Ganoderma lucidum spore powder was used as raw material,  ethanol  with a volume fraction of  70%  as extractant.  We adopted a combination of enzymatic  hydrolysis and ultrasound assisted extraction method,  set different liquid-solid ratios,  ultrasound time,  enzymatic hydrolysis time,  and enzyme dosage  as  four factors for a one-way test and designed a response surface experiment to  determine the optimal extraction method and its influencing factors. The   Ganoderma triterpene were separated and purified by using macroporous resin chromatography. By optimizing the  separation and purification process, the optimal elution resin,   eluent volume fraction,  flow rate of the upper sample solution and the mass ratio of the upper sample solution were determined. The compositional differences of the total  Ganoderma triterpenes were analysed by high performance liquid chromatography (HPLC). Though the pre-experimental analysis, the results show that the enzyme + ultrasound assisted extraction is more efficient compared to the single extraction method. Ethanol is used as an extractant to extract triterpenoids from Ganoderma lucidum can enhance the purity of triterpenoids. Under optimal conditions, the  rapid and accurate determination of the triterpene content can be achieved, providing a theoretical basis for the separation and purification of Ganoderma triterpenes.

We considered a  class of tumor-immune model, discussed the existence  conditions  of their equilibrium points, and used characteristic equations to analyze the local kinetic stability of each equilibrium point,  proving that the model underwent Hopf bifurcation under the corresponding conditions. By calculating the first Lyapunov coefficient, it can be concluded that if the coefficient is not zero, the model undergoes Hopf bifurcation,  the bifurcation is supercritical if the coefficient is less than zero, and the bifurcation is subcritical if the coefficient is greater than zero. Finally, numerical simulations are used to validate the theoretical analysis results.

Mesenchymal stem cell exosomes (MSC-Exos) are a class of nanoscale vesicles with great potential in experimental research  and clinical applications. They contain a variety of biomolecules,  including miRNA,  mRNA,  proteins and lipids,  and have the function of  mediating  cell signaling and participating in regulation of receptor cells. Based on the important role of  MSC-Exos, we review the significant effects of  MSC-Exos in promoting tissue repair,  immune regulation and neuroprotection from the research progress and clinical applications,   especially in the treatment of autoimmune diseases,  neurodegenerative diseases,  cardiovascular diseases and tumors. We analyze a series of unsolved problems and application popularization challenges in its clinical application,  including elucidation of mechanism of action,  separation,  extraction and purification technology,  formulation of standardized production rules,  determination of dosage and administration route,  enhancement of stability,  and reduction of immunogenicity. This provides a basis for addressing these limitations to achieve widespread clinical application of MSC-Exos.

Aiming at the problems of the limitation of obtaining global features in image recognition and the difficulty in improving recognition accuracy, we proposed  an image recognition method based on the lightweight model of random augmentation Swin-Tiny Transformer.  The method combined the random data augmentation based enhancement (RDABE) algorithm to enhance image features in the preprocessing stage, and adopted the Transformer’s self-attention mechanism to obtain more comprehensive 
high-level visual semantic information. By optimizing the Swin-Tiny Transformer model and fine-tuning the parameters on a maize disease dataset, the applicability of the algorithm was verified on maize diseases in the agricultural field, and more accurate disease detection was achieved. The experimental results show that the lightweight Swin-Tiny+RDABE model based on stochastic 
enhancement has an accuracy of 93.586 7% for maize disease image recognition. The experimental results compared with the excellent performance lightweight Transformer and convolutional neural network (CNN) series models with consistent parameter weights show that  the accuracy of the improved model is higher than that of the  Swin-Tiny Transformer, Deit3_Small, Vit Small, 
Mobilenet_V3_Small, ShufflenetV2 and Efficientnet_B1_Pruned models by 1.187 7% to 4.988 1%, and can converge rapidly.

