, we  proposed an improved lightweight UAN  detection algorithm YOLO-LDD based on YOLOv5n.  Firstly, on the basis of YOLOv5n, a diversified branch  module DBB and C3 module were introduced to  fuse and  reconstruct into  C3_DBB module, enhancing the representational capacity of individual convolutions. Secondly, a reparameterized structure convolution RepConv was introduced into the neck network to improve detection speed. Finally, the model was compressed by using the layer-adaptive magnitude-based pruning (LAMP) method to reduce the number of parameters. Experimental results show  that the proposed algorithm can maintain excellent detection performance while reducing computational and storage demands, and improve  efficiency and inference speed of the model. The  average accuracy reaches  96.7%, the  parameter count is reduced by 73% compared to YOLOv5n, the computational load is reduced by 60%,  and a detection speed is increased by  1.6 times.

Firstly,  the basic reproduction number R₀ of the SIVS (Susceptible-Infectious-Immune-Susceptible) epidemic model is solved by the method of next generation matrix, through the threshold, the disease-free equilibrium point always exists, and the endemic equilibrium point only exists when R₀>1, furthermore, the conditions of extinction and persistence of the disease are determined. Secondly, the stability and the bifurcation situations of the model at the equilibrium point are proved by the properties of Jacobian matrix, Jury criterions and the construction of Lyapunov function. The results show that when R₀<1, the disease-free equilibrium point is globally asymptotically stable, and the transcritical bifurcation occurs when R₀=1. When R₀>1, the endemic equilibrium point is locally asymptotically stable, if the limitation on contact rate β in reality is ignored, the model will produce the period-doubling bifurcation and even chaotic phenomena at the endemic equilibrium point. Finally, numerical simulation and sensitivity index method are used to verify the  theoretical analysis results, it is concluded that improving the vaccination rate and recovery rate can effectively reduce the incidence of the disease.

Aiming at the problem of the structural stability and difficulty in decomposition of p-aminobenzoic acid (PABA), its long-term existence could lead to water pollution, we prepared   a three-dimensional layered FeAl-LDH@FeS_x-NBC catalyst based on biochar (BC)  by  using  hydrothermal method, and constructed  photocatalytic degradation system to degrade  PABA in water. The results show that FeAl-LDH@FeS_x is successfully loaded onto biochar doped with N element.  When the catalyst dosage is 0.3 g/L and the  pH=5, the photocatalytic system exhibits the best degradation effect of PABA, with a removal rate of 95.4% after 210 min. After 5 cycle tests,  FeAl-LDH@FeS_x-NBC still has  a high removal rate of PABA,  indicating good repeatable utilization. The main free radicals for  degradation in this system are superoxide radical (O^-₂),  photogenerated hole (h⁺),   light irradiation causes the separation of  photogenerated electrons (e^-) and h⁺ on the catalyst surface,  where e^- is captured by oxygen to form O^-₂ and h⁺ is captured by hydroxide ions to form hydroxyl radical (^.OH),  thereby promoting the generation of active components in  the entire system.

Based on an improved  spatial pyramid attention module, we  enhanced the performance of lightweight networks in fine-grained image classification tasks. By combining global and local features, the  improved model enhanced the classification performance of lightweight networks without significantly increasing the number of parameters. The experimental results  on the Stanford Dogs dataset show  that the lightweight network equipped with this module significantly improves accuracy, even surpassing some classical models. This method expands the application scope of lightweight networks on resource-constrained devices and provides an efficient and low-computational-cost solution for fine-grained image classification problems.

Aiming at the problem of poor fusion performance in traditional multimodal data feature fusion algorithms, the author proposed a
 multimodal data feature fusion algorithm based on deep learning and D-S theory.  Firstly, within the framework of deep learning, a restricted Boltzmann machine (RBM) was used to train multimodal data. Based on the characteristics of the data and task requirements, an RBM model structure was constructed for multimodal data feature selection. Secondly, based on the selected features, the author calculated the distance between similar modal data, determined the trust function, and set a threshold to remove abnormal data, achieving preliminary fusion of similar modal data. Finally, by calculating the distance between heterogeneous modal data and feartures of different levels, the author determined the trust function of heterogeneous data, and combined with D-S theory, multimodal data feature fusion was achieved. The experimental results show that the purity of the proposed algorithm can reach up to 1.0, and the standardized mutual information can reach up to 0.3, indicating that the proposed algorithm can obtain accurate multimodal data feature fusion results.

Aiming at the problem of  insufficient data volumes or low accuracy of labeled images in the field of remote sensing image change detection, which led to the model being unable  to fully learn features, and affected  the accuracy of detection, we proposed an improved  FCA-EF model based on the U-Net network. Firstly, the model was based on multi-head self-attention mechanisms and Transformer module of feedforward neural networks to establish encoding layers. Through long-distance skip connection mechanism, the  global features of the data were extracted in the encoding layer, achieving  information transfer between different layers. Secondly,  the model used convolutional neural network (CNN) module as the backbone to establish  decoding layers, extracted deep local features by using  the local perceptual characteristics of CNN module,  and fused the global features extracted by the encoder via long-distance skip connection mechanism to enhance the model’s ability to capture details and accuracy of  change detection. Thirdly, a new label filling and optimization method was proposed to address the problem of incomplete information representation in label image,  and its effectiveness was confirmed through ablation experiments. Finally, combined with the FCA-EF model and label filling method, the proposed method achieved excellent results inthe change detection of remote sensing images from Jilin-1 satellite. Compared with other classical models, the  overall accuracy, F₁ score, recall rate,  intersection over union (IoU) and other indicators were improved, effectively improving the accuracy of remote sensing image change detection.

Aiming at the problem of how to fully integrate the complementary and diverse information of multi-view data to improve the clust
ering performance, we proposed a multi-view subspace clustering based on adaptive weighted consensus self-representation. Firstly, we introduced sparse mutual exclusion to learn view-specific sparse self-representation matrix, and then used adaptive weighted learning of multi-view consensus self-representation matrix to fuse the self-representation learned from various views. Secondly, we integrated the learning of multi-view consensus matrix and clustering indicator matrix into a unified optimization model, so that self-representation learning and clustering could promote each other. Finally, we conducted experiments on six commonly used multi-view datasets, and compared them with nine related methods. The experimental results show that the proposed method has obvious information fusion effect and improves clustering effect.

We studied the  molecular mechanism of antioxidative activity of stamen nelumbinis   by network pharmacology and molecular docking technology,  and  verified the free radical scavenging ability of stamen nelumbinis  through  in vitro experiments. The results show  that the antioxidant effects of stamen nelumbinis   mainly relies on the regulation of biological processes such as MAPKs signaling pathway and PI3K/AKT signaling pathway. The stamen nelumbinis  has a certain ability to clear 1,1-diphenyl-2-picrylhydrazyl radical (DPPH^.) and hydroxyl radical (^.OH),  and the scavenging rates of DPPH^. and ^.OH are 83.6% and 53.43%,  respectively when the mass concentration is 0.8 mg/L. The high performance liquid chromatography (HPLC) detection reveals that the stamen nelumbinis  contains flavonoids such as kaempferol,  lignans,  and quercetin, which exert antioxidant effects.

Aiming at  the problem of poor  performance of entity relationship extraction in current domain knowledge graphs, we proposed a research method for entity relationship extraction models oriented towards domain knowledge graphs. Firstly, we established an entity relationship extraction model consisting of an encoding and decoding module, an entity recognition module, and an entity relationship extraction module. In the entity relationship extraction model, a bidirectional long short-term memory neural network was used to encode text sentences, and the feature representation vectors of the encoded text sentences were input into a deep neural network-based entity recognition module for entity recognition of text sentences, and  the recognition results were input into the entity relationship extraction module based on convolutional neural networks for  entity relationship extraction. Secondly,  the entity relationship triplet obtained from entity relationship extraction was input into the encoding and decoding module for decoding operation, achieving the final entity relationship extraction for domain oriented knowledge graph. The experimental results show that the proposed method has better entity relationship extraction effect and overall application effect.

Aiming at the problems of poor image quality, lack of polarization information, and inadequate target texture details in current  infrared polarization image fusion,  we proposed an  infrared polarization image fusion method based on composite domain multi-scale decomposition. Firstly, in the spatial domain, a two-scale decomposition of the source image was performed by using a bootstrap filter to obtain the detail and base layers, in the frequency domain, a multi-scale multi-directional decomposition of the base layer image was performed by using a non-subsampled shear-wave transform to obtain the low-frequency sub-band image and high-frequency  sub-band image.  Secondly, the principal component analysis-adaptive pulse coupled neural network fusion rule was used for  high-frequency sub-band,  an improved convolutional sparse representation was used for coefficient merging for the low-frequency sub-bands, and  local energy weighting and selective fusion rules based on pixel similarity were used for detail layed fusion. Finally, the fused image was reconstructed by using an inverse transformation in the composite domain. Experimental results show  that the proposed method outperforms other comparative fusion methods in  subjective visual performance and eight objective evaluation metrics,  indicating that the method has many advantages in infrared polarization image fusion and can effectively enhance the quality of fused images.

Aiming at the problem that organism populations in nature were not able to react quickly to environmental changes or  interactions amongst populations. By introducing two time delays  as branching parameters, we analyzed the corresponding characteristic equations and  discussed  the local stability of the system at each equilibrium point and the existence of Hopf bifurcation. Firstly, we obtained explicit formulas that determined  the direction of Hopf bifurcation  and the stability of periodic solutions  when two time delays equal to  τ by using the central manifold theorem and canonical type theory. Secondly,  numerical simulation was used to verify the  accuracy of theoretical analysis. The results show that the stability of the system changes  and  a Hopf bifurcation is  generated when the time delay surpasses a critical value. Time delay is introduced  into biological models can help predict population dynamics more accurately.

Firstly, we solved the problem of the maximum, second-maximum and second-minimum values of the reduced Sombor index 
of n(n≥5) order  unicyclic graphs, and the corresponding extremal graphs by using  graphical transformations and unique classification methods. Secondly, we considered the problems of the second-maximum and second-minimum values of the reduced Sombor index  of  n(n≥6) order bicyclic graphs, and the corresponding extremal graphs, gave the maximum, second-maximum 
and second-minimum values of the reduced Sombor index  of  n(n≥5) order  unicyclic graphs, and characterized the corresponding extremal graphs. At the same time, we also confirmed the second-maximum and second-minimum  values of the reduced Sombor index  of  n(n≥6) order bicyclic graphs, and the corresponding extremal graphs.

By using the intuitionistic similarity as a perturbation parameter, we  estimated the robustness of the reverse triple I sustaining algorithm and reverse triple I restriction algorithm for IFMP and IFMT problems. The results show that the output results will not significantly change due to small changes in the input, indicating that both algorithms have good robustness.

Firstly, we defined a class of essentially quasi-symmetric non-negative tensors, which encompassed a broader class of tensors covering essentially positive tensors, weakly positive tensors and generalized weakly positive tensors. Secondly, we gave an algorithm for the H-spectral radius of an essentially quasi-symmetric non-negative tensor  by applying the property that the H-eigenvalues of the tensor were invariant under diagonal similarity transformations, and used  numerical examples to  illustrate the effectiveness of the algorithm.

We considered extending  the quasi-effective stability for nearly integrable Hamiltonian systems. We gave  the quasi-effective stability theorems for nearly integrable generalized Hamiltonian systems and Poisson systems under the KAM (Kolmogorov-Arnold-Moser) type non-degenerate condition. Unlike the general Hamiltonian systems, the action variables and angular variables of the generalized Hamiltonian systems and Poisson systems  under discussion could generally have different dimensions.

Aiming at the problem that noise, echo and other factors interfered with the quality and intelligibility of the signal in the process of speech signal transmission, we proposed a speech signal enhancement method based on optimized variational mode decomposition algorithm and improved wavelet threshold. Firstly, the modal decomposition parameters were optimized by using sparrow search algorithm, and the modal components were obtained by resolving the speech signal. Secondly, according to the correlation coefficient and center frequency between the modal component and the original signal, the high-frequency noise component was eliminated, and the modal component close to the original signal was retained as pure speech, while the other modal components were regarded as noisy speech, and the wavelet threshold processing was carried out. Finally, the pure speech and the processed noise modal components were reconstructed to obtain the enhanced speech signals. The results show that the method has better speech enhancement effect than a single method, the optimized variational mode decomposition algorithm and the improved threshold and threshold function achieve better enhancement effect than the traditional methods, which is suitable for all kinds of noise environment, and effectively improve the quality and intelligibility of speech signals.

Aiming at the problem that the estimation accuracy of the existing estimation methods of the direction of arrival (DOA) was low under the condition of low signal-to-noise ratio, small fast beat and multiple sources, we proposed a DOA estimation method based on parallel coordinate descent algorithm. Firstly, the airspace was uniformly divided into equal angles, and the super-complete redundant dictionary was constructed. Secondly, the sparse signal was reconstructed by using the idea of parallel coordinate descent algorithm, and the sparse coefficient matrix of the signal in spatial space was obtained. Finally, the l₂-norm of the sparse matrix row vector was mapped to the spatial grid to obtain an accurate DOA estimate. The simulation experiment results show that the proposed method is superior to subspace algorithm, greedy algorithm and convex optimization algorithm under the conditions of low signal-to-noise ratio, small fast beat and multiple sources, and has lower root mean square error (RMSE), higher DOA estimation accuracy and higher operational efficiency.

We considered the long-term dynamic behavior of solutions to hyperbolic Cahn-Hilliard equations with linear memory terms. Under the action of time-dependent velocity propagation, the existence and regularity of the attractor in  time-dependent  space of the equation were proved by using asymptotic prior  equation, operator  decomposition method and modified pullback attractor theory.

Based on a three-dimensional predator-prey model, we discussed the cooperation between prey populations and their impact on the predation process. Firstly, we analyzed the existence and stability of equilibrium points of the system by using dynamical system theory, and proved the periodic oscillation characteristics of equilibrium points in prey free populations. Secondly, the theoretical results were verified through numerical simulation. The numerical simulation results show that the equilibrium point E₁ of the prey free populations y and the equilibrium point E₂ of the prey free populations z are both periodic oscillations, and the amplitude of the oscillations gradually increases with the increase of the cooperative effect.

Aiming at  the problem of low prediction accuracy of traditional machine learning algorithms on Cleveland and Hungary dataset, we proposed a heart disease prediction method based on Bayesian hyperparameter optimization gradient boosting trees. Firstly, the K-nearest neighbor algorithm was used to fill in the missing values in the dataset, Min-Max standardization and One-Hot encoding were used  to process the data, and  the gradient boosting tree algorithm was used to predict the heart disease. Secondly, Bayesian optimization and ten-fold cross validation were used to search for the best combination of hyperparameters of the algorithm. The experimental results show that  the prediction accuracy of the optimized gradient boosting tree algorithm can reach 90.2% on the Cleveland heart disease dataset, and the prediction accuracy can reach 81.4% on the Hungarian heart disease dataset, outperforming  traditional machine learning methods such as decision tree, support vector machine and the K-nearest neighbor, it  can assist doctors in the diagnosis of heart disease.

Aiming at the problems of a large number of parameters and the long training time of convolutional neural networks, we proposed
 a facial expression recognition method based on a lightweight attention residual network. Firstly, we rebuilt the model by using  the residual network as a skeleton, and  improved the model performance by reducing the number of layers and improving the residual module. Secondly, the depthwise separable convolution was introduced to reduce the number of model parameters and computational effort. Finally, the squeeze and excitation module of ReLU function was replaced by Mish function to adaptively 
adjust the channel weight. The model was validated by using the classical ten-fold cross-validation mode on two public datasets CK+ and JAFFE,  and obtained  accuracies of 98.16% and 96.67%, respectively. The experimental results show that the proposed method provides a better trade-off between model identification accuracy and complexity.

