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 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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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  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.

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 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.

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.

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.

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 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.

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.

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.

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.

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.

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 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.

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.

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.

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.

 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 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.

 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.

 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.