The purpose of mobile Internet information accessibility (MIIA) was to ensure that mobile application content was equally accessible, convenient, and barrier-free for all users, including those with visual impairments.  We systematically review the latest research progress in the field of mobile Internet information accessibility, focusing on the analysis and summary of research achievements in  semantic representation and understanding of mobile GUI, accessibility detection and layout repair. The analysis shows that from traditional heuristic rule methods to deep learning-driven automated tools, related technologies have gradually improved detection accuracy and adaptability, while also revealing challenges in addressing complex dynamic interactions and diverse user needs. We have provided an outlook on  future research directions.  MIIA technologies have significantly improved  the digital experience for visually impaired users, but they still need continuous innovation and optimization  to achieve a truly inclusive digital society.

Aiming at the problems of high input dimensionality and long training time in traditional game intelligent  algorithm models, we  proposed a novel deep reinforcement learning game intelligent  guidance algorithm that integrated state information transformation and reward function shaping techniques. Firstly, using  the interface provided by the Unity engine to directly read game backend  information effectively compressed  the dimensionality of the state space and reduced the amount of input data. Secondly, by finely designing  the reward mechanism, the convergence process of the model was accelerated. Finally, we conducted comparative experiments between the proposed algorithm model and existing methods  from both subjective qualitative and objective quantitative perspectives. The experimental results show that this algorithm not only significantly improves the training efficiency of the model,  but also markedly enhances the performance of the  agent.

We consider a variant of the classic problem of  the traveling salesman problem (TSP) in combinatorial optimization problem: 
 the close enough traveling salesman problem (CETSP).  Firstly, we comprehensively introduce the history, solving methods, and algorithms for both TSP and CETSP, including exact algorithms (such as branch and bound method, linear programming) and heuristic algorithms (such as particle swarm optimization, greedy algorithms, etc.). The TSP requires finding the shortest path to visit each city  once and return to the starting point given a list of cities and distances. CETSP is a generalization of TSP, allowing the visiting point for each target to be chosen from within a specified neighborhood, rather than  exact location. It is  suitable for practical applications that can  tolerate errors, such as logistics distribution, intelligent transportation, and wireless sensor networks, etc. CETSP has higher flexibility and adaptability, which can significantly reduce computational resources and time consumption, particularly for large-scale problems with greater advantages. Secondly, we introduce  the potential  of CETSP in practical applications, especially in logistics, industrial manufacturing, traffic planning, information and communication, offering effective solutions for improving efficiency, reducing costs, and promoting intelligent decision-making. Finally, we have identified some future research directions for CETSP.

Aiming at the shortcomings of existing methods in the image segmentation performance of small and medium-sized organs in the abdomen, we proposed  a network model based on local and global parallel coding  for multi-organ image segmentation in the abdomen. Firstly, a local coding branch was designed to extract multi-scale feature information. Secondly, the global feature coding branch adopted the  block Transformer, which not only captured the global long distance dependency information but also reduced the computation amount through the combination of intra-block Transformer and inter-block Transformer. Thirdly, a feature fusion module was designed to fuse the context information from two coding branches. Finally, the decoding module was designed to realize the interaction between global information and local context information, so as to better compensate for the information 
loss in the decoding stage. Experiments were conducted on the Synapse multi-organ CT dataset, compared with the current nine advanced methods, the average Dice similarity  coefficient  (DSC) and Hausdorff distance (HD) indicators achieve the best performance, with 83.10% and 17.80 mm, respectively.

Aiming at the problem that the connected temporal classification model needed to have output independence assumption, and there was strong dependence on language model and long training period, we proposed  a speech recognition method based on connected temporal classification model. Firstly, based on the framework of traditional acoustic model, spectrogram feature extraction network based on attention mechanism was trained by using prior knowledge, which effectively improved the discrimination and robustness of speech features. Secondly, the spectrogram feature extraction network was spliced in the 
front of the connected temporal  classification model, and the number of layers of the recurrent neural network in the model was reduced for retraining. The test analysis results show that the improved model shortens the training time, and effectively improves the  accuracy of speech recognition.