We consider Gorenstein FP-injective complexes, firstly, we  prove that  a complex G is Gorenstein FP-injective if and only if there is an exact sequence …→E^-1→E⁰→E¹→E²→… of FP-injective complexes with G=Ker(E⁰→E¹) on coherent rings. Secondly, we  prove that  a complex G is Gorenstein FP-injective if and only if G_m is a Gorenstein FP-injective module for each m∈Z under certain conditions.

Aiming at the problem of low-quality initial solutions and insufficient diversity, we proposed a random forest model that introduced the Logistic chaos mapping to improve the optimization of the sea horse optimization algorithm. Firstly, after improving the sea horse optimization algorithm, it was combined with the random forest algorithm to improve the discriminative accuracy of the classic random forest algorithm. Secondly, in order to  verify the  performance of new model, comparative experiment  was conducted by using  five models for four evaluation metrics. The experimental results show that the model has accuracy rate of  96.15%,  precision of 100%, recall rate of 92.31%, and  F₁-Score of 96.00%, which improves the performance of the  random forest method.

Firstly, by providing  a Hom-Lie algebra and its representation,  we proved that a strong quasi-trace function on  a Hom-Lie algebra could induce a 3-Hom-Lie algebra and its representation, thereby proving that a generalized Reynolds operator on a Hom-Lie algebra was also  a generalized Reynolds operator on the  induced 3-Hom-Lie algebra. Secondly, we studied the mutual derivation properties of Hom-NS-Lie algebras and generalized Reynolds operators, and gave the adjoint relation of the corresponding categories.

Aiming at the problem of safety hazards of insufficient bridge crack detection, we  proposed a bridge crack detection algorithm based on YOLOx-s, combined with a small unmanned aerial vehicle platform. Firstly, we added a residual hole convolution module in  the backbone to solve the problem of   large scale changes and complex backgrounds in drone images. Secondly, we added a coordinate attention mechanism module in  PANET to improve the detection rate of small targets. Finally, we replaced the loss function with Focal loss to enhance the learning of positive samples and improve the stability of the model.  The experimental results show that compared with the YOLOx-s algorithm, the proposed method improves detection accuracy by 3.72 percentage points. On embedded devices, this method has better accuracy than other mainstream algorithms and can achieve real-time detection, which can be better applied in bridge crack detection for unmanned aerial vehicle.

By using the fixed point theorem, the author study the existence of radial positive solutions for the boundary value problem of the Kirchhoff type biharmonic equation. When the nonlinear term f satisfies appropriate  conditions, the author proves that there is  at least one radial positive solution to the problem.

Firstly, aiming at  the problems of long adjustment time, delay and hysteresis in the traditional proportional integral derivative (PID)  control system, we proposed using the improved hunger games search (THGS) algorithm  to optimize the parameters of the traditional PID controller. Simulation experiments were carried out by using crop growth model, soil moisture transport model and soil fertilizer transport model. The results show that the  PID controller optimized by THGS algorithms is superior to other controllers in terms of adjustment  time and starting amount, which effectively improves the performance of the control system.

By using the relevant methods of Nevanlinna theory, we studied the standard solution of higher order complex linear difference equations and obtained the finite order meromorphic solution of the equation was standard solutions when the coefficients and solutions of the higher order complex linear difference equations satisfied certain conditions.

Firstly, by introducing the notion of distributors of groups, we give some properties of distributors of groups. Secondly, we generalize  the corresponding results of commutators and p-commutators in group theory, and  prove that the mapping f from group G to group H is a group homomorphism if and only if the f-distributor of group G is 1. Finally, as an application, we calculate the number of homomorphisms from a class of metacyclic groups to dihedral groups.

In order to meet the security requirements of user privacy data transmission, we proposed a security protection method for user privacy data transmission under homomorphic encryption. Firstly, by using  feature space recombination technology for data reconstruction,  semantic correlation fusion method was used to capture user privacy data features while  adaptively scheduling, 
and fuzzy clustering was performed on the captured feature quantities to determine user privacy data attributes. Secondly, combining the attributes of user privacy data, a combination method of homomorphic encryption algorithms and deep learning was used to encrypt and transmit user privacy data point-to-point, ultimately achieving secure protection of user privacy data transmission. The simulation experiment results show that the proposed method has good data encryption effect,  low communication overhead, and  can better ensure the security and reliability of user privacy data transmission.

We proposed a novel real-time vehicle speed prediction method based on Gaussian process regression (GPR) technology, which accurately and effectively predicted the velocity of the preceding vehicle while quantifying the uncertainty of the prediction. This method introduced a combination kernel function SEM of squared exponent (SE) and Matern, and improved the combination kernel function to SEM*. This effectively balanced the advantages and disadvantages of a single kernel function for vehicle speed prediction, and a particle swarm optimization method for real-time solution in hyperparameter optimization was adopted. The simulation analysis of 2 s vehicle speed prediction under transient operating conditions shows that under the FTP75 working  condition, compared to the radial basis SE kernel function with better single kernel performance, the SEM method reduces the mean absolute error (MAE) and root mean square error (RMSE) standards by 10.09% and 7.23% respectively, while the SEM* method reduces the two error indicators by 8.02% and 8.13% respectively compared to the SEM method. Under typical urban working conditions, the SEM reduces MAE and RMSE standards by 3.44% and 4.16% respectively compared to the SE method, while the SEM* reduces the two error indicators by 3.57% and 2.17% respectively compared to the SEM method. At the same time, the SEM* method reduces the maximum single calculation time relative to the SE method by 0.3 s under the FTP75 working condition, and the cost paid under typical urban conditions is an increase in the maximum single calculation time relative to the SE method by 0.015 s, but the calculation time is still within 0.1 s of the sampling time, which has real-time performance. 

Based on the intelligent optimization method combining genetic algorithm and improved particle swarm optimization algorithm, we optimized the vehicle sliding mode controller, and on the basis of which it was applied to the semi-vehicle suspension model. Firstly,  the body attitude compensation fuzzy controller was designed by using the fuzzy control method. Secondly,  the final semi-active suspension control strategy was determined by combining the two control strategies to suppress the body pitch angle. The experimental results show that the controller  has excellent performance, which can effectively suppress the variation of the body pitch angle during the process of driving and improve the smoothness of the vehicle travel.

Aiming at the problem of very weak surface magnetic resonance  signals  and  susceptibility to electromagnetic noise interference, 
we proposed a harmonic noise reduction method for surface magnetic resonance based on variational mode decomposition.  This method adopted an improved variational mode decomposition-based method for power frequency harmonic elimination, and set the mode number and initial center frequency according to spectral analysis, solving the problem of slow computational efficiency caused by  conventional harmonic modeling denoising methods, which could only handle single-acquisition data. The experimental results show that the method achieves good effect of  harmonic component estimation in complex noise scenarios such as  multiple fundamental  frequencies or fundamental frequency variations over time,  and can  quickly and effectively eliminate power frequency  harmonic interference, significantly improving the signal-to-noise ratio of surface  magnetic resonance detection data.

We study the D(2)-vertex sum distinguishing total coloring problem of a tricyclic graph with non zero tree height by using analytic method, contradiction method, and the Combinatorial Nullstellensatz, and obtain an upper bound on the D(2)-vertex sum distinguishing total coloring for this type of graphs is Δ(G)+3.

In order to realize the comprehensive reuse of solid waste,  the iron/sludge-based biochar catalyst  was prepared by using the mixed sludge of activated sludge and Fenton iron sludge from the sewage treatment section of steel plant in Anshan, Liaoning Province as raw materials， and kaolinite as binder by a mixing-extrusion and pyrolysis method. The structure was characterized and the preparation process conditions were optimized. We optimized the process parameters of catalytic ozonation degradation of simulated wastewater containing quinoline as the target pollutant, and studied the stability and catalytic mechanism of catalyst. The experimental results show that the surface of catalyst is rough with a rich porous structures, and the catalyst mainly contains Fe₃O₄，CaCO₃ and ZrO₂ crystals. The optimal preparation conditions for the catalyst are a binder addition of 12.5%, pyrolysis temperature of 800 ℃, and pyrolysis time of 3 h. Under the conditions of initial pH=7, catalyst dosage of 50 g,  and  initial mass concentration of 50 mg/L of quinoline, the removal rate reaches 76.31% after 10 min of reaction. The catalyst has good stability,  and the removal rate of quinoline only decreases by 0.09 percentage points  after continuous  use for five times. There are two types of   hydroxyl radical (^.OH) and superoxide anion radical (O^.-₂), as well as singlet oxygen  (¹O₂) non  free radicals  in the catalytic system, with  O^.-₂   playing a dominant role in the reaction. The change of Fe²⁺/Fe³⁺ ratio before and after the reaction indicates that the redox cycle of Fe²⁺/Fe³⁺ participates in the catalytic degradation reaction. This study provides a new idea and method for the reuse of solid waste and the efficient treatment of coking wastewater.

We investigated a wavelength-controlled Bloch surface wave high-performance biosensor. Based on impedance matching method, we optimized the system parameters of the biosensor,  and applied it to detection of glucose solution mass concentration. The biosensor was composed of a grating coupled with one-dimensional photonic crystal structure. Strong localized Bloch surface waves could be excited near the grating structure. The results show that the quality factor of Bloch surface waves can be optimized by adjusting the thickness of the buffer layer, the periods of the photonic crystal, and the incident angle, thereby improving the sensing performance of biosensors. Combining the high-quality factor and high wavelength sensitivity of Bloch surface waves, the sensing performance of this biosensor in glucose mass concentration detection can reach 708.1(g/mL)^-1.

Aiming at the problem of multiple mentions of entities and the noise of entity pairs in the document-level relation extraction task,  we  proposed a relation extraction model (EUT model) based on entity type information. The model  improved the relation extraction results through two sub-tasks:  entity type judgment and  a priori of the relation types produced by the type pairs. 
After the entity type judgment task labelled entities by type, then categorized all mentions of the entity by type, so that multiple mentions of the entity produced richer and similar feature representations. The relation category prior task enabled the model to obtain a prior of the  relation distribution  generated by the head and tail types of entity pairs, and reduced erroneous entity pair noise through the categories of entity pairs. In order to verify the effectiveness of the EUT model,  the  experiments were conducted on two document-level datasets, DocRED and Re-DocRED. The experimental results show that the model effectively utilizes the entity type information and achieves better relation extraction results compared to the base model, indicating that entity type information has an important impact on document-level relation extraction.

Aiming at the problems of insufficient acoustic  feature extraction under sample scarcity conditions, we proposed a small sample sound event detection method based on channel  and spatial compression.  The method constructed a dual compression attention mechanism to screen features  in channel dimension and achieved  feature focusing in the spatial dimension, effectively improving the feature discrimination ability of the prototype network in small sample scenarios. The experimental results show that F₁-score  of the method on the dataset DCASE (detection and classification of acoustic scenes and events) reaches 66.84%, an improvement of 4.11 percentage points compared to the prototypical network, providing more reliable technical  support for practical applications such as wildlife monitoring and ecological environment assessment.

By using  the critical point theory, we prove the existence of the non-trivial solution of the finite difference scheme for the three-point boundary value problem and get the existence result of the numerical correlation solution for the above continuous problem.

We studied the composition of  two flavonoids,  isorhamnetin-3-O-glucoside and isorhamnetin-3-O-rutinoside, their binding behavior with Zein, and the stability of two  flavonoid-Zein systems by using spectral analysis and  computer simulation method, and  revealed the optimal binding mode, binding site and the stability of the complex system formed by two flavonoids and Zein.  The experimental results show that  two flavonoids bind to Zein through hydrogen bond and van der Waals forces, leading to static quenching of intrinsic fluorescence of Zein and altering its secondary structure of Zein.

We studied the D(2)-vertex sum distinguishing edge-coloring problem of the corona graph of a cycle and a simple graphs by using combinatorial nullstellensatz, constructing coloring function and mathematical induction. We obtained  that the bound of D(2)-vertex sum distinguishing edge-coloring of the corona graph of a cycle and a simple graphs was Δ(G)+1, and then we derived that the bound of the corona graph of a path and a simple graphs was Δ(G)+1.

Aiming at  the problem of low network throughput caused by uneven resource allocation, we proposed a mathematical modeling method for virtual network resource load balancing allocation. Firstly, we set an objective function for resource load allocation, calculated the optimal ratio between remaining resources and remaining bandwidth of  server links, and mapped  virtual network resource based on the calculation results. Secondly, we used the network ability factor parameters such as computing power rate, communication rate, path capability, and correlation degree to reflect the load balancing situation of resources. Finally,  based on the obtained virtual network node capability indicators, we set resource attribute scheduling cycles, introducd fairness factors, updated  throughput of the link,  obtained a virtual network resource load balancing allocation model, and  achieved resource load balancing allocation based on this model. The experimental results show that the proposed method effectively improves the balance of resource allocation, resulting in a significant increase in network throughput.

By combining the complemented and abelian conditions of Sylow subgroups, and utilizing  the supersolvable property of traces of maximal subgroups, we studied the question of whether G was a solvable group (if each maximal subgroup of G had a supersolvable trace), and obtained some sufficient and necessary conditions for solvable groups.

By using the stability and bifurcation theory of differential equation, we studied the dynamic properties of a class of reaction-diffusion models for plankton with a non-local competition. Firstly, we gave the conditions for the existence and stability of positive constant equilibrium solutions. Secondly, we gave the conditions for the occurrence of Hopf bifurcation and steady-state bifurcation at the positive constant equilibrium solution, and calculated the properties of these bifurcations. Finally, we explained the  theoretical analysis results through numerical simulation.

Aiming at  the problem that the emotional factors of the public were not considered enough in the existing related theme models, which was difficult to accurately excavate them, and the real-time dynamic evolution of social texts was considered to weaken the clustering ability of the model, the author  proposed a text clustering algorithm based on the dynamic theme emotin model by adding  the emotional layer to the model to extract the polar features of social text emotion, and introducing a prior distribution function. The experiments were carried out by using real COVID-19 Twitter text datasets.  The experimental results show that the performance of the model is better than the baseline model,  and   the discrimination of emotional features is improved, so that  the text theme and the corresponding emotional polarity can jointly generate time nodes, and then  the model has the ability to deal with time evolution.

Aiming at how to utilize the implicit information in multi-view data and avoid the problem of sub-optimal clustering performance 
in the subsequent processing, we proposed a multi-view clustering algorithm with low\|rank tensor based on consistency and difference. Firstly, the algorithm simultaneously considered the consistency and differential information of views, and superimposed multiple consistent similarity matrices in a tensor  constrainted by low-rank  to explore the higher-order correlations of the information between views, thus obtaining higher-quality similarity matrices. Secondly, clustering results were directly obtained by learning a consistent non-negative embedding matrix. Thirdly, an adaptive weighting strategy was used to consider the importance of different view data. Finally, the effectiveness of the algorithm on the multi-view clustering problem was verified by comparison experiments with other algorithms on six real datasets.

Aiming at  the problem of uneven initial solution distribution in the traditional gray wolf optimization algorithm, we proposed an enhanced gray wolf optimization (EGWO) algorithm. Firstly, we introduced nonlinear convergence factors to improve gray wolf optimizaiton algorithm. Secondly,  the Sobel sequence was integrated into the improved gray wolf optimization algorithm to increase the population diversity. In order to verify the effectiveness of the proposed algorithm, EGWO algorithm was applied to UAV path planning, and compared with the traditional gray wolf optimization algorithm based on multiple evaluation indicators. Experimental results show that the EGWO algorithm has better performance, and  can quickly and accurately plan and control the flight path of UAVs in complex environments, as well as improve the flight efficiency of UAVs in swarm control.

