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.

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 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.

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.

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 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 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.

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 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.

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.

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.

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.

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.

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. 

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 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.

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.

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 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.

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*.

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.

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, 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.

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.

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 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.

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 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.

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.

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 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.

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.

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.

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 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.

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 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.

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.