With the rapid depletion of fossil fuels and increasing pollution,  the development and utilization  of clean energy are becoming increasingly important. Photocatalytic technology that  converts solar energy into clean hydrogen energy  is  an effective solution. It is necessary to solve the contradiction between  the bandgap of photocatalysts and the intensity of sunlight  due to limitations in water splitting electrode potential. Therefore,  it is highly significant to develop and utilize photocatalysts with visible light  response capability. We review  the development and principles of photocatalysts,  discuss their immense potential for advancement, and introduce the most  common photocatalysts and  current research progress.

Aiming at the problem of  the navigational challenges for visually impaired users on diverse webpages, we proposed a method for automatically identifying navigation bars to improve  webpage accessibility. Firstly, by designing heuristic rules, elements within the navigation bars were  autonomously extracted based on the ordered element arrangement within the navigation bar, as well as rules such as hyperlinks and succinct textual content within sub-elements. Secondly, a decision tree binary classification algorithm was used to categorize elements with pronounced feature disparities in the navigation bars. Finally, the identified navigation bar elements were subject to the injection of Landmark attributes. In experimental evaluations of  100 websites, the method successfully identified  92.6% of navigation bar elements, and the infusion of Landmark attributes significantly improves website accessibility, thereby ameliorating the user experience for visually impaired individuals.

Aiming at the problems of the complicated underwater image imaging environment resulted in the subsequent image analysis often being affected by color bias and other factors, we proposed a deep convolutional neural network image restoration method based on multi-scale features and triple attention multimodal fusion. Firstly, the deep convolutional neural network introduced the image multi-scale transformation feature on the basis of extracting the image spatial feature. Secondly, by using channel attention, supervised attention and non-local attention, the scale correlation and feature correlation of image features were mined. Finally, by designing a multimodal feature fusion mechanism, the above two types of features could be effectively fused. The proposed method was tested on the open underwater image test set and compared with the current mainstream methods. The results show that this method is superior to the comparison method in quantitative comparison such as peak signal-to-noise ratio and structural similarity, as well as qualitative comparison such as color and details.

Based on the properties of the matrix structure, we used the block matrix techniques to give the specific form for the Moore-Penrose generalized inverse of the adjacency matrix of caterpillar trees with any number of vertices and any diameter length, which provided theoretical support for further study of the algebraic properties of caterpillar trees.

Aiming at the problem of insufficient feature extraction resulting in low classification accuracy of the traditional encrypted traffic classification model, we  proposd an encrypted traffic classification model based on an improved convolutional neural network combined with Transformer by using deep learning techniques.  In order to improve the classification accuracy, firstly, we cut and filled the dataset,  and completed standardization processing. Secondly, the multi-head attention mechanism in the Transformer network model was used to capture long-distance feature dependencies, and the convolutional neural network was used to extract local features. Finally, the Inception module was added to achieve multi-dimensional feature extraction and feature fusion, and the model training and encrypted traffic classification were completed. The experimental verification was conducted on the 
ISCX VPN-non-VPN 2016 public dataset, the experimental results show that the classification accuracy of the proposed  model reaches 98.5%, with the precision rate, recall rate and F₁ value  all exceeding  98.2%, which show better classification effect compared with other models.

We proposed a new nonmonotonic adaptive accelerated Levenberg-Marquardt algorithm for solving nonlinear equations. The algorithm used a new adaptive function to update the Levenberg-Marquardt parameter, which could enhance the consistency between the model and objective function during too-successful iterations, thereby accelerating the convergence rate of the algorithm. Numerical experimental results show that the proposed algorithm has good numerical computational performance.

We proposed an improved approximate optimal gradient method to solve the unconstrained objective function in the graph partition problem. We first used  the modified BFGS updating formula and selected the linear combination of BB class step sizes as scalar matrices to obtain  the approximate optimal step sizes, then we introduced parameters to improve the classical Zhang-Hager line search form, construced the algorithm framework  and gave the proof of R-linear convergence. The experimental results show that the improved algorithm improves the performance of the original algorithm.