We studied the effect of non-stoichiometric ratio of Na⁺ and Bi³⁺ on the microstructure and electrical properties of Na_0.5+xBi_0.5-xTi_0.99Mg_0.01O_3-δ by adjusting the mole fractions of Na and Bi under the condition of maintaining constant total amount of A-site elements （x(Na)+x(Bi)=1） and  constant mole fraction of Mg doping. Samples of Na and Bi with different mole fractions were synthesized by using sodid-state method, and their structures and microstructures were characterized by X-ray diffraction (XRD) and scanning electron microscopy (SEM). The electrochemical properties were evaluated by electrochemical testing. The results show that changing the mole fraction of Na and Bi can significatly affect the grain size and conductivity of the simple. The sample exhibits optimal grain and grain-boundary conductivity performance when x=0.02. Therefore, controlling the mole fraction of Na and Bi can effectively modulate the electrical performance of materials, providing experimental guidance for the development of high-performance oxygen ionic conductors.

By using Leray-Schauder fixed point theorem, we study a class of fully fourth-order nonlinear ordinary differential equations. The existence and uniqueness of the positive solutions are proven under the condition that the nonlinear term f grows at most linearly. Under the condition that f satisfies the superlinear growth, the existence of positive solutions are obtained by introducing a Nagumo-type condition to limit that f(t,x₀,x₁,x₂,x₃) is quadratical growth on x₃ at most.

Rana dybowskii residue was used as raw material， the  Rana dybowskii residue peptides (RDRP) was abtained  under enzymatic hydrolysis conditions, and then  were chelated with selenium ions (Se⁴⁺) to prepare  Rana dybowskii residue peptide chelated selenium (RDRPCS). We characterized the synthesized compounds, studied the optimized conditions for chelation reaction, and investigated their anti-inflammatory activity through in vitro cell models. The experimental results show that  Se⁴⁺ reacts with RDRP to form chelates.  RDRPCS has sufficient metal binding sites,  with chelating sites being  amino,  hydroxyl,  and C=O.    The optimization result of chelation process is that temperature is 60  ℃,   pH=6,  time is 65 min,  and a mass ratio is 2.5∶1， the efficiency of chelation reaction under this conditions is 70.7%.  Different concentrations of chelates have inhibitory effects on the release of  NO, TNF-α,IL-6 and IL-1β in RAW264.7 inflammatory cell model.

The author investigated the thermal convection flow of Oldroyd-B fluids in a fluid-porous medium two-layer system heated from below, and analyzed the effects of viscoelastic properties of the Oldroyd-B fluid on oscillatory instabilities and its dominant branches under a vertical magnetic field. It was assumed that the flow in the porous medium was controlled by a modified Darcy’s law, and the boundaries were subject to isothermal conditions. Linear stability analysis of the control equations was conducted, and neutral curves for different parameters were obtained by using the Chebyshev collocation method. The results show that the effects of the thickness ratio and Chandrasekhar number on convective stability are opposite, and increasing the thickness ratio can gradually diminish the bimodal characteristics of the neutral curve. Additionally, as the magnetic field intensity increases, the start time of oscillatory convection is delayed, and the convective dominant branch shifts from short-wave branch to long-wave branch. After the conversion, the effect of magnetic field intensity on thermal convection stability is relatively small.

Aming at the problem of  the computational complexity caused by the exponential increase in the number of partitioning schemes with the number of vertices in large-scale graph partitioning problems, and the inefficiency and imprecision of traditional genetic algorithms when dealing with large-scale problems, we proposed a hybrid genetic algorithm. Firstly, the algorithm  performed optimal matching on individuals encoded in binary, identified and screened out good genes,  effectively narrowing down the search range and focusing on more promising search areas. Secondly, in order to avoid the illegal solutions that might arise from traditional crossover operations, the algorithm abandoned the random crossover strategy and only generated one potential solution. Finally, by introducing a tabu search operator in the mutation operation to generate complete individuals, thereby enhancing  local search capability of the algorithm and achieving a dynamic balance between global and local searches. Experimental results of applying this hybrid genetic algorithm to the partitioning problem of ultra large-scale integrated circuits show that the algorithm can effectively improve the quality of solutions for large-scale graph partitioning problems.

We considered a class of two-dimensional singularly perturbed reaction-diffusion problems with  discontinuous reaction terms. Firstly, using spatial contrastive  structural theory, boundary layer function methods, smooth seaming method, and asymptotic differential inequality methods, we constructed  asymptotic expansion of the problem with solutions for the internal layer and boundary layer up to the n order, where n was an arbitary constant. Secondly, we  proved the existence and local asymptotic stability of the solution with internal layer,  and constructed high-precision asymptotic expansion of the solution. Finally, we applied the obtained theoretical results  to a numerical example.

We established a multi-stage dynamic model to reflect the  characteristics of product  word-of-mouth communication based on  the laws of product word-of-mouth communication. Firstly, using qualitative analysis and stability theory, we analyzed the existence and stability of the model’s equilibrium points, and gave the conditions for the existence of backward bifurcation. Secondly, the Lyapunov function was used to demonstrate the global asymptotic stability of  the model’s information-free equilibrium point and the positive equilibrium point when a=0.  Finally, we  found  that the model  underwent saddle-node bifurcation, Hopf bifurcation, B-T bifurcation, and degenerate Hopf bifurcation through numerical simulation. The results show  that the coupling effect between product buyers and active disseminators of product word-of-mouth has a significant effect on the dynamic process of word-of-mouth communication.

We used disturbance observer to study the adaptive sliding mode synchronization of permanent magnet synchronous motor (PMSM) fractional-order chaotic system. We considered uncertainties and unknown external disturbances through the fractional-order disturbance observer and verified the obtained conclusion through numerical simulation. The results show that the master-slave system of the PMSM chaotic system achieves sliding mode synchronization under  appropriate disturbance observer, sliding mode function, controller and the adaptive law.

Aiming at the problem that existing multilingual models were inefficient in utilising multilingual datasets in the pre-training process, which led to a more insufficient cross-language contextual learning ability and thus language bias, we proposed a cross-language text similarity model based on the alternating language data  reconstruction method. This method formed reconstructed pre-trained text pairs by symmetrically replacing Chinese and English words in the parallel corpus, and used the above text pairs to perform targeted pre-training and fine-tuning processing based on data reconstruction for the multilingual large model mBERT (BERT-based-multilingual). In order to verify the feasibility of the model, experiments were conducted on the United Nations parallel corpus dataset, and the experimental results show that the similarity checking accuracy of this model outperforms that of mBERT and the other two baseline models. It can not only  further improve the accuracy of cross-language information retrieval, but also  reduce the research cost of multilingual natural language processing tasks.

Aming at the problems  of diversity and poor image quality in agricultural disease image datasets, we  proposed a multisource agricultural disease image dataset construction method based on hierarchical annotation and adaptive preprocessing. Firstly, images were collected from different regions, crop types, and growth stages by using devices such as smartphones, professional cameras, and drones to ensure data diversity. Secondly, we constructed a hierarchical annotation system that  covered three levels of agricultural disease type, severity, and location, we used tools such as LabelImg and LabelMe for annotation, and requested expert review. Finally, we applied adaptive preprocessing methods, including automatic cropping, normalization, denoising and enhancement, to adjust parameters based on image features to improve quality. The experiment used a convolutional neural network (CNN) model based on the ResNet-50 architecture for validation, and the results show that hierarchical annotation and adaptive preprocessing methods significantly improve the quality of the dataset and model performance, the model achieves accuracy, recall, and F₁ score of 92.5%, 91.8%, and 92.1%, respectively, which are better than the training results of other datasets.

In order to  improve efficiency of road traffic, by using  the minimum traffic navigation  cloud sacle  given number of road nodes and vehicles, we  proposed a performance analysis model based on target map and cloud center related parameters. Firstly, we analyzed  the target map and the relevant parameters of the cloud platform that affected  navigation performance.  Secondly, we  considered the number of road nodes and vehicles, as well as virtual machines of  different scales and frequencies, and conducted three sets of experiments.  Finally, we  verified the effectiveness  of the model by using real datasets. The experimental results show that the proposed performance analysis model can accurately calculate the minimum scale of  navigation cloud that satisfies the constraint conditions.

Aiming at the pricing problem of American options under the time-fractional Black-Scholes model, we  proposed an effective numerical solution method.  Firstly, the linear complementarity model satisfied by the American option was transformed into a nonlinear parabolic problem on a bounded domain by using the variable substitution and penalty method. Secondly,  the semi-implicit finite difference method was used to solve the problem, and the error results of the method and the non negativity proof of the solution were given. Finally, numerical experiments were used to verify the correctness and effectiveness of the proposed method.

Aiming at the modeling problem of Z-valued time series data with volatility, we proposed a Z-valued Taylor-Schwert generalized autoregressive conditional heteroscedasticity model based on Poisson distribution. Firstly, some statistical properties of the model were derived. Secondly, the unknown parameters in the model were estimated by using the condition maximum likelihood estimation method, and the asymptotic properties of estimators were proved. Thirdly, numerical simulations were conducted to demonstrate the  performance of the estimation method. Finally, a real daily stock return data was considered, and the superiority of the proposed model over existing models was proved through analysis of the fitting results of the data.

Aiming at the problem of traditional methods  relying too much on local features and neglecting global features in texture classification, we proposed a feature extraction method based on the combination of local and non-local patterns.  The method integrated two algorithms: local phase quantization and non-local binary patterns. Firstly, two algorithms were used to  extract feature  from the preprocessed image separately. Secondly, the feature histograms of the two methods were weighted and fused. Finally, texture classification was performed by using the chi-square distance and the nearest neighbor classifier. In order to validate the effectiveness of the proposed method, a dataset of Manchu Eight Banners flag images was constructed, and the algorithm was applied to the classification task of the dataset. Experimental results show that, compared to single algorithm, the new algorithm has higher classification accuracy and robustness on multiple datasets.

Aiming at the problem of emergency resource allocation for natural disasters, we proposed a Q-learning algorithm based on dynamic Boltzmann Softmax (DBS) and dynamic exploration rate (DER) (DBSDER-QL).  Firstly, the DBS strategy was used to dynamically adjust the weights of action values, promoting stable convergence of the algorithm and solving the problem of excessive of  the maximum operator. Secondly, the DER strategy was used to improve convergency and stability of the algorithm, solving the problem of the fixed exploration rate Q-learning algorithm not fully converging to the optimal strategy in the later stage of  training. Finally,  the effectiveness of the DBS and DER strategies was verified by ablation experiments. Compared with 
 dynamic programming, the greedy algorithm, and traditional Q-learning algorithm, the experimental results show  that DBSDER-QL algorithm is significantly better than traditional methods in terms of total cost and computational efficiency, showing higher applicability and effectiveness.

Aiming at the problem that it was difficult to balance the diversity and convergence of multi-objective particle swarm optimization algorithms, we proposed a dynamic population-based multi-objective particle swarm optimization algorithm. The increase or decrease of the population size of this algorithm depended on the resources in the archive, thereby  regulating the population size. On the one hand, particles were added by local perturbation based on grid technology to increase the local search ability of particles and improve the diversity of the algorithm. On the other hand, in order to prevent the population size from overgrowing, non-dominated ordering and population density were used to control the population size and  accelerate the algorithm search progress, avoiding premature convergence. Five comparative algorithms were selected for experiments on test functions, and the experimental results show that this algorithm has obvious diversity and convergence advantages.

Aiming at the problem of dynamicity of  the wireless local area networks (LAN), which led to the changes of the validity of data labels with time, and required regular  updates and relabeling of data,  increasing the difficulty of data label labeling, we proposed  an adaptive labeling method for multimodal data labels in  wireless local area networks. Firstly, the repetitive wireless LAN multimodal data was cleaned by using dynamic sliding neighbor sorting algorithm, and the multimodal data was fused by using recurrent  neural network to obtain more comprehensive data information. Secondly, the fused wireless LAN  data was divided into deterministic set and fuzzy set, and the deterministic set data was labeled by using support vector machine, and the fuzzy set data was labeled by using K-nearest neighbor (KNN) classifier, thus achieving  the adaptive labeling of wireless LAN multimodal data labels. The experimental results show that the deduplication ratio of the proposed method is always above 12%, the consistency index is 0.992 8, the average absolute percentage error is 0.453 9, the ROC curve is closer to the upper left corner of the coordinate axis, the AUC value is 0.982 4, and the memory occupancy rate is always below 10%. The wireless LAN multimodal data labeling effect is good.

By using the bifurcation method, the author study the bifurcation behavior of nodal solutions for two-point boundary value problems of fourth-order Kirchhoff type beam equation. When M and f satisfy suitable conditions, the author obtain  the existence results of their nodal solutions.

Aiming at the problems of low recognition accuracy and poor sensitivity of Googlenet model, we proposed a hyperparameter optimization Googlenet model by using  the improved sea-horse  optimization (SASHO) algorithm.  Firstly, the sea-horse optimization algorithm was improved by using Sobel sequence and adaptive weight algorithm. Secondly, the four basic neural networks were compared to select the most suitable Googlenet for this dataset as the basic recognition model. Finally, the improved SASHO algorithm was used to optimize the parameters of Googlenet model, and a new model SASHO-Googlenet was constructed. In order to verify the effectiveness of SASHO-Googlenet model, the SASHO-Googlenet model was compared with the model optimized by the other four swarm intelligence algorithms for seven indicators. The results show that the accuracy rate of SASHO-Googlenet model is 95.36%, the sensitivity is 95.35%, the specificity is 95.39%, the accuracy is 96.47%, the recall rat
e is 95.35%, the f_measure is 95.90%, and the g_mean is 95.37%. Experimental results show that the SASHO-Googlenet  model has the best comprehensive performance.

By using the function decomposition and the inequality technique, with the aid of the theory of boundedness for generalized fractional integral operator commutators on the L^p spaces, the author discussed the boundedness of the commutator T_σ,b generated by the generalized fractional integral operator T_σ and the Lipschitz function b on non-homogeneous metric measure spaces. The results show  that the  T_σ,b is bounded from Morrey spaces M^p1_q1(μ) to M^p2_q2(μ), and also bounded from Morrey spaces M^p_q(μ) to RBMO(μ) spaces.

Firstly, we established and discussed a four-dimensional ecoepidemiological model in which both prey and predator populations were infected, and the infected population had self-recovery ability. Secondly, we established the corresponding optimal control model and  used Pontryagin’s maximum principle to calculate its optimal control strategy. Finally, we investigated the dynamic behaviors of the model and its optimal control strategy by using numerical analysis. The results show that the recovery rate of diseases has a significant impact on the dynamic behavior of the system.

Firstly, we gave the definition of function matrix projection synchronization. Secondly, by using the active control method, the function matrix projection synchronization was realized between two disturbed fractional-order motor chaotic systems, and the effectiveness of the controller was demonstrated by using two methods. Finally, the correctness and effectiveness of the synchronization theoretical analysis were verified by MATLAB numerical simulations.

Aiming at the problem that the filling of missing values in time series usually relied on the predictions of existing data, and  the complexity and uncertainty of time series often led to errors in the prediction results. In order to ensure the effectiveness of data filling, we proposed a time series missing data filling method based on generalized center clustering. Firstly, we calculated the distance between objects and classes, as well as between classes, quantified the relative positional relationship between data points and cluster centers, and obtained the spatial relationship between data. Secondly, we used information bottleneck algorithms to cluster the generalization centers in space， dividing time series datasets containing missing data into the same class. Finally, we calculated the cluster radius, divided the outlier data generated by the generalized center clustering into usable and weakly usable randomly damaged data, set a fluctuation threshold, and compared the randomly damaged data within the fluctuation threshold with a string of the unified attribute values in the cluster, achieving the  missing data filling in the time series. The experimental results show that this method has high standardized mutual information and hit rate in the clustering process,  and  can ensure a data replenishment rate of over 80% when filling in missing data, indicating that this method can effectively improve the integrity of time series data.

We studied the stability of a class of hyperbolic systems with balance laws under delayed feedback control and the spectral analysis of the system operator  by using the strictly weighted Lyapunov function method and asymptotic analysis technique. Firstly, the well-posedness of the systems was verified by using operator semigroup theory. Secondly, the exponential stability of the closed-loop system was analyzed by constructing a strictly weighted Lyapunov function. Finally, according to  the asymptotic analysis technique, the asymptotic expressions of eigenvalues and eigenfunctions were obtained. The result shows that the system is exponentially stable when the feedback parameters and delayed value satisfy certain inequality constraints, and when the modulus of eigenvalues tends to positive infinity, the real part of the eigenvalues tends to a negative constant.

We discussed the existence of radial symmetric solutions of a Kirchhoff equation of  nonlinearity with gradient term on an annulus in R^N(N≥2) by using the Leray-Schauder fixed point theorem. Under the nonlinearity satisfied certain  conditions which allowed the nonlinearity might be superlinear growth of any order on unknown function term, and quadratic growth on the gradient term of unknown function, the existence results of radial symmetric solutions were obtained.

In order to reduce the risk of network intrusion, the author proposed an intelligent detection method for network intrusion nodes based on niche genetic algorithm. Firstly, aggregation processing was implemented for the attack behavior of network intrusion,  a two-person attack and defense game model was used to analyze the attack and defense status of the network. By comparing the utility strength of attack and defense, a comprehensive analysis of the network’s security was carried out. Based on the analysis results, the localization of the attack source was achieved through convolutional neural networks. Secondly, based on  rough set theory, the fitness function for network intrusion node detection was determined by using niche genetic algorithm. According to  the intelligent detection rules of network intrusion nodes, an intelligent detection model for network intrusion nodes was established to obtain the final detection results. Experimental results show that this method can effectively improve the accuracy of locating intrusion attack sources and detecting intrusion nodes. The macro F₁  score of the detection results of this method is greater than 0.96, indicating that this method can effectively achieve the design expectations.

Aiming at  the problem of low accuracy of traditional support vector machines (SVM), we proposed an LDBO-SVM model. Firstly, 
in order to solve the problem of uneven distribution of the initial solution of the original dung beetle optimization algorithm, the Logistic chaotic map was introduced into the algorithm to construct the LDBO algorithm. Secondly, the LDBO algorithm was used to optimize the internal penalty factor and kernel parameters of the traditional support vector machine, and the LDBO-SVM model was constructed. Finally, in order to verify the performance of LDBO-SVM model, LDBO-SVM model was compared with the 
improved SVM by using five other population intelligent optimization algorithms. The experimental results show that the accuracy of LDBO-SVM model reaches 94.53%, and  can accurately predict student achievement, providing assistance for  teachers to improve their teaching plans.

Aiming at the problem of frequent earthquakes and other natural disasters, based on the research on distributed fiber-optic sensing technology and the sensing principle and basic theory of Michelson fiber-optic interferometer, we designed a vector seismic sensor. The sensitive part of the fiber-optic seismic sensor was mainly composed of elastic thin sheets, mass blocks, circular rings and sensing fiber-optic  components. We conducted strain effect analysis of the sensor and designed overall scheme of the system. The signal generator was used to simulate earthquakes with the signal amplitude of  1 and the frequencies of 300,500 Hz, respectively. The results show that the composite materials are ideal materials for the vibrating thin sheet, which can significantly improve the sensitivity of the system and reduce the system errors. The detection sensitivities are 0.08 g and 0.3 g, respectively. The amplitude of the seismic signal is basically consistent with the signal amplitude detected by the sensor, and it has a good frequency response, which can be used for detecting seismic waves.

We studied the chiral transition mechanism of the bis-α-alanine chelating Ca(Ⅱ) complex (α-Ala)₂→Ca(Ⅱ)  by using the M06-2X and MN15 methods of density functional theory (DFT). The results show that the chiral transition of (S-α-Ala)₂→Ca(Ⅱ) undergoes  two processes:  Firstly,  one of the α-Ala in (S-α-Ala)₂→Ca(Ⅱ) isomerizes from the S-type to the R-type to obtain R-allo-α-Ala→Ca(Ⅱ).  Secondly,  the S-α-Ala in R-allo-α-Ala→Ca(Ⅱ) isomerizes again to R-α-Ala to obtain (R-α-Ala)₂→Ca(Ⅱ).   The free energy barrier for the (S-α-Ala)₂→Ca(Ⅱ) isomerization to the R-allo-α-Ala→Ca(Ⅱ) tachycritical step under the implicit aqueous solvent  is 221.5 kJ/mol from the transition state where the H proton migrates from the chiral C atom to the  N atom， the free energy barrier drops to 93.1 kJ/mol in dominant aqueous solvent. The free energy barrier for the R-allo-α-Ala→Ca(Ⅱ) isomerization to (R-α-Ala)₂→Ca(Ⅱ) tachycritical step is 233.8 kJ/mol for the implicit aqueous solvent  from the transition state where the H proton  migrates from the chiral C atom to the  N atom, the free energy barrier  drops to 116.7 kJ/mol in the dominant aqueous solvent. Therefore,  the chiral transition rate of (S-α-Ala)₂→Ca(Ⅱ) is slow in physiological environments,  and   bis-α-Ala chelate calcium can be safely used for supplementation of living organisms with elemental calcium and α-Ala.

We proposed a  two-level algorithm based on the virtual element discretization for both  steady-state and time-dependent PNP (Poisson-Nernst-Planck) equations. This algorithm first decoupled and linearized the PNP equations using the linear virtual element solution, and then solved them in the quadratic virtual element space. Compared with the commonly used Gummel algorithm for solving the PNP equations, this algorithm could accelerate the solving speed. Numerical experimental results, including both 
 steady-state and time-dependent PNP equations, show that compared with the Gummel algorithm with the linear virtual element, the two-level algorithm has  higher accuracy, and consumes less CPU time and is more efficient at  comparable accuracy.

Firstly, we used the potential well theory, the inverse Sobolev inequality, Fountain’s theorem and other tools to discuss  the blow-up problem of the solution to a class of pseudo-parabolic equations with variable exponential logarithmic nonlocal terms and singular potentials, and obtained the results of the solution of the problem to blow-up in finite time at arbitrarily high initial energy levels. Secondly, by combining  the Gagliardo-Nirenberg interpolation inequality and  Sobolev embedding method, and by constructing auxiliary functions, we gave the upper and lower bounds estimates for  the blow-up time of the solutions to the problem  under appropriate conditions.

By using  the weak convergence methods for nonlinear partial differential equations (PDEs), the author proved the existence of solutions to a class of quasi-linear elliptic equations with gradient term and zero-order term. The main characteristic of the equation was  that the coefficient function of the gradient term b∈L^N(Ω), but its  norm ‖b‖_N,Ω was not required to be sufficiently 
 small. Firstly, by segmenting the bounded domain Ω, the solution sequence {u^t}_0<t<1 was  split into a sum of some subfunctions, and the energy estimate of the subfunction was limited to small  subdomain. Secondly, the author obtained the energy estimate of  {u^t}_0<t<1 on W^1,p₀(Ω) by using  iterative techniques. Finally, with the help of Boccardo-Murat’s technique, the author proved the almost everywhere convergence of the gradient solution sequence {u^t}_0<t<1, and determined the convergence element  of the nonlinear term of the equation based on this convergence.

The NaBi(MoO₄)₂ electrode was prepared by the pressed sheet method,  and the material was modified by doping with Y³⁺. The morphology,  structure and electrochemical properties of the electrodes were characterized by X-ray diffraction (XRD), scanning electron microscope (SEM), transmission electron microscope (TEM), ultraviolet-visible-diffuse reflectance spectrum (UV-Vis-DRS) and electron spin resonance (ESR),  and the performance and reaction mechanism of the photocatalytic degradation of sildenafil were also investigated. The experimental results show that the NaBi(MoO₄)₂-based electrode  has a lamellar structure and high purity,  with the size ranging from about 37.5 nm to 24.6 nm. In the optimal electrolyte Na₂SO₄ solution with a concentration of 0.5 mol/L  and the optimal bias voltage of 1.5 V, sildenafil  can be completely removed after 70 min.

Aiming at the problem that uneven distribution of nodes led to  incomplete network coverage, the uneven position and density of nodes increased the complexity of deployment, and the search for the optimal node was prone to getting stuck in local optimal solutions in a multi hop wireless network, the author proposed  a non-uniform node deployment algorithm for  multi hop wireless network based on ant colony algorithm. Firstly, the author obtained the minimum weighted distance decision variable to reduce the transmission distance between Sink nodes and various sensors. Secondly, the author calculated the energy consumption of nodes, minimized node network loss, constructed a node deployment optimization model, and introduced compromise planning method to expand the multi-objective model into a single objective processing. Finally, the author introduced ant colony algorithm to solve the model, which could effectively traverse the potential solution space and quickly find the optimal deployment plan. The experimental results show that the  network coverage of proposed algorithm is 97%, with a maximum energy consumption of only 1.56×10^-7 J, which can effectively reduce network energy consumption. The survival cycle can reach up to 1 500 rounds, and the optimal node deployment plan can be obtained.

In order to reduce the maximum temperature of the electronic components on printed circuit board (PCB) and optimize the scheme of thermal design. We constructed a mathematical model of the steady-state temperature field of electronic components on PCB by using the micro-element body heat balance method according to the principle of heat transfer, and verified the effectiveness of the model  by using the thermal simulation software ICEPAK for electronic products. We made  discretization improvement based on the surface-simplex swarm evolution algorithm, and used the improved discrete surface-simplex swarm evolution (DSSSE) algorithm to adjust the layout of distributed electronic components on PCB. Simulation results show that the proposed algorithm can reduce the maximum temperature of the electronic components on the PCB and has a fast convergence speed.

By using the definition of sub-linear expectation and corresponding  inequalities, we gave the strong limit theorems for weighted sums of END sequence under sub-linear expectations,  and further studied the Marcinkiewicz-Zygmund type strong law of large numbers and Strassen-type invariance principle.

Aiming at the modeling problem of overdispersed, zero-and-one inflated integer-valued time series data with interdependent structures between individuals, we proposed a first-order generalized integer-valued autoregressive model with zero-and-one inflated Poisson-Lindley innovation. Firstly, we gave some statistical properties of the model, including expectation, variance, autocovariance, and transition probability. Secondly, the conditional maximum likelihood estimation method was used to estimate the unknown parameters of the model. Finally, the model was applied to a set of real data for fitting, and some evaluation criteria were used to verify the model. The case analysis results show that the model has a good fitting effect.

By using the function decomposition of the central Morrey spaces with variable exponent and hierarchical estimation methods, and with the help of the boundedness of the parameterized Marcinkiewicz integral operators with rough kernels on the  Lebesgue spaces with variable exponent, we gave the boundedness on the central Morrey spaces with variable exponent.

We characterized Na_0.52Bi_0.48-2xLi_xSr_xTi_0.99Mg_0.01O_3-δ（x=0,0.005,0.010,0.015) polycrystalline oxygen ion conductors prepared at a sintering temperature of 1 000 ℃ by using X-ray diffraction (XRD), scanning electron microscopy (SEM), Raman spectrum, and AC impedance spectroscopy to study the effect of the co-doping concentration of Li⁺ and Sr²⁺ on the crystal structure, microstructure and electrochemical properties of the series of the samples. The results show that with increase of co-doping concentration of Li⁺ and Sr²⁺, no obvious impurity peaks were observed in all samples, and the unit cell parameters and unit cell volumes first decreases and then increases with the increase of doping concentration. When x=0.010, the grain conductivity reaches its maximum value, which is about twice that of the undoped sample. When x=0.010, the apparent grain-boundary conductivity and the macroscopic grain-boundary conductivity of the sample reach their optimal values, which are superior to other doped samples.

Aiming at  the challenges of high-dimensional medical image data in survival analysis, we proposed an accelerated failure trace regression model. The regression parameters were estimated by using Kaplan-Meier weighting and the Peaceman-Rachford algorithm. The numerical simulation results show that the estimation performance of the accelerated failure trace regression model is better than that of the traditional Lasso regression model. We apply the model to Alzheimer’s disease image data to further verify its effectiveness and practical value.

We designed and synthesized  a crotonyloxy-substituted zinc porphyrin (TMPTPPZn) complex， which was copolymerized with methyl methacrylate (MMA) to obtain a zinc porphyrin/polymethyl methacrylate (PMMA) copolymer (TMPTPPZn-PMMA). Then using polyacrylonitrile (PAN) as the spinning solution, we prepared composite fibers TMPTPPZn-PMMA/AgX/PAN loaded with TMPTPPZn-PMMA and AgX(X=Cl,Br,I) by using electrospinning technology. The morphology of the composite fibers was studied by scanning electron microscopy (SEM),  the thermal stability of the composite fibers was studied by using thermogravimetric analysis (TGA), and studying their catalytic activity for the degradation of organic dyes. The results show that the TMPTPPZn-PMMA/AgCl/PAN,  TMPTPPZn-PMMA/AgBr/PAN and TMPTPPZn-PMMA/AgI/PAN all have high photocatalytic activity and 
can effectively catalyze the degradation of organic dyes in wastewater. After 240 min of visible light irradiation,  the degradation rates of methylene blue (MB) by the three composite fibers are  96.02%,94.75% and 90.91%,  and the degradation rates of rhodamine B (RhB) are 93.40%,94.71% and 96.54%,  respectively.

We considered the initial (boundary) value problem for the two-dimensional  chemotaxis-shallow water  model with vacuum, and  established a new blow up criteria for the local strong solutions of the model by using the energy method and some important inequalities. We also gave  some new factors that  affected the extension of strong solutions.

We established an expanded energy level system model of 2-(2′-hydroxyphenyl)benzothiazole (HBT) molecule and proposed corresponding numerical simulation algorithm for the dual-wavelength fluorescence phenomenon of organic molecule HBT in specific polar solutions， and verified the accuracy and effectiveness of the proposed algorithm.  The simulation results are similar to the experimental results, indicating that there is a competitive relationship between the fluorescence of HBT molecules at different wavelengths in specific  polar solutions. 

The adsorption mechanism of inert gases CH₄，N₂ and CO₂ on coal surface was analyzed by using density functional theory (DFT) M062X method. According to the Millikan charge distribution of each atom in the  coal molecules,  adsorption vacancies on the surface of coal molecules were determined. The adsorption models of CH₄，N₂ and CO₂ as single component gases  on the coal surface were established on each adsorption vacancy. By analyzing and comparing the microscopic parameters such as bond length,  bond angle,  adsorption distance and adsorption energy of each adsorption model,  the author obtains that  the affinity order of the three kinds of gas adsored on coal surface is  CO₂>CH₄>N₂, and reveals  the microscopic states of CH₄，N₂ and CO₂ adsorption on coal surface.

We considered  the existence of pullback attractors in non-autonomous wave equations. Firstly, we proved the well-posedness of its solution  according to the uniform sector operator theory. Secondly, the bounded dissipation of the process was obtained by constructing an appropriate functional. Finally, the asymptotic compactness of the process was verified according to the 
operator decomposition technique, and ultimately the existence of the pullback attractor was obtained.  This study not only considers time-dependent damping, but also time-dependent diffusion and time-dependent nonlinear terms. When these time-dependent coefficients meet the appropriate conditions, the existence of the pullback attractor is proven.

By using Leray-Schauder degree theory and method of upper and lower solutions, the author  study the existence and multiplicity of positive solutions for the elastic beam equation with nonhomogeneous boundary conditions.  When the nonlinear term f satisfies suitable conditions, the author prove that there is a positive number b*, such that there are at least two positive solutions to the problem when 0<b<b*, there is exactly one positive solution to the problem when b=b*, there is no positive solution to the problem when b>b*.

By using the discharging method, we  study the local strict neighbor-distinguishing edge coloring problem of sparse graphs, and obtain that if G is a graph with maximum degree at most four and maximum average degree mad(G)<16/5,  then the local strict neighbor-distinguishing index of G is at most 10.