 Based on gene therapy as a fundamental treatment for diseases, it brings new ideas and methods for the treatment of rheumatoid arthritis (RA). We review  the relevant research advances  of gene therapy for rheumatoid arthritis,  including small interfering RNA (siRNA), micro RNA (miRNA),  DNA,  CRISPR/Cas9 system,  deoxyribonuclease and some other technologies,   providing reference ideas for the application of  gene therapy in the field of RA and offering more  effective and targeted treatment plans for the patients with RA. 

A complex symmetric  operator refers to a linear operator with a symmetric matrix representation  on a  Hilbert space. We review the main research  advances  and  several open problems of complex symmetric operators in recent years, involving special complex symmetric operators, reducing subspaces, the norm closure problem, and algebraic properties  and so on.

Sclerotinia sclerotiorum (Lib.) de Bary is a worldwide and necrotrophic phytopathogenic fungi with a wide host-range. Sclerotinia stem rot (SSR) caused in soybean and rapeseed by S.sclerotiorum has caused huge economic losses to agricultural production. The pathogenic mechanism of S.sclerotiorum is complicated,  which not only has a necrotrophic phase that directly kills cells,  but also includes a short biotrophic phase that needs to suppress plant immunity. S.sclerotiorum has a wide variety of pathogenic factors,  including key regulatory factors that mediate the formation of infection structure or stress resistance,  hydrolytic enzymes that degrade plant cell components,  oxalic acid,  effector that induce plant cell death or inhibit plant immunity,  etc. We have reviewed the infection model of S.sclerotiorum, summarized  the roles of various pathogenic factors,  especially effector proteins,  in the pathogenesis of S.sclerotiorum. Combined with the latest research,  we have prospected the new pathogenic mechanism of S.sclerotiorum,   providing theoretical basis for the prevention and control of crop Sclerotinia diaease.

We considered the dynamic bifurcation  problem of a class of cross-reaction-diffusion models with Holling-Ⅱ functional response function under non-homogeneous Dirichlet boundary conditions. Firstly, the critical crossing conditions for the corresponding linearization problem eigenvalues were obtained by using the spectral analysis theory. Secondly,  the environmental carrying coefficient was selected as the bifurcation parameter, the analytical expression of the dynamic transition type and bifurcation solution of the system was obtained by using the center manifold reduction and the dynamic bifurcation theory. Finally, by using the finite difference method, the pattern change patterns of the system were given under  different parameter conditions.

By constructing the cohomologies complexes of Rota-Baxter Lie algebra homomorphisms, we discuss the formal deformation of Rota-Baxter Lie algebra homomorphisms and prove that Rota-Baxter Lie algebra homomorphism is rigid when the 2th-cohomology group of the deformation complex is zero.

Aiming at the problem that existing methods could not fully capture the intrinsic structure of data without considering the higher-order neighborhood information of the data, we proposed an unsupervised feature selection algorithm based on graph filtering and self-representation. Firstly, a higher-order graph filter was applied to the data to obtain its smooth representation, and a regularizer was designed to combine the higher-order graph information for the self-representation matrix learning to capture the intrinsic structure of the data. Secondly, l_2,1 norm was used to reconstruct the error term and feature selection matrix to enhance the 
robustness and row sparsity of the model to select the discriminant features. Finally, an iterative algorithm was applied to effectively solve the proposed objective function and simulation experiments were carried out to verify the effectiveness of the proposed algorithm.