Aiming at the problems of poor learning performance and high fluctuation in the deep deterministic policy gradient (DDPG) algorithm for tasks with some large state spaces, we proposed a multi-actor deep deterministic policy gradient algorithm based on progressive k-means clustering (MDDPG-PK-Means) algorithm. In the training process, when selecting actions for the state at each time step, the decision-making of the actor network was  assisted based on the discrimination results of  the k-means clustering algorithm. At the same time, as the training steps increased, the number of k-means cluster centers gradually increased. The MDDPG-PK-Means algorithm was applied to the MuJoCo simulation platform, the experimental results show that, compared with 
 DDPG and other algorithms, the MDDPG-PK-Means algorithm has better performance  in most continuous tasks.

We considered the blow-up phenomena of solutions to  a class of fourth-order parabolic equations. Firstly, we  introduced a new inequality. Secondly, under appropriate conditions, we  proved that the solution to the equation blew up in finite time and gave an upper bound estimate for the blow-up time. Finally, using the new inequality and differential inequality techniques, we obtained a lower bound estimate for the blow-up time of the solution.

On the basis of the FitzHugh-Nagumo(FHN) neuron model containing phototubes, we connected the inductors in series with phototubes to construct a photosensitive neuron model. Firstly, we plotted the time-space diagram and membrane potential phase diagram of the network under different coupling strengths by numerical simulation. Secondly, we changed the amplitude of the external excitation source of the neuron and the output voltage amplitude of the phototube separately, and calculated the order parameter SI under the corresponding parameters. Finally, the values of the amplitude of the external excitation source and the output voltage amplitude of the phototube for each neuron were randomly selected from a normal distribution, we constructed a non-all-identical neural network, changed the coupling strength and the standard deviation of the normal distribution, and calculated the corresponding order parameter SI. The results show that, when the coupling strength increases within a certain parameter range, the network can transition from asynchronous to chimera state, and ultimately achieving synchronous. The appropriate value of amplitude can expand the coupling strength interval corresponding to chimera state. In the non-all-identical neuron network, the coupling strength interval corresponding to the chimera state is positively correlated with the value of the standard deviation.

We considered the existence of radial solutions to Dirichlet problems for a class of p-Monge-Ampère systems with multiparameter. By utilizing the fixed point index theorem on cones, we prove the existence results of radial solutions when the parameters are large enough and nonlinear terms satisfy  appropriate growth conditions.

Let H be a Hilbert space over the real or complex field F, N be a non-trivial nest on H and τ(N) be the associated nest algebra. Suppose s: τ(N)→τ(N) is a map without additivity and linearity. With the help of method of algebratic decomposition, we prove that if 3s(X^.Y^.Z)=s(X)^.Y^.Z+X^.s(Y)^. Z+X^.Y^.sZ) for any X,Y,Z∈τ(N ) with XYZ=0, then s is an additive centralizer.

By using tools such as weighted boundedness of the Hardy-Littlewood maximal operator and the pointwise estimates for the Sharp maximal function, we gave the boundedness of multilinear strongly singular Calderón-Zygmund operators and their multilinear commutators generated by BMO (bounded mean oscillation) functions on product of weighted Morrey spaces over RD(reverse doubling)-spaces.

Aiming at the problem of  the high computational cost of fitness in traditional genetic algorithms for complex high-dimensional optimization problems, we proposed an improved genetic algorithm Gamma based on manifold learning and multiple linear regression.  The Gamma algorithm reduced the  dimensionality of  the population data through manifold learning, and combined AP clustering with a multiple linear regression model to reduce the calculation times of fitness function and improve algorithm optimization efficiency. Experimental results show that the Gamma algorithm achieves optimization results similar to traditional methods with fewer fitness calls in complex engineering such as the optimization of truss dome structures and multiple  classic Benchmark functions. It has a  promising application prospect in handling with complex high-dimensional optimization problems, effectively enhancing computational efficiency and reducing time costs.

By using the test function method, combining properties of the Heisenberg Laplace operator and K function, and utilizing relevant differential inequality techniques, we studied the rupture problem of the initial value problem solutions for  a class of wave equations (systems) with convolution terms and weak damping terms in n-dimensional space. The results show that there is no global weak solution to the problem when the initial value satisfies certain assumptions. This obtained result gives the influence of parameters in the convolution term on rupture of the solution, and provided a reference for the study of existence of solutions to wave equations (systems) with weak damping and convolution type nonlinear terms in high dimensional spaces.

By using the local linking theorem in critical point theory and the theory of variable exponent Sobolev space, the author proved the existence of nontrivial solutions for Kirchhoff-type equation with p(x)-Laplacian operator without  assuming  the  (AR) type superlinearity condition held.

Aiming at the problem of insufficient detection accuracy of rotated small objects in remote sensing images under  limited scale, diverse orientations, and complex background conditions, we  proposed a Transformer network  method with dual-domain query enhancement and rotation awareness. The method used  convolutional neural network  to extract multi-scale features and introduced a joint enhancement in both spatial and frequency domains at the encoding end. The  spatial  adaptation module captured geometric structure features by using multi-scale receptive fields, while a frequency adaptation  module  extracted directional information through  wavelet transform. After  cross-domain fusion, a feature query  with both spatial and frequency 
perception capabilities was generated. We introduced a rotation-aware module at the encoding end to dynamically estimate spatial offsets during the Transformer decoding process, achieving precise alignment of rotated small objects at multiple scales. The experimental results show  that the proposed method significantly improves detection accuracy of rotated small objects on public remote sensing image datasets,  verifying  its effectiveness and robustness under complex background conditions.

We established a Dengue fever transmission model that considered spatial heterogeneity and the advective effect of wind by using the theories of monotonic homogeneity and  chain transitive sets. The results  show that the basic reproduction number R₀ determines the global threshold dynamics of the model: when R₀≤1, the disease goes extinct;  when R₀, the disease persists. Numerical analysis results show  that R₀ varies non-monotonically with the advection rate, and  increasing the density of alternative hosts is helpful for disease prevention and control.

Aiming at  the problems that the traditional K-Means algorithm was sensitive to initial centroids, prone to local optima, and failing to fully mine the potential semantic features of clustering results, we proposed a  K-Means clustering algorithm based on heuristic crossover strategy optimization. Firstly, the algorithm used  a density-driven heuristic crossover initialization strategy to screen representative parent points in high-density regions, and  introduced a crossover coefficient to dynamically generate diverse initial centroids to  reduce the volatility of clustering results caused by random initialization. Secondly, during the clustering iteration process, by combining the information of parent points with the intra-cluster mean update rule, the centroid positions were dynamically adjusted through crossover operations, which solved the problem of inter-cluster overlap caused by the local optima of the traditional algorithm. Finally, the optimized clustering results were input into a multi-layer perceptron, which utilized its nonlinear mapping ability to mine potential features and  achieved  deep fusion of clustering results with  deep semantic features. Experimental results show that the contour coefficient, Davies-Bouldin index, and adjusted Rand index of the algorithm reach 0.634, 1.398 and 0.621, respectively, which are significantly superior to other improved algorithms, effectively improving clustering accuracy, stability, and interpretability of the algorithm.

 We designed and synthesized a metal organic framework material tpe-UiO-67 with UiO-67 type by using biphenyl dicarboxylic acid modified with tetraphenylethylene as a linker  with  aggregation induced emission (AIE) properties and a mixed ligand strategy. We characterized it by using  Fourier transform infrared spectroscopy， X-ray powder  diffraction， ¹H nuclear magnetic resonance spectra and thermogravimetric analysis, and applied it to detect nitrofuran antibiotics in aqueous solutions. The experimental results show that  tpe-UiO-67 has stable chemical properties  and excellent luminescence performance, and can detect nitrofuran antibiotics in aqueous solution with high sensitivity. The fluorescence quenching efficiency is linearly correlated with antibiotic concentration when the antibiotic concentration in the environment is not less than  2.0 × 10^-5 mol/L.

Aiming at the problem that the data obtained by different sensors might be uncertain and inconsistent due to the influence of  sensor’s own error and external interference, in order to effectively eliminate the contradictions and conflicts between data and improve the data fusion effect, we proposed a multi-ensor data fusion algorithm based on fuzzy clustering. Firstly, the D-S (Dempster-Shafer) evidence theory was used for preliminary data fusion, the distance between heterogeneous data was calculated and the corresponding trust function was determined, and different sensor data were corrected and coordinated to improve data consistency. Secondly, we introduced fuzzy clustering method to optimize the preliminary fusion results of multi-sensor data, 
grouped data points into clusters with similar features, and determined the initial clustering center. Finally, we used  fuzzy clustering algorithm to group data and improve the accuracy and robustness of data fusion results. The experimental results show that the proposed algorithm has high fitting goodness and shard reception rate in multi-sensor data fusion, and overall energy consumption is low, with excellent overall performance.

Aiming at the  problem of  the performance bottleneck caused by gradient synchronization in data-parallel deep learning tasks, we proposed a dynamic sparse gradient fusion algorithm. The  algorithm synergistically modelled  gradient compression, pipeine techniques, and tensor fusion technology to establish  a theoretical model of the impact of sparse gradient fusion behavior on accuracy. Based on this, the  gradient fusion scheme was found to accelerate gradient synchronization while improving validation accuracy, so as to solve the problem of unstable validation accuracy caused by sparse gradient fusion. Experimental results show that the sparse gradient fusion algorithm reduces communication time by  1.63 times  compared to layer-wise sparsification method, and reduces convergence time by  2.68 times compared to existing sparse gradient fusion algorithms.

The channels and time segments of electroencephalogram (EEG) signals in the process of emotion generation contained rich emotional information, and different time segments held varying importance in emotion recognition. The challenge was how to capture key features and highlight key time segment information, we proposed a  multi-|dimensional feature  emotion recognition method based on EEG. This method fully utilized  frequency, spatial,  temporal characteristics, and attention information of physiological signals. By constructing a four-dimensional feature matrix combined with a depthwise separable network and embedding a convolutional sliding window to adaptively extract the spatial-frequency features of EEG signals. Meanwhile, a multi-head attention mechanism was integrated into the temporal convolutional neural network to highlight  important time series information and achieve emotion recognition. The accuracy of wake-up and potency of the proposed method on the DEAP dataset is 97.49% and 97.36%, respectively, and the accuracy of the method on the SEED dataset is 96.60%, which is about 3% higher than that of the mainstream method. The experimental results verify the superiority of the model in physiological signal emotion recognition.

We constructed 4 order unitary matrices by using tensor product based on three classes of 2 order unitary matrices. The results show  that the complete sets of the mutually unbiased bases are still mutually unbiased under four classes  of unitary transformations, but the complete sets of the mutually unbiased bases are no longer mutually unbiased under the other five classes of unitary transformations. The sum of l₁ norm of coherence of Bell-diagonal states under the four-dimensional mutually unbiased bases is no more than 9.

Aiming at the problem that the conventional soft actor-critic (SAC) algorithm lacked exploration capability and state representation in complex environments, we proposed an improved soft actor-critic (ISAC) algorithm. Firstly, the ISAC algorithm  introduced a prioritized experience replay (PER) mechanism, which dynamically evaluated the priority of experience samples by using the temporal differential errors, thereby enhancing the utilization of crucial experiences and improving learning efficiency of the algorithm. Secondly, the algorithm integrated  generative Transformer architecture  into the actor network to strengthen its ability to dynamically capture state features, thereby significantly improving its performance in complex optimization tasks. Finally, we conducted an application experiment  on the dynamic scheduling optimization problem of university logistics staff. The experimental results show that, compared with the original  SAC algorithm and the classic deep Q-network (DQN) algorithm, the proposed ISAC algorithm has smaller errors in dynamically fitting human resource demand, which effectively demonstrates its 
advantages and practicality in practical applications.

Aiming at the problem that the copper component in the neutralization gun of X-ray photoelectron spectroscopy was extremely easy to be contaminated and corroded, taking the Thermo Scientific NEXSA type X-ray photoelectron spectroscopy as an example, by studying the working mechanism and structural properties of the neutralization gun, and combining with the scanning electron microscope and energy dispersive spectrometer to analyze the contamination on the surface of the corroded copper mesh, we proposed an improved method of electroplating inert metal film on the copper mesh. By comparing the surface contamination
 of copper and gold standard samples built in the instrument under the long-term test environment in the analysis chamber through the full spectrum scanning test, we determined the coating material and process, and conducted performance test of the improved neutralization gun. The results show that the gold electroplating on copper mesh does not affect the normal use of the neutralization gun, the improved neutralization gun still has a good neutralization effect on insulating samples, and the service life can be increased by more than 5 times of that before improvement, greatly improving its corrosion resistance performance.

We used the Kuratowski measure of noncompactness and Sadovskii’s fixed point theorem to study the initial value problem of fractional non-autonomous delay evolution equations in Banach spaces. We proved the existence of mild solutions to the problem under weaker noncompactness measures and growth conditions.

Aiming at the problem of low prediction accuracy when classical machine learning algorithms (e.g., decision trees, random forests) modelled complex implicit interaction relationships, we proposed a fluctuation  prediction model based on recurrent neural networks and an attention mechanism. We first calculated the complex interaction relationships among various  influencing factors through the attention mechanism, and then used  recurrent neural networks to learn the hidden variable representations of the model, thereby achieving precise prediction. The results of simulation and comparative experiments with multiple classical prediction models show that the  prediction accuracy of proposed model is significantly higher than other machine learning models,  providing a more efficient and accurate solution for the field of volatility prediction.

Aiming at the common problem of  low drug loading rate of polydopamine (PDA)-based nanocarriers,  we synthesized   Fe₃O₄@PDA nanoparticles (NPs) with a unique spindle-shaped structure, which could  achieve a drug loading rate of up to 90% (900 ug/mg),  significantly surpassing traditional PDA-based  carriers. The experimental results show that the spindle-shaped Fe₃O₄@PDA has good  biocompatibility,  efficient photothermal conversion ability,  and excellent  near-infrared (NIR) absorption ability,  which can control  drug release under pH/NIR dual response. Due to its embedded Fe₃O₄,   spindle-shaped Fe₃O₄@PDA NPs can be used as  contrast agents for photoacoustic and magnetic resonance imaging, and for  chemo-photothermal synergistic  therapy guided by dual-modal imaging.

Rare-earth small molecule chelator  was used to prepare antibody markers of severe acute respiratory syndrome coronavirus 2(SARS-CoV-2), and SARS-CoV-2 antigen was detected by time-resolved fluorescence immunochromatography. The experimental results show that the linear range of the method is 0.04—100 ng/mL,  the linear equation is y=0.007 2x+0.033 2, the correlation coefficient R²=0.999 5. The detection limit is 0.028 ng/mL. The intra-assay and inter-assay coefficients of variation are less than 6.72%,  and the recovery rate is  94.35%—103.00%. The method has the advantages such as good precision,  low detection time (less than 20 min),  low cost,  and simple operation.

Aiming at the problems existing in the process of face image posture correction, such as ignoring detailed features, blurring the texture of the face image after correction, and excessive gap between the face features and the identity features of the original image, we proposed a face correction method based on the dual discriminator and dual attention mechanism of the generative adversarial network. Firstly, while using the dual discriminator to determine the face identity and face posture, we designed a face representation attention module to enhance the overall features of the face, prevented the loss of face-related information, and improved the model’s ability to perfect face images. Secondly, we designed an adaptive edge-enhanced attention module. By using the adaptive attention mechanism and Sobel filter, the edge detail features and key features of the face were enhanced to generate a frontal face with realistic facial features and contours. Finally, a new normalization layer CrossNorm was adopted to improve the robustness under distribution changes,  and the results of testing  experiments on the Multi-PIE dataset and the CFP dataset show that the proposed model generates frontal face images with better face correction effects compared to the comparison model.

Aiming at the problem that  deepfake  detection algorithms  had low detection effect on neural texture (NT) forgery methods in FaceForensics++(FF++) dataset,  we  proposed a reverse knowledge distillation network (RKD-Net) by improving  fine-grained feature extraction of face images. Firstly, the RKD-Net used  reverse knowledge distillation (RKD) as the main framework, 
preserving  the rich fine-grained information of the input face images. Secondly, spatial and channel reconstruction convolution (SCConv) was inserted between the encoder and the decoder to enhance the representation of fine-grained information from both spatial and channel dimensions. Finally, a residual coordinate attention (RCA) classifier was used to enhance the real and detailed features  output by  the reverse knowledge distillation network, and classify the face images input to the network according to these different features. The experimental results  show that RKD-Net achieves  the best detection effect of NT forgery methods  
while guaranteeing the  detection effect of  other  forgery methods.

We considered the existence of weak solutions to  elliptic coupled systems with p-Laplace operators and Hardy type singular terms in the whole space R^N. New criteria for the existence of at least one and at least two weak solutions were established by using  variational methods combined with  critical point theorems when the sign-changing nonlinearities satisfied suitable hypotheses.

 In order to develop a novel organic zinc supplement, Polygonatum rhizoma polysaccharide from the medicinal and edible herb Polygonatum rhizoma was chelated with zinc sulfate to prepare Polygonatum rhizoma polysaccharide chelate zinc. We optimized the chelation process,  characterized and evaluated the chelated compound by using UV-Visible spectroscopy,  Fourier transform infrared spectroscopy (FT-IR),  scanning electron microscopy (SEM),  and an in vitro Caco-2 cell absorption model experiments. The experimental results show that the optimal chelation process is at a temperature of  60 ℃,  pH=7,  t=60 min and a polysaccharide-to-zinc  ratio of 8∶1, the chelation rate can reach 58.7% under the conditions. Zn²⁺ adsorbs onto Polygonatum rhizoma polysaccharide and forms chelates with  carboxyl,  hydroxyl,  and carbonyl groups as  chelating sites. The  expression levels of zinc transport proteins ZnT-4,ZnT-6 and ZnT-8 are increased in Caco-2 cells. Therefore, the prepared Polygonatum rhizoma polysaccharide chelate zinc has good chelating properties and potential to promote zinc absorption.

Firstly, aiming at the problems of  the traditional K-means algorithm’s assumption of feactre equality in  processing high-dimensional heterogeneous data, which led to  the neglect of important features,  high sensitivity of clustering results to the preset number of clusters, and strong dependence on the selection of initial centroids, we proposed an adaptive dynamic feature weighting K-means algorithm (ADFW-K-means), which integrated multiple techniques, such as dynamic feature weighting, 
K-means++-optimized initialization, the elbow rule for cluster number selection, an empty cluster handling mechanism, and an adaptive cluster number adjustment strategy. Secondly, the experiments conducted on the targeted selection graduates dataset of  Jilin University from 2022 to 2024. The experimental results show that compared with traditional clustering algorithms, 
the  ADFW-K-means algorithm achieves significant improvements in three core metrics of  silhouette coefficient, clustering stability, and business interpretability,  effectively overcoming the inherent limitations of traditional methods, significantly enhancing the accuracy and robustness of clustering for complex high-dimensional heterogeneous data.

When the nonlinear term satisfied the subcritical growth condition, long-time dynamical behavior of solutions for nonlocal nonclassical diffusion equation with time-dependent memory kernels was discussed. We first used  Galerkin approximation method to obtain the well-posedness and regularity of the solution, and then used decomposition technique and integral estimation method to prove the existence and regularity of the time-dependent global attractors.

The author  investigated a class of abstract non-autonomous impulsive evolution equations in Banach spaces and proved the
 Lipschitz pseudo-orbit shadowing property for the problem under relatively weak conditions by using the contraction mapping principle. The obtained results are not only applicable to specific cases, but also have universality for general equations.

Let T be a formal triangular matrix ring, where R and S are associative rings with identity element, C is a faithfully semidualizing (S,R)-bimodule. It is showed that: 1) M is a Ding C-projective left S-module; 2) N is Ding C-injective left R-module. The obtained conclusions establish links between Ding C-modules and Ding modules through T.

Aiming at the problem of  the information overload caused by the explosion of big data teaching resources and the insufficient accuracy of traditional retrieval-augmented generation (RAG) in multi-source information fusion, we proposed a big data knowledge learning method based on GraphRAG. Firstly, we designed a Chinese prompt template to drive GraphRAG to automatically extract course entities and relationships, constructed an initial knowledge graph, and persisted it to Neo4j graph database. Secondly, through entity alignment and relationship completion, manually organized knowledge points were integrated with the automatically constructed graph to form a unified and evolving knowledge graph database. Finally, the community summaries pre generated by GraphRAG were utilized to achieve global semantic search, while relying on the Neo4j graph database to achieve precise local retrieval of knowledge points. The experimental results show that the proposed method is significantly better than traditional RAG in terms of question answering accuracy, response correlation, and smoothness of multi\|source information integration.

We proposed a direct measurement schemes for the concurrences of photonic hyperentangled states based on quantum-dot-microcavity coupling system. The hyperentangled states were encoded in the polarization and spatial mode degrees of freedom (DOF) of photons. The schemes for entanglement measurement of both DOFs were constructed by error-heralded controlled-phase-flip gates through the single-photon input-output process of the quantum-dot-microcavity system. By transforming the concurrences into the detection probabilities of odd parity state, the schemes achieved efficient measurement of the concurrences of hyperentangled states. The schemes could not only independently measure the concurrence in each DOF, but also overcome the quantum operation distortions caused by cavity loss and imperfect coupling in traditional schemes. The research results show that the schemes have high experimental feasibility and robustness, providing a new approach for measuring hyperentangled states in quantum information processing.

We used femtosecond laser processing technology to improve the optical absorption rate of SiC in the infrared band (especially within the 10.3~12.6 μm range), in order to solve the problem of traditional processing techniques being difficult to finely process and having low absorption rates. We used femtosecond laser direct writing technology to generate specific micro/nanostructures on the surface of SiC by adjusting key parameters of laser processing, and analyzed the surface morphology and optical properties of the processed samples by using scanning electron microscopy and Raman spectrum. The results show that the surface morphology of SiC can be effectively modulated through femtosecond laser processing, and its infrared absorption rate is significantly improved, with a maximum absorption rate of 92%. The nanostructures can reduce the reflectance of materials and enhance the excitation of surface phonon polaritons, thereby enhancing the infrared light absorption capacity of materials.

Aiming at the problem of modeling mixed frequency data, we proposed an autoregressive U-MIDAS (unrestricted mixed data sampling) quantile regression model. Firstly, we combined the nested Lasso penalty method and  the spike-and-slab prior for Bayesian parameter estimation and variable selection. Secondly, the superiority of this method was proved by numerical simulations. Finally, this method was applied to predict the annualized quarterly growth rate of  nominal gross domestic product (GDP) in the United States. The results show that the proposed method has  good prediction accuracy.

In order to gain a deeper understanding of users’ learning habits and development trends, and to dynamically adjust educational resources based on user needs and behaviors, we proposed a  dynamic evolution model of user learning behavior based on complex network clustering algorithm. Firstly, we designed a complex network clustering model to obtain the user learning behavior community. Secondly, we obtained  the distribution of data association rules through semantic binary analysis, and used  multiple regression methods to mine the association rules,  obtaining a user learning behavior feature distribution model. Finally, we obtained user learning behavior interest features, which were used as input to obtain a dynamic evolution model by adding  attention mechanism  to the gated recurrent unit network.  The experimental results show that the proposed method can effectively distinguish between behavior data that users in the learning community are interested in and not interested in. The AUC value is closer to 1, indicating that the proposed method has better performance and stronger practicality.

Aiming at  the problems of difficult hyperparameter selection and high volatility of prediction results in the temporal convolutional network, we proposed a temporal convolutional network model based on an improved northern goshawk optimization algorithm. Firstly, we proposed an improved northern goshawk optimization algorithm based on a hybrid strategy, which enhanced global exploration and local exploitation capabilities of the algorithm by integrating Sine chaotic mapping for population initialization, 
introducing a nonlinear inertia weight adjustment strategy, and combining with  the Lévy flight mechanism. Secondly, we took  the prediction error of the temporal convolutional network as the optimization objective, and used the improved northern goshawk optimization algorithm to automatically search for its optimal hyperparameter combination for constructing a time series 
prediction model. Experimental results on the power load forecasting task show that the proposed prediction model has significant advantages in prediction accuracy and result stability compared to other improved temporal convolutional network models. It provides an efficient and robust automated optimization method for solving the hyperparameter selection problem of temporal convolutional networks, improves the accuracy and reliability of temporal convolutional network models in complex time series prediction tasks, and has practical application value.

Aiming at  the compactness problem of dual Toeplitz operators on Fock spaces with general Gaussian measures. We first defined logarithm-type complete square functions, and then by constructing a family of auxiliary functions, and using methods such as scaling and multiplication operator decompositions, we gave  necessary and sufficient conditions for the boundedness and compactness of dual Toeplitz operators on Fock spaces with general Gaussian measures. This extended the research methods of  dual Toeplitz operators on Fock spaces to the general Gaussian measure Fock spaces.

Aiming at the problem of accurate modeling and efficient control of complex dynamic systems, we discussed  the optimal control model of nonlocal nonlinear equations with 0<s≤1 order fractional Laplacian operator. Firstly, the existence and uniqueness of the solution to the equation were proved by using Schauder fixed point theorem and Gronwall inequality. Secondly,  the boundedness of the solution to the equation was established by introducing the measure theory. Finally, the existence of the optimal control function solution to the equation was proved by using the weak lower semicontinuity of the cost functional.

We considered a predator-prey model with alternative prey and Michaelis-Menten type harvesting. Firstly, we discussed the existence and stability of its boundary equilibrium points and interior equilibrium points. Secondly, taking the coefficient of Michaelis-Menten type harvesting as the bifurcation parameter, we proved the existence of Hopf bifurcation at its interior equilibrium point and its properties by using the Hopf bifurcation theorem. Finally, we verified the correctness of the theoretical results through numerical simulations by using MATLAB software.

Aiming at the problem of uneven distribution and  asymmetric characteristics  in practical image distortion. In order to improve the quality of the image and make it closer to the real situation, the distortion in different regions and directions of the image was finely adjusted to restore the original shape of the image, we proposed  a machine learning based asymmetric geometric correction method for distorted images. Firstly, the visual effect of the image was improved and details were enriched by using histogram equalization for brightness compensation. Secondly, we selected some key points or feature points from the preprocessed distorted image, and used the normalized product correlation algorithm to locate and correct all distortion control points required by the positional relationship of these points. Finally, we used the BP neural network in machine learning to learn and fit the complex nonlinear relationship between the original image and the distorted image. Through training, we enabled BP neural network to more accurately describe the distortion characteristics of the image. The network outputs coordinates closed to the control point, thereby achieving asymmetric geometric correction of the distorted image. The experimental results show that the proposed method has good generalization ability and the ability to handle complex asymmetric distortions, which  can effectively improve the accuracy of image distortion correction and increase the average resolution of each image by 465.3 PPI.

Aiming at the problem that the significant disparities in  residual energy among nodes led to uneven energy consumption,  affecting  load balancing, limiting  information transmission efficiency, and  increasing packet loss rates  in wireless sensor networks employing non-uniform clustering, we  proposed a load-balanced non-uniform clustering routing algorithm for wireless sensor networks. Firstly, we used a hybrid energy-efficient distributed clustering protocol to perform non-uniform clustering of nodes in wireless sensor networks,  calculated the clustering probability for each node and selected the node with the highest probability as a candidate cluster head node. Secondly, we designed a node  evaluation function based on  residual energy of nodes and its distance to neighbors, calculated the evaluation function value of each node, elected the  node with the highest evaluation function value as the  cluster head  to construct a cost function,  selected relay nodes to enhance transmission efficiency, and  formed an inter-cluster multi-hop routing algorithm. Finally, we distributed the data transmission tasks to  multiple nodes in the network to  reduce single-node energy consumption and achieve  non-uniform clustering routing load balancing in wireless sensor networks. Experimental results show that  the residual energy of each node in this algorithm  only  fluctuates around 6 J, and the fluctuation amplitude of the curve is small. The network packet loss rate is low at 0.22% when   transmitting 2 000 bit data volumes, indicating high  load balancing.

By constructing the edge-coloring and total-coloring algorithms based on the characteristic trees,  combined with combinatorial analysis, we obtain that the adjacent vertex distinguishing multiplicative edge chromatic number of Halin graphs is not more than 3, and the adjacent vertex distinguishing multiplicative total chromatic number of Halin graphs is 2. The  results show that the adjacent vertex distinguishing multiplicative 1-2-3 conjecture and multiplicative 1-2 conjecture are valid for Halin graphs, respectively.

Aiming at the problems of weak electromagnetic interference immunity, continuous external power supply, complex installation process, low signal-to-noise ratio, and insufficient sensitivity of conventional power grid dance monitoring systems, we proposed a novel cable disturbance monitoring system. The system employed a dual-ended Mach-Zehnder interferometric (MZI) optical path structure, which could achieve long-distance, large-scale, and multi-dimensional online monitoring and structural safety warning to locate the position of the dance in real-time. The sensor core adopted a thin-walled sensitivity-enhanced cable sleeve design, which integrated a laser MZI optical path composed of high-sensitivity micro-optical fiber and couplers inside. This interferometer had excellent response characteristics to vibration. After being encapsulated within a specialized metal housing to form an integrated dance monitoring sensor. The experimental results show that the natural frequency of the finite element of the sensor is 106.77 Hz, and the relative error with the measured date is only 1.65%. The relative sensitivity of the detector in the range of 0—140 Hz is 41.25—66.78 dB(rad/Pa), which confirms its ability to detect the high sensitivity of the dance signal.

We discussed a class of  inverse problem of  time fractional order diffusion equations by using the fractional order Tikhonov regularization method. We gave selection criteria for the regularization parameter under  prior and posterior conditions, and gave rigorous  proofs of the convergence of the method. Numerical experimental results show that  the fractional order Tikhonov regularization method is effective in solving this problem.

Let R be a ring, and S be a multiplicative subset of R. Firstly, we introduce the notion of Gorenstein u-S-injective modules by mean
s of the theory of Hom functors. Secondly, we study the homological properties of Gorenstein u-S-injective modules by using the u-S-Five Lemma and the method of constructing pull-back diagrams. Particalarly, it is shown that an R-module M is Gorenstein u-S-injective if and only if Extⁱ_R(E,M) is u-S-torsion module for any u-S-injective R-module E and any integer i>0, and M admits a proper left u-S-injective-resolution. The class of Gorenstein u-S-injective modules is closed under finite direct sums.

A formula for calculating the determinant and permanent of the adjacency matrix of a graph based on Sachs subgraphs on the graph was given, the author gave a vertex-deletion recursive formula for calculating the determinant and permanent of the adjacency matrix of the graph  respectively, and used  these recursive formulas to provide a method for calculating the determinant and permanent of the adjacency matrix of the color-ball graph  respectively. The results show that the determinant of the adjacency matrix of the color-ball graph is equal to the total differential of a function with 16 variables, and the permanent of the adjacency matrix of the color-ball graph is equal to the total differential of a function with 4 variables.

Aiming at the problem of poor pose and lighting robustness in complex environments, we proposed a facial expression recognition method that integrated an extended local binary pattern and multi-scale network structure. The method expanded the receptive field of the traditional local binary pattern and enhanced spatial correlations between pixels, reducing noise interference of lighting on facial expression recognition. By evenly dividing  the feature maps  into several subsets in the channel dimension, and multi-scale features of the feature map were extracted by using different  numbers of identical convolutional blocks, it effectively processed facial  pose variations. Experimental results on the Fer2013 and RAF-DB datasets show  that the proposed method can effectively improve  the accuracy and robustness of facial expression recognition, offering an effective solution for  facial expression recognition in complex environments.

Firstly, we used  the Jury criterion and spectral radius method to study the switching dynamics models of systems with pulse time-delay harvesting and birth, proved the  asymptotic stability of the periodic solutions of the pulse systems and gave the threshold for population extinction. Secondly, we considered the continuous survival of the population and the amount of harvest, discussed the reasonable values of the harvest delay under different circumstances, and verified the theoretical results by numerical simulation.