Aiming at  the non-selective expansion  and training deficiencies of the DoubleMix algorithm during data augmentation, we proposed a supervised contrastive learning text classification model based on double-layer data augmentation, which effectively improved the accuracy of text classification when training data was scarce. Firstly, keyword-based data augmentation was applied to the original data at the input layer, while selectively enhancing the data without considering sentence structure. Secondly, we  interpolated  the original and augmented data in the BERT hidden layers, and  then send them to the TextCNN for further feature extraction. Finally, the model was trained by using Wasserstein distance and double contrastive loss to enhance text classification accuracy. The comparative experimental results on SST-2, CR, TREC, and PC datasets show that the classification accuracy of the proposed method is 93.41%, 93.55%, 97.61%, and 95.27% respectively, which is superior to classical algorithms.

We proposed a new classification of rock thin section images based on mixture of expert model by using  five common  rock thin sections as the research object to construct a dataset. The model learned the characteristics of each rock image from the thin section images and classified them. Firstly, multiple image classification models based on convolutional neural network(CNN) and Transformer (such as ResNet50, MobileNetV3, InceptionV3, DeiT, etc.) were used to train the data. Secondly, models with better performance were selected,  a mixture of experts model was built to obtain the final prediction result. The  ACC and AUC of lithology recognition reached 85.33% and 96.69% on the validation set and 87.16% and 96.75% on the test set. Finally, by combining a mixture of experts model with  multiple models, combining  advantage of each model,  balancing their contributions between each model, we improved the accuracy and robustness of classification results, making the obtained classification results more reliable and stable.

By using  variational methods and corresponding critical points theorems, we investigated a class of nonlocal elliptic equations Navier boundary value problems with p-biharmonic operators. We obtained two existence theorems for nontrivial generalized solutions 
 when nonlinear terms satisfied super-linear conditions.

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.

Aiming at the problem that  identifying  essential proteins in  biological experiments was time-consuming and laborious, and using
 computational methods to predict essential proteins could not effectively  integrate biological information,  we proposed  a deep learning framework. Firstly, a weighted protein interaction network was constructed by using network topology structure, gene expression data and gene ontology (GO) annotated data. Secondly, feature vectors were extracted from subcellular localization data, protein complex data and gene expression data by using feature graph network and bi-directional long short-term memory cells, respectively. Finally,  these feature vectors were input into the task learning layer to predict essential proteins. The experimental results show that, compared with  existing computational methods, the proposed method has better predictive performance.

Aiming at the problems that the classical deep learning algorithm was difficult to extract facial features effectively and the accuracy of character identification was difficult to reach the ideal accuracy due to factors such as illumination, shooting angle and image quality, we proposed an  age recognition algorithm based on strong facial semantics. Firstly, the feature weights of facial regions were enhanced by the attention matrix to achieve the purpose of extracting feature regions. Secondly, a cascaded bi-directional long short-term memory (Bi-LSTM) network was used to learn the feature dependency relationships between temporal frames 
and  compensate for the influence of missing features on recognition accuracy. When tested on IMDB-WIKI facial dataset and Adience dataset, the age recognition accuracy of the algorithm reached 78.34% and 77.89%, respectively. Experimental results show that compared with other methods based on deep learning algorithms, the proposed algorithm has higher accuracy in the task of person age recognition based on image datasets.

Based on non Markov chain denoising diffusion implicit model (DDIM), we proposed  probability method of denoising diffusion based on  rough sets. The rough set theory was used to equivalently partition the sampled original sequence, construct the upper and lower approximation sets and roughness of the subsequences on the original sequence, and obtain the effective subsequences of the non Markov chain DDIM when the roughness was the lowest. The comparative experiments were conducted by the denoising diffusion probability model (DDPM) and DDIM,  and the experimental results  show that the sequence obtained by proposed method is an effective subsequence, and the sampling efficiency on this sequence is better than that of the DDPM.