We established a dynamic model of a four-roll cold strip rolling mill under Gaussian white noise excitation. We simplified the system into an Ito stochastic differential equation by using the stochastic averaging method for quasi-non-integrable Hamiltonian systems. Through the maximum Lyapunov exponent of the system’s invariant measure and stochastic bifurcation theory, we analyzed the local stability and stochastic Hopf bifurcation of the system. and verified the effectiveness of the theory of stochastic averaging method by using Monte Carlo simulations. The numerical simulation results show that as the deformation resistance of the rolled material increases, the system bifurcates and loses stability.

Firstly, we introduced the W operator on harmonic Bergman space and gave the concept of slant Toeplitz operators.  Secondly, we studied the spectral structure and compactness of the W operator, and gave the integral representation of slant Toeplitz operators, which  provided a theoretical basis for subsequent research on  the compactness and boundedness of slant Toeplitz operators.

Aiming at the problem of underutilization of job locality and  low prediction accuracy in high-performance computing systems, we  proposed a job runtime prediction algorithm considering locality. The algorithm comprehensively utilized the global and local features of job log data, and improved prediction accuracy through a voting mechanism that combined with machine learning prediction and locality-based time-series prediction. Experimental results show that on actual scheduling log datasets such as 
 Unliu Gaia and PIK IPLEX, the JRPL algorithm outperforms or is not inferior to the machine learning algorithms  as the baseline in all  three  metrics: average absolute error, average prediction accuracy, and hit rate. This research result provides an improved prediction model for job scheduling in high-performance computing systems, which hepls to make more accurate execution time forecasting, improve system resource utilization, and reduce computational costs.

Aiming at the problem of complex image content, diverse action postures, and significant background interference in the task of sports image classification,  we proposed a sports image classification algorithm based on an improved ResNet50 model. Firstly,  a squeeze-and-excitation module was embedded within the residual structure to adaptively enhance key channel features and improve feature expression capability. Secondly, on this basis, a feature pyramid network was introduced to achieve effective fusion of multi-scale features, and enhance the model’s perception ability of objects at different scales. Finally, classification prediction was performed through global average pooling and  fully connected layers. Experimental results show  that the classification accuracy of the proposed method is about  5% higher than that of the conventional ResNet50 model, fully demonstrating  its robustness and superiority in handling complex actions and diverse backgrounds. The experimental results  not only validate the effectiveness and feasibility of the proposed method,  but also provide more reliable technical support and practical reference for applications in sports video analysis,  intelligent sports training and other related fields.

The author considers  the existence of positive solutions for the boundary value problems of a class of singular second-order ordinary differential equations. Based on the Krasnoselskii fixed point theorem, the author  proves that there exists a constant λ₀>0, such that the problem has at least one positive solution when λ∈(0,λ₀).

We established an optimization model for the refractive index inversion problem in the terrain parabolic equation based on  the framework of optimal control theory. Firstly, through rigorous mathematical analysis, we proved the existence of minimum value  for the objective functional and its necessary conditions. Secondly, we proved  the local uniqueness and stability of the minimum value to the problem.

We designed the material parameters of transformation thermodynamic devices and gave time-domain finite element simulations by using the layered approximation idea and effective medium theory. Firstly, we derived the ideal material parameters of the three devices: heat cloak, heat concentrator and heat rotator by using the theory of transformational thermodynamics. Secondly, we eliminated the non-uniformity of the parameters and designed the layered structure by using the idea of layered approximation, and in order to eliminate the anisotropy of the layered structure, we used the effective medium theory to design the isotropic material parameters. Finally, we gave numerical test results to verify the performance of the device and the feasibility of the design. The results show that when the number of layered layers is higher, the designed device realizes better thermal effects, which can achieve the same effect as the ideal device.

Firstly, we used the cubic B-spline finite element method to solve a class of fourth-order semi-linear parabolic equation with the variable coefficient, and proved the stability and convergence of the semi-discrete scheme. Secondly, by using the Crank-Nicolson method to discretize the time variable, we obtained the fully discrete scheme and discussed the stability and convergence of the fully discrete scheme. Finally, in the numerical example, we used the Picard iteration method to handle the nonlinear term and obtained the convergence order of the finite element method according to L² norm and H² norm.

Aiming at the challenges of single-frame infrared small target detection, we proposed an infrared small target detection method based on feature separation and global context. Firstly, aiming at the problem of insufficient features of small targets, we designed a feature separation module that captured the difference of target background contrast  by central differentical convolution, and combined  fast Fourier convolution to extract the edge gradient information, achieving  efficient separation of target features and background noise. Secondly, aiming at the problem of feature loss caused by downsampling, we constructed a global context extraction module  to perform cross-scale global modeling of deep features,  preventing the loss of target features in the deep layers of the network. The experimental results  on multiple public datasets show that this method  significantly improves mIoU, nIoU and F₁ indicators compared with advanced algorithms such as AGPCNet and DNANet,  optimizes the performance of infrared small target detection algorithm and improves the perception ability of complex scenes.

The author considers the existence of positive solutions for the first-order semi-positone problem. Based on the fixed point theorem of  Krasnoselskill, the author proves that there exists λ*>0, such that the problem has at least one solution when 0<λ<λ*.

We considered the existence of positive ground state solutions for a class of critical Kirchhoff-Choquard type problems. Firstly, we used the properties and integral estimates of the truncated function to classify the upper critical exponents, and applied some integrable conditions to the potential function. Secondly, by introducing the Nehari manifold and utilizing the Ekeland variational principle, we obtain that there is at least one positive ground state solution to the problems under appropriate parameter assumptions.

By using the  flexible, robust, and  widely  applicable characteristics of the Interquantile regression model, we established an additive Interquantile regression model for data with right-censored response variables, time-dependent covariates, and partially nonlinear structures to  avoid the instability issues that traditional quantile regression models might encounter when estimating adjacent quantiles separately, we also estimated the unknown parameters of adjacent quantile intervals through a weighted rank estimation process combined with differential evolution algorithm. The simulation research results show the excellent performance of the proposed method under finite samples, and it is applied  to the Stanford heart transplant data in the United States.

Using enzymatic lignin as raw material, porous lignin based carbon materials were constructed by optimizing the KOH activation process. The effects of parameters such as  carbon-alkali ratio,  activation temperature and activation time on the structure of lignin-|based porous carbon materials were studied   by using a one-step activation method. We tested the electrochemical properties of the prepared materials in a three-electrode system and assembled symmetrical supercapacitors by using KOH as the electrolyte to test the cycling stability of the material during continuous charge and discharge processes. The results show that  when the  activation temperature is 700 ℃,  the carbon-alkali ratio is 4∶1,  and the activation time is 2 h,  a porous carbon sample (ELC_700-2-4) with a high specific surface area (3 067 m²/g) and high microporosity (62.18%) can be prepared. In the three-electrode system,  the material exhibits excellent electrochemical performance in KOH as the electrolyte,  and the specific capacitance can reach 443 F/g at 1 A/g. The specific capacitance of ELC_700-2-4 electrode is 250 F/g at 1 A/g,  and the capacitance retention rate after 10 000 cycles is 95.55%,  indicating that the electrode has excellent cycling stability during continuous charging and discharging. The energy density of symmetrical capacitor is  8.6 W.h/kg when the power density is 500.16 W/kg. 

We studied the effects of doping with four types of atoms, S,N,P,Si, as well as the adsorption of seven small molecules, NO,,NO₂,NH₃,CO,CO_2,SO₂ and H₂S on the geometric structure and electronic properties of two-dimensional B₄C₃ materials. The results show that compared with the intrinsic B₄C₃ material with bandgap of 2.020 eV, the bandgap width of both doped and small molecule adsorption systems is reduced. The bandgap value of the N-doped system is the smallest among the four systems, indicating that doping N atoms has the most significant effect on the electronic properties of B₄C₃. After NO₂ adsorption, B₄C₃ changes from semiconductor to metal, indicating that B₄C₃ can effectively detect NO₂ gas.

Based on a nonlinear demand function, we established a  fishery economic model with  multi-agent  completely uncooperative, and discussed the local stability and multi-stability of the system, as well as the influence of related parameters on the local and global dynamics of the system. The  results show that it will help multiple participants obtain better returns when the cost parameters and the price elasticity are small, but  the market demand is large, and the intrinsic growth rate can be effectively controlled within a certain range.

We studied  the mechanism of the reaction between 2α-Ala→Mg²⁺ (bis-alanine chelating magnesium)  and  ^.OH (hydroxyl radical) in the aqueous phase environment of living organisms (1.013×10⁵ Pa,  310.15 K) at the level of M06-2X/6-311+G(d,p)//MN15/6-311++G(3df,2pd)  theory, and investigated two reaction channels of  2α-Ala→Mg²⁺ and ^.OH for the hydrogen abstraction and addition. The calculation results show   that the energy barrier for the hydrogen abstraction reaction is from 20.1 to 62.3 kJ/mol,  all of which are exothermic reactions. The energy barrier for the addition reaction is from 65.7 to 70.9 kJ/mol,  with a slight endothermic reaction. Therefore,  2α-Ala→Mg²⁺ in living organisms can easily scavenge ^.OH by abstracting H atoms.

Aiming at the problem of the low sensitivity, poor portability and easy influence by environmental temperature of glucose sensors based on biological enzymes, we developed and designed a high sensitivity flexible glucose sensor, and  prepared flexible glucose sensors with Au electrodes based on polyimide (PI) by using the screen-printing technique. We doped reduced graphene oxide (rGO) to improve electrode conductivity and enhance sensor sensitivity when preparing the glucose oxidase mixed solution. Additionally, we designed a portable detection system that could achieve in situ detection and temperature compensation correction through data processing, thereby reducing the impact of temperature on bioenzyme activity and enabling them to work normally at different environmental temperatures. The experimental results show that the glucose sensor has a detection sensitivity of 58.9 μA/(mmol·cm²) within 0—1.2 mmol/L, a detection limit of 5 μmol/L, and exhibits good selectivity, making it suitable for monitoring glucose concentration in human sweat.

Let n be a positive integer and R be an associative ring with identity. Firstly, the definition of n-Tor-pair over the ring R is introduced. Secondly, some properties of n-Tor-pairs are given, and hereditary n-Tor-pairs are discussed. Finally, the equivalent characterization of the direct product of modules in X having finite X-projective dimension is given when (X,Y) is an n-Tor-pair.

Let R be a ring, and S be a multiplicative subset of R. Firstly, based on the u-S-flat modules, we introduce the concept of Gorenstein u-S-flat modules,  and  use the long exact sequence theorem and the properties of u-S-flat modules to study the homological properties of Gorenstein u-S-flat modules, and give equivalent characterizations of Gorenstein u-S-flat modules. Secondly, we  prove that the class of Gorenstein u-S-flat modules is projective solvable class if and only if it is closed with respect to extensions.

By using prior estimates and differential inequality technique, the author discussed the influence of base perturbations on the stability of heat conduction inside a semi infinite cylinder. The author proves that as the disturbance amplitude decreases, the solution converges exponentially to the solution corresponding to a completely flat base. This result has certain theoretical significance for  the robustness of heat conduction model and the potential impact of small geometric irregularities on heat transfer prediction.

Aiming at the problem that wireless access nodes  in wireless communication networks were affected by changes in network status during communication and found it difficult to quickly adapt to these changes, reconfiguring network resources, and affecting communication efficiency and stability, we proposed an instant equilibrium allocation algorithm for multi node electronic information resource communication. Firstly, based on graph theory, a network communication graph and a conflict graph were constructed, and the communication relationships of each node in the communication network were determined by using the communication graph. The vertex coloring algorithm was used to color the conflict graph, and the orthogonal pairing method was 
used to select the links with the strongest orthogonality in the channel for pairwise pairing,  completing the communication link grouping. Secondly, a balanced allocation model  with the goal of minimizing communication delay and maximizing energy efficiency was established. The reverse differential tunicate swarm algorithm was used to solve the model. Through operations such as mutation, crossover, and selection, the search process of the algorithm was accelerated and optimization efficiency was improved. The optimal solution that met the conditions was found in the shortest number of iterations, resource allocation was completed, and the optimal allocation scheme was ultimately determined. The experimental results show that the highest packet loss of the proposed algorithm is only 3.12%, the lowest communication delay can reach 0.1 ms, and the Jain fairness index is always above 0.9, which can improve the efficiency and stability of the communication network.

We used laboratory simulation methods  to investigate the effects of freeze thaw (FT) and microplastics on transformation of arsenic (As) speciation in  soil. The results show that under the condition of not adding microplastics,  FT leads to an increase in the proportions of organic-bound As and weakly crystalline iron oxide-bound As (3.67% and 4.17%),  while the proportion of manganese oxide-bound As and extremely difficult to  crystallize iron oxide-bound As decreases (0.28% and 5.33%). Adding polyethylene (MP-PE) under FT can reduce the proportion of organic-bound As (0.96%), increase th proportion of manganese oxide-bound As,  sulfide-bound As,  and crystalline iron oxide-bound As(1.55%,  0.60%,  and 2.05%). Adding butylene adipate-co-terephthalate (MP-PBAT) under FT can reduce the proportion of water-soluble As and crystalline iron oxide-bound As (1.33% and 2.65%),  and increase the proportion of  manganese oxide-bound As and extremely difficult to  crystallize iron oxide-bound As (1.11% and 3.82%). Under the condition of not adding microplastics, FT significantly increases the bounding strength coefficient IR between As and soil by 1.85%, but  adding MP-PBAT under FT, IR significantly decreases by 6.27%. The IR value is positively correlated with water-soluble As,  organic-bound As,  and manganese oxide-bound As, and  negatively correlated with the effect of the crystalline iron oxide-bound As. The research results  provide theoretical  basis for revealing  the environmental behavior of As in contaminated soils and evaluating the  ecological risks of As, and provide important  reference value   for the treatment and risk management of As-contaminated soil.

We considered a stochastic SEIQR monkeypox epidemic model with  Gaussian white noise. Firstly, the existence and uniqueness of the global positive solution for the stochastic model were proved by using stopping time theory. By constructing a Lyapunov function and combining it with  Ito formula, the asymptotic behavior of the solutions of stochastic model near the disease-free equilibrium point and endemic equilibrium point of the corresponding deterministic model was given. Secondly, we gave conditions for the average persistence of the solutions and disease extinction of the stochastic model. Finally, numerical simulations were conducted to examine the impact of noise on the model. The results show  that the stochastic model perturbs near the equilibrium point of the deterministic model, and  the degree of perturbation is  positively correlated with  the noise intensity. When the noise is sufficiently large, the disease will become extinct.

By using edge-moving operations and the Perron-Frobenius theorem, we discussed the problem of the spectral radius of the complement distance  of tree graph.  We determined the unique trees with maximum  and minimum spectral radii of  the complementary distance, respectively, and  determined the graph with the minimum spectral radius of  the  complementary distance in the complementary graph of the tree,  as well as the graph with  the i-th largest spectral radius of complementary distance, where  i=1,2,…,(n-2)/2.

By using graph transformation method, we determined the largest total Mostar index for n-order cactus graph G with k cycles, 
and characterized the corresponding extremal graphs, when 2n+k>18 and n≥3k+1,  Mo_t(G)≤2n²+3nk-6n-25k+k²+4, and its equal sign holds if and only if G is the graph composed of attaching k end-blocks of length 4 and (n-3k-1) pendant edges to a common vertex. Furthermore, by discussing the classification of  the remaining cactus graph, we obtained the second-largest total Mostar index and characterized the corresponding extremal graphs.