SWEET (sugars will eventually be exported transporters) proteins are a novel class of sugar transporter proteins that mediate the bidirectional transmembrane transport of sugars in cells and play important functions in plant growth and development,  including phloem loading,  phytohormone transport,  flower,  fruit and seed development,  interactions between plants and pathogen, and symbiosis between plants and microorganisms.  SWEET proteins are important participant in the process of plant-pathogen interactions. We summarize the response mechanisms of SWEET proteins in biotic stresses, as well as the metabolic characteristics,  regulatory pathways and specific defense responses of SWEET genes when plants are infected with different pathogens (bacteria,  fungi,  nematodes and virus). We also discuss  the use of gene editing tools to edit SWEET genes to enhance plant resistance to pathogens and their application in agriculture. The aim is to provide a reference for in-depth research on the mechanism of  SWEET proteins involvement in plant-pathogen interactions and the use of SWEET genes for disease resistance breeding.

Aiming at  the problems that  the whale optimization algorithm was prone to getting stuck in local optima and had drawbacks such as slow  speed control response and large overshoot of brushless DC motor, we  proposed an improved whale optimization algorithm (IWOA) for optimizing proportional integral derivative (PID) parameters in brushless DC motor speed control. The algorithm combined Gaussian mutation factor, adaptive weight factor, and dynamic threshold to optimize the whale optimization algorithm. The simulation experiment results show that the  improved whale optimization  PID speed control algorithm of brushless DC motor has faster  convergence rate, smaller overshoot phenomenon, and better robustness.

We considered a class of dynamic fuzzy systems, which consisted of fuzzy Atangana-Baleanu fractional differential inclusion and variational inequalities, called fuzzy fractional differential variational inequalities (FFDVI). It included the two fields of fuzzy fractional differential inclusion and variational inequalities, expanding the researchable problems in fuzzy environments. The model captured the desired features of the fuzzy fractional differential inclusion and fractional differential variational inequalities within the same framework. By using Krasnoselskii fixed point theorem, the existence of solutions of FFDVI under some mild conditions was obtained.

We considered an  independent replicatedly observed model of  INAR(1) (PLINAR(1)) process with Poisson-Lindley marginal distribution for overdispersed replicatedly observed time series data. Firstly, by using conditional least squares estimation, Yule-Walker estimation, quasi-likelihood estimation, and conditional maximum likelihood estimation methods to estimate the parameters of the model, we discussed the asymptotic properties of the estimators and gave predictions for the model. Secondly, through numerical simulations, the performance of different estimation methods and the impact of replicated observations were compared. Finally, a data set of the number of sunspot groups per week from replicated observations was fitted to this model, the fitting results validated the effectiveness of the model.

We review  the  floorplanning methods for very large scale integration (VLSI), explore the significance of floorplanning in integrat
ed circuit design, and its impact on chip area, interconnect length, and design cycle. Firstly, we  review the development history of integrated circuit technology, emphasize the role of floorplanning in determining the position, size, and rotation angles of modules. Secondly, we provide a detailed introduction to four main categories of VLSI floorplanning methods: intuitive construction methods, analytical methods, iterative methods and machine learning methods. Thirdly, we discuss two commonly used  MCNC and GSRC benchmark datasets, which are crucial for testing and evaluating floorplanning methods in the VLSI design field. Finally, we summarize the research progress in the field of floorplanning and point out future research directions.

The first-principles pseudopotential plane wave method based on density functional theory was used to investigate the geometric structures and electronic properties of H,F,Zn,K,Al doped two-dimensional (2D) MgCl₂ monolayer materials. The results show that the crystal structures of these doped systems distort in different degrees. Due to the influence of s-state electrons of H,Al and Zn, the impurity levels of doped MgCl₂ appear in the forbidden bands, while the impurity levels of F and K doped systems appear in the valence bands. Compared with the 5.996 eV band gap of intrinsic MgCl₂ material, the band gap widths of H,F,Al,K and Zn doped systems decrease to 5.665,5.903,4.409,5.802,5.199  eV, respectively. The charges around the impurity atoms of five
 doped systems are redistributed. The charge transfers are consistent with the charge density difference results. Compared with the intrinsic work function 8.250 eV of MgCl₂, the work functions of H,F,Al,K and Zn doped systems decrease to 7.629,7.990,3.597,7.685,7.784 eV, respectively.