Aiming at  the problem of minimizing latency and energy consumption in service migration in dynamic Internet of Vehicles, we proposed a service migration strategy based on graph neural networks. Firstly, we established a system model to model the service migration problem as a multi-objective optimization problem that minimized latency and energy consumption. Secondly, we  transformed the problem into a Markov decision process, and defined the states, actions, and reward functions. Finally, a graph convolutional neural network was used  to extract features from edge network topology and node information, and combining  task information to propose a deep reinforcement learning task migration decision algorithm based on graph convolutional neural networks to make service migration decisions. Simulation experiment results show that the proposed algorithm outperforms other baseline algorithms in reducing average task latency and energy consumption, and can provide an effective solution for efficient, low consumption, and stable service migration in the environment of Internet of Vehicles.

Let R be an associative ring with identity, V and W be classes of left R-modules, and Y be classes of right R-modules. Firstly, we define (V,W,Y)-Gorenstein flat modules, and give an equivalent characterization of (V,W,Y)-Gorenstein flat modules. Secondly, we  prove that this class is closed with respect to  direct sums, direct summands and kernels of epimorphisms under certain conditions.

We investigated the global structure of positive radial solutions for a class of quasilinear elliptic boundary value problems with Dirichlet boundary conditions based on  bifurcation theory. Specifically, by introducing two critical exponents f₀ and f_∞,  under two typical cases of  f₀∈(0,∞), f_∞=0 and f₀=∞, f_∞=0, we prove the existence of unbounded connected branches emanating from bifurcation points, which utimately asymptotically extend to infinity along the λ-axis.

Aiming at  the problem that the traditional BIRCH algorithm was prone to excessive intra-cluster variance or excessive merging when dealing with indicator data with strongly correlated features and uneven distribution, we proposed an improved BIRCH algorithm  that integrated an autoencoder and a dynamic threshold strategy. Firstly, this algorithm  utilized an autoencoder for nonlinear feature mapping and dimensionality reduction, weakening the influence of inter-feature correlation on the distance metric and improving the compactness and discriminability of the data representation. Secondly, we designed a dynamic threshold strategy to adaptively adjust the clustering radius based on local sample density and cluster size, enhancing the algorithm’s adaptability to unevenly distributed data. Finally, we  constructed a clustering feature tree by using the improved feature space and adaptive threshold strategy to achieve efficient and stable hierarchical clustering, and applied to intelligent clustering analysis of multidimensional data of university teachers. Experimental results show that the improved algorithm achieves superior performance on multiple clustering evaluation metrics, significantly improving  stability and accuracy of clustering.

Aiming at the problem  that traditional spectral clustering-based subspace clustering methods were prone to outlier interference and thus show degraded clustering performance when there were outliers in high-dimensional data, we proposed an active block diagonal subspace clustering method based on automatic weighting. The method first assigned a corresponding weight to each data point, identified outliers in the data through weight differences, then actively reduced its contribution in the representation matrix to construct a better representation matrix and improved the  clustering performance of the model. Experimental results on 10 datasets compared with 8  algorithms show that the average clustering accuracy, normalized mutual information, and adjusted Rand index of the proposed method are generally better than the comparison algorithms on datasets with 10% or 20% outliers. It performs the best or ranks in the top three on more than half of the datasets in general clustering tasks. Therefore,  the method can not only efficiently handle high-dimensional data clustering with outliers, but also maintain competitiveness in general clustering tasks, providing an effective solution to enhance the robustness of high-dimensional data clustering and having high practical application value.

In order to reduce the resource consumption in distributed denial of service (DDos) attack detection in software defined networks and improve the detection accuracy, we proposed a two-level joint detection model based on φ-entropy and IDBO-RF. Firstly,  abnormal traffic was filtered to complete the first level trigger detection by calculating the φ-entropy of the destination IP address. 
Secondly, the hyperparameters of the random forest were optimized by using the improved dung beetle optimization algorithm to construct the IDBO-RF model. Abnormal traffic was   mapped through the optimal feature subset to the IDBO-RF model for secondary confirmation detection of DDoS attacks. Through public datasets and simulation experiments, the proposed model effectively shortens the detection time, reduces controller resource consumption of the software defined networks, and achieves an accuracy of over 99% in both binary and multi-classification  detection of DDoS attacks, the average detection time is only 1.21 s, and the CPU occupancy rate for controller is only 33.45%, demonstrating  good generalization performance.

We discussed two-parameter inverse problems for a class of coupled models of temperature field and crystallization coupling model, proposed stable numerical algorithms to identify nucleation rate and growth rate, and verified anti-noise performance of the proposed algorithms. We embedded the coupled model into the loss function of a deep neural network, updated the neural network parameters based on loss function minimization, and obtained approximate solution to the forward problem. For the inverse problem, we constructed a loss function with regularization terms and proposed a regularized physics-informed neural networks (PINNs) algorithm. The numerical results show that the regularized PINNs algorithm can effectively solve the inverse problem of the temperature field and crystallization coupling model, and has noise resistance stability.

Let S be a ring, and H(S) be the quaternion ring on S. We consider the (m,n)-Jordan centralizers and (m,n)-Lie centralizers on the quaternion ring. By using the generator analysis method, we prove that the (m,n)-Jordan centralizers are standard centralizers, a
nd the (m,n)-Lie centralizers are standard Lie centralizers.

Firstly, by using  the divergence theorem and  geometric analysis methods, we  studied the rigidity problem of compact η-Ricci-Bourguignon solitons, and obtained two key integral formulas for  the potential vector field of the soliton and the dual vector field of η. Secondly, under different integral conditions, we obtain rigidity results of the soliton, which  proves that the soliton is either an η-Einstein manifold or an Einstein manifold.

Aiming at the problem that malicious Web page links and plugins could be attached to other files through constant confusion and deformation, traditional detection methods were difficult to achieve accurate detection, we proposed a Web page attack redirection confusion detection method based on multimodal deep neural networks. Firstly, we extracted the features of  Web page attacks: attribute class, keyword class, var class, and word class, and converted them into 8-dimensional sensitive feature vectors to 
calculate their corresponding real values. Secondly, the Web page and real values were input together into a multimodal deep neural network for training. Finally, accurate attack redirection confusion detection results were obtained through the output of the Web page classifier. The experimental results show that the detection rate of the proposed method is about 98%, which can effectively detect redirection confusion in Web page attacks while ensuring a high detection rate.

Aiming at the multi-depot vehicle routing problem with time windows, we constructed a model with the goal of minimizing total cost,  proposed an improved dung beetle optimizer algorithm based on multi-strategy, and solved it. By introducing a hierarchical system to update rolling dung beetles, it established communication with top-tier beetles to enhance the algorithm’s search capability. Differential variation was designed to perturb the positions of reproductive dung beetles and  reduce the likelihood of getting stuck in local optima. Probability-driven random foraging behavior was devised for foraging dung beetles, enabling them to randomly explore broader search spaces to find potential optimal solutions. Adversarial learning was using to generate reverse 
solutions for thief dung beetles, increasing the probability of finding better candidate solutions and strengthening the algorithm’s optimization capability. This algorithm was using to solve the multi-depot vehicle routing  problem with time windows. Comparative experiments with six other intelligent algorithms on the Solomon dataset show that the proposed algorithm is superior to other comparative algorithms and has good  search capabilities and application value.

Aiming at the quality and efficiency problems caused by insufficient utilization of multilayer relations in large-scale group decision-making, we proposed  a group consensus decision-making method based on multilayer network structure detection. The method  modelled multilayer relations of decision-makers as distinguishable coupled organizations, developed  an interactive restart random walk algorithm to map opinion propagation, detected community structure and influence distribution, and optimized detection efficiency by using nearest neighbor approximation incremental computing. The calculation  examples and simulation results verify that it can strengthen the leading role of decision-makers with strong influence, reduce conflicts, achieve the balance between high consensus and efficient computing, and provide an effective approach for group decision-making in complex coupled environments.

Under humid conditions, we prepared polycaprolactone (PCL) ordered photonic films by using solvent evaporation self-assembly method. We obtained highly ordered porous through films by controlling the solution concentration. We used ion sputtering method to adsorb a layer of metal on the surface of the through films, and replaced silver ammonia solution with silver. The results show that this silver-coated ordered porous through film has a double-layer ordered porous structure, and its conductivity is significantly enhanced. Compared with the single-layer film, the light transmittance of the double-layer film is limited by the incident angle and can achieve the function of directional light transmission. The properties of the heat-treated photonic films change, exhibiting high-temperature resistance and enhanced light transmittance at all angles. This directional light transmission ordered array film has the characteristics of electromagnetic shielding.

 In order to increase relative molecular weight of deuterohaemin-β-AlaHisThrValGluLys (DhHP-6), we synthesized mPEG-DhHP-6 through PEGylation, and adjusted the volume ratio of  dimethyl sulfoxide (DMSO)  and phosphate buffered saline (PBS) to achieve a  yield of around 95%. The stability and activity of of mPEG-DhHP-6 have been improved compared to DhHP-6. mPEG-DhHP-6 can significantly reduce the incidence and duration of ventricular tachycardia and ventricular fibrillation after ischemia-reperfusion in rats, and can be used to protect cardiovascular system.

Aiming at the problem of sparse covariance matrix estimation, we proposed a sparse covariance matrix estimator based on the MCP (minimax concave penalty) penalized log-likelihood, and solved it by using  the coordinate descent algorithm. The simulation results show that the proposed method can achieve  smaller L₁ norms, Kullback-Leibler distances, and Frobenius norms compared to the Lasso penalty and SCAD (smoothly clipped absolute deviation) penalty methods when estimating sparse covariance matrices in most cases, especially under the AR(1) model setting, the performance is more outstanding. In addition, the superior performance of the MCP penalty method for practical applications is verified by analyzing the protein concentration data measured by flow cytometry.

We studied the initial-boundary value problem of a class of non-Newtonian fluids with initial vacuum and linear damping. Under the condition that the initial energy was small and the initial value met certain compatibility, we used the technique of weighted energy estimation and Zlotnik inequality to overcome the nonlinearity of the viscous term of the momentum equation, and proved that the density function had a uniform upper bound of time. Furthermore, we adopted the continuity method to obtain the existence and uniqueness conclusion of the global strong solution of the initial-boundary value problem of non-Newtonian fluid.

Aiming at the problem of low tracking accuracy in trajectory tracking control of 5-degree of freedom (DOF) parallel mechanisms caused by model uncertainties, external disturbances, and input saturation, we proposed a discrete integral sliding mode control algorithm with time-varying disturbance compensation considering input saturation. Firstly, to address the problem of input saturation,  while considering the limitations of  input assignment and input rate of change, we designed a discrete saturation compensation auxiliary system to  eliminate the input saturation characteristics. Secondly, we designed a time-varying disturbance compensation discrete integral sliding mode controller to  achieve real-time compensation for lumped disturbances, thereby reducing system steady-state error while suppressing chattering. Finally, through simulation experiments, a comparative analysis was conducted between the proposed method and the disturbance compensation discrete sliding mode control algorithm, 
considering both with and without input saturation. The experimental results show that the proposed algorithm outperforms the comparative algorithms in terms of control accuracy and saturation constraints, and can effectively achieve high-precision trajectory tracking control of parallel mechanisms considering both lumped disturbances and input saturation, with high engineering application value.

We prepared magnesium hydroxide by using the ammonia bubbling method. When the temperature ranged from 303.15 K to 353.15 K, we measured the solubility of magnesium chloride in different concentrations of ammonium chloride aqueous solution and deuterium volume fractions of 1.65×10^-4，1.30×10^-4，7.0×10^-5 water and ordinary water. We correlated the solubility data by using Apelblat equation and empirical equation, and calculated the solubility entropy, enthalpy, and standard Gibbs free energy change of magnesium chloride in ammonium chloride aqueous solution by using the modified Van’t-Hoff equation. The results show that under the same solvent conditions, the solubility of magnesium chloride increases with increasing temperature. Under the same temperature conditions, the solubility of magnesium chloride increases sequentially in ammonium chloride solution, ordinary water, and low deuterium water. The higher the concentration of ammonium chloride, the lower the solubility, and the lower the deuterium content, the higher the solubility. The Apelblat equation and empirical equation both show good correlation results, with a total relative error of 0.66%. The entropy change is the main factor affecting the dissolution process of magnesium chloride.

Aiming at the problem that the search space of the traveling salesman problem (TSP) grew exponentially with the increase of the number of cities, making it difficult for the algorithm to traverse all possible paths in a limited time, and was susceptible to the accumulation of pheromones during the search process, leading to premature convergence to local optimal solutions. In order to quickly converge to high-quality solutions when solving TSP, we proposed an analysis method for solving  TSP problem of  dual population ant colony algorithm based on path contribution evaluation. Firstly, we established a TSP mathematical model in the form of a weighted graph. Secondly,  two independent populations were introduced for parallel search: One population used an elite ant system to update pheromones, quickly converged using existing information, and obtained the shortest path of TSP; the other population used a strengthening  sub path evaluation mechanism to update pheromones,  jumped out of the local optimal solution by searching for new solution spaces, and  obtained the shortest path of TSP. Thirdly, by comparing and analyzing the shortest paths of the two populations, the shortest path with the smaller value was obtained as the global optimal path. Finally, introducing a path contribution evaluation mechanism to update the pheromones of the two populations again, we obtained the final TSP solution. Experimental results  show that this method can effectively solve and analyze TSPs of different scales. It can not only shorten the length of the path, but also obtain the shortest path that traverses all cities and returns to the starting point, and the data distribution effect is better.

We used a p-order random coefficient integer autoregressive RCINAR(p) model with dependent Bernoulli counting series to solve the analysis problem  of data with correlated characteristics of counting variables. We obtained the statistical properties of the model, the conditional maximum likelihood estimation of the parameters, and their asymptotic normality, and the effectiveness of the model was verified through the analysis of actual data,  accurately capturing data  correlations and trends. These results show  that the estimators of the model converge to the true values as the sample size increases.

Aiming at  the impact of factors such as  occlusion, pose variations and lighting on facial expression recognition, we proposed a facial expression recognition method based on local correlation and multi-scale spatial attention. Firstly, through the local correlation module, local features were combined with global features to enhance the connections between local features, thereby improving recognition performance of the model in complex environments. Secondly,  the multi-scale spatial attention mechanism was adopted to extract and fuse spatial structural information at different levels, enhancing the robustness of the model.  Experimental results show that the proposed method demonstrates superior facial expression recognition performance on the RAF-DB and AffectNet datasets, validating its effectiveness and generalization ability.

Aiming at the problem of the widespread presence of antibiotics such as sulfamethoxazole （SMX） in water bodies, which posed a threat to the ecosystem and human health, and were difficult to effectively remove by using conventional wastewater treatment processes，  we prepared a few-layer carbon nitride catalyst (Ni@C₃N₄) loaded with single-atom nickel,  which could efficiently electrocatalytically degrade sulfamethoxazole by generating hydrogen peroxide (H₂O₂) via an oxygen reduction reaction (ORR). Structural characterization show that nickel is highly dispersed in the few-layer carbon nitride matrix in the form of single-atoms and significantly modulates the electronic structure of the few-layer carbon nitride to optimize the active site distribution. Electrochemical test results show that Ni@C₃N₄ has excellent two-electron selectivity and rapid reaction kinetics. Under acidic conditions (pH=3), Ni@C₃N₄ can generate H₂O₂ via the two-electron pathway,  and degradation rate of sulfamethoxazole can reach 81.3% within 120 min, which is significantly better than that of the undoped carbon nitride catalyst. Kinetic analysis results show that the degradation process conforms to a pseudo-first-order reaction model. The research results provide new ideas for the treatment of antibiotics in water bodies.

Aiming at the problem that the amount of energetic material samples synthesized by diamond anvil in the high-pressure generating device was small, it was difficult to meet the needs of the test equipment for the lower limit of sample volume, it was difficult to separate the high-pressure synthesized samples from the sample cavity, and it was difficult to use the existing equipment to characterize the samples. We designed and independently built an observation system that could achieve 
controllable laster stimulus response over time for micrometer samples, and used the system to test some energetic materials. The results show that the system can effectively record the stimulated explosion process of energetic materials, realize the detonation observation of micron-level energetic materials, and provide a more intuitive method for judging the energetic characteristics of energetic materials.