We studied the existence of the global smooth solutions for degenerate Gourset problem of a class of hyperbolic conversation law systems. Firstly, we introduced  characteristic angles α,β, and established characteristic decompositions for α,β and pressure 
P. Secondly, the characteristic decompositions of  α,β were used to obtain the invariant region, and then the maximum norm estimate of the characteristic angles were obtained. Finally, the gradient estimates of the solution were established by the characteristic decomposition of pressure P and continuity method, which proved the existence of the solutions to the degenerate Gourset problem.

Exploring the dynamic detail characteristics of protein folding,  assembly,  and phase separation at the molecular level is currently the focus and difficulty of research in this field, and  coarse-grained model have become a key strategy to address these issues. We review the development history of coarse-grained model of protein, introduce two commonly used coarse-grained  models, and explain their modeling methods,  potential energy functions,  and applications in practical biological systems. By demonstrating the application advantages of these models in simulating complex protein systems,  we review  the unique value of coarse-grained model in significantly reducing computational resource consumption, as well as their  potential and significance in advancing the study of large-scale protein dynamic processes.

Aiming at  the problem that the current traditional method of analyzing target background difference using polarization parametric images did not fully consider the unique polarization properties generated by light acting on objects, we proposed a target background difference feature analysis method based on the statistical characteristics of polarization direction features, from a new  polarization direction information to analyze target background difference. Firstly, the polarization direction vector image was constructed by extracting the polarization direction information from the polarization angle image, which solved the problem that the polarization angle image could not be used effectively and directly due to too much noise. Secondly, the orthogonal difference calculation was carried out for the four polarization direction intensity images respectively to obtain the polarization orthogonal difference component images, and the information of the polarization angle intensity images around the ±α polarization direction was supplemented to obtain the polarization direction statistical images. By extracting the three polarization feature images of the four polarization directions, the problem of traditional polarization parametric images with less prominent target in the complex background was solved. The experimental results show that objects of different materials have different polarization directions, and the polarization direction feature image obtained by extracting the polarization direction information can more clearly identify the target in the complex background. The objective evaluation index show that the polarization direction feature image corresponding to the polarization direction orientation of the target area in the polarization direction vector image is richer in expressing the information of the target, and is more informative than the polarization direction feature image corresponding to other polarization directions.  Therefore, the polarization vector image can be used to quickly extract the polarization feature image with prominent target features.

We considered a class of sum of squares (SOS) convex polynomial optimization problems with spectrahedral uncertainty data in both objective and constraint functions. Firstly, an alternative theorem for SOS-convex polynomial system with uncertain data was established in terms of SOS conditions. Secondly, we introduced a SOS relaxation dual problem for this SOS polynomial optimization problem and characterized the robust weak and strong duality properties between them. Finally, a numerical example was used to demonstrate that the SOS relaxation dual problem could be reformulated as a semidefinite  programming problem.

Aiming at the problem that the cellular Internet of Things involved large-scale device connection and identity authentication management, and attackers cuold use various methods  to forge identity information, which made the difficulty of  anonymous access  user identity authentication increase, the author proposed  an  anonymous access user identity authentication algorithm for cellular Internet of Things. Firstly, the 5G network was used as the dynamic application scenario of the cellular Internet of Things system, and the system parameters were preseted. Secondly, according to the user’s identification number and public key, the forged name was used to generate the user’s anonymous access information, and the registration was anonymously saved to the local. Finally, based on the concept of decentralization, the decryption results of the unit public key and the adjacent group key, the random number encryption information and the unit Hash value were compared to authenticate the user identity. The experimental results show that the proposed algorithm effectively shortens the time required for identity authentication and batch message authentication, reduces the number of bytes required for data transmission, with a time cost of only 13 ms, a computational cost of only 4 ms,  and a communication cost of only 210 bytes. Moreover, it can successfully resist 15 types of identity authentication attacks.