We considered the initial  problem of  derivative  Schrodinger systems with time-dependent potentials and quadratic nonlinearities in high-dimensional （d≥3）space. Firstly, under the condition of mass resonance, we obtained the priori estimates of solutions to the systems by using the tools such as energy inequalities and embedding theorems. Secondly, we proved the global existence of solutions for the nonlinear Schrodinger systems with small initial value  by using priori estimates. Finally, by constructing auxiliary functions, we demonstrate that the solutions to the systems are asymptotically free under the condition of mass resonance.

We considered the existence of time-dependent global attractors for a class of Kirchhoff-type wave equations with  memory terms, nonlocal strong damping, and nonlinear perturbations. Firstly, we gave the well-posedness result of the solution to the problem. Secondly, we obtained the existence of a pullback absorbing set for the dynamical system in the corresponding solution space by using  energy estimates. Finally, we proved the asymptotic properties  of its process by using the method of contraction functions, thereby the existence of the time-dependent global attractor was established.

By constructing a modified energy functional, we  investigated the temporal growth of higher-order Sobolev norms for the nonlinear Schrodinger equation (NLS) in two-dimensional Euclidean spaces. Based on results for cubic nonlinearities, we established a polynomial bound applicable to arbitrary higher-order nonlinearities. The obtained results improved the theory of higher-order regularity evolution for NLS.

Without the separability condition for C*-algebras, based on the definition of tracial approximate divisibility, and by employing the structural properties of centrally large subalgebras, we prove that tracial approximate divisibility is hereditary with respect to centrally large subalgebras. Let A be an infinite dimensional unital simple C*-algebra and B be a centrally large subalgebra of A. If B has tracial approximate divisibility, then A also has tracial approximate divisibility.

By using  the weight function method, the Euler-Maclaurin summation formula, Abel’s summation by parts formula and the differential mean value theorem, we gave a new half-discrete Mulholland-type inequality involving  multiple upper limit function and  partial sums, and discussed the equivalence  of the best constant factor with multiple parameters in the new inequality.

We gave an adaptive  regularization method  for solving monotonic variational inclusion problems in  Hilbert space. Firstly, we used adaptive rules to eliminate the dependence of iterative step-sizes on operators in the convergence analysis of existing algorithms. Secondly, we combined regularization technique to establish strong convergence theorems for solving variational inclusion problems. Finally,  the convergence and superiority of the  proposed algorithm were demonstrated through image reconstruction experiment.

Let U_6n=〈a,b|a²ⁿ=b³=1, a^-1ba=b^-1〉 be a finite group. By using spectral theory and representation theory of groups, we study the perfect edge state transfer problem of  Cayley graphs over U_6n groups, and characterize  the necessary and sufficient conditions for allowing perfect edge state transfer to occur on Cay(U_6n,S).

We considered the w-core EP inverse in involutive rings and discussed its properties from two aspects. On the one hand, the w-core EP decomposition was defined, and a new characterization of the w-core EP inverse was given through the w-core EP decomposition, and some new properties of the w-core EP invertible element were discussed. On the other hand, e=a^D_w(aw)^k+1, f=wa^D_w(aw)^ka and the projection element p=awa^D_w were introduced. The w-core EP core inverse was equivalently characterized
 by using e,f and the projection element p, and the w-core EP order a≤_wb was defined accordingly. The properties and its equivalent characterizations of the w-core EP order were studied.

We introduced the concept of Ω-BCK algebras in the framework of fuzzy equalities. Firstly, we replaced the crisp equalities in BCK algebras with fuzzy equalities and gave the definition of Ω-BCK algebras. Secondly, we characterized the substructures of Ω-BCK algebras and proved the necessary and sufficient conditions for the determination of Ω-BCK subalgebras. Thirdly, by using fuzzy congruence relations, we obtained the relationship between Ω-BCK algebras and BCK algebras. Finally, we generalized the partial order relation of BCK algebras and defined the E-partial order relation of Ω-BCK algebras.

We considered a class of jump-diffusion SEIR epidemic models and determined the threshold for the disease to occur or not. Firstly, the threshold A was theoretically determined through a simplified limiting system. Secondly, by using comparison principle, we proved that when A<0, the disease became exponentially extinct. Finally, by constructing an appropriate Lyapunov function, we proved that when A>0, the transition probability function of the solution of a stochastic system converged to the unique invariant measure, with the convergence speed of arbitary order polynomial convergence.

Based on the mean field theory of complex networks, we  established a SEIR (susceptible, exposed, infectious, removed) model with periodic contagion  rates. Firstly, we determined the positive invariant set of the system and used  the spectral radius method of the linear integral operator to give the expression of the basic reproduction number R₀. Secondly, by using  the principle of comparison, we prove that the disease-free equilibrium point of the system is globally asymptotically stable when R₀<1, and there exists at least one positive periodic solution in the system and the system is uniformly persistent when R₀>1. Finally, the correctness of the theoretical analysis  is  verified by using numerical simulations, and  the results show  that the greater the maximum degree of nodes in the network, the greater the absolute density of infected people, indicating that the network structure has a significant impact on the spread of infectious diseases. In addition, through numerical simulations, we obtain that when R₀>1,  the system has a unique globally asymptotically stable  positive periodic solution, which enriches the theoretical analysis results.

Aiming at the problems that there were  the lack of explicit sentiment clues, mixed sentiment features, polysemy features  and context dependence features in implicit sentiment analysis, we  proposed a Chinese implicit sentiment analysis method based on hierarchical knowledge enhancement and sememe knowledge. We first introduced a sentiment pre-training model based on  bidirectional encoder representation technology of converters  to enhance the ability of  sentiment clue recognition. Then 
we handled mixed sentiment features through character-level information acquisition, region moving box learning, global information learning, and multi-pooling operations. At the same time, we combined sememe knowledge and density matrix, utilized the HowNet knowledge base to allevite polysemy issues, and integrated  with bidirectional long short-term memory network 
features to tackle context dependence features. Experimental results show that the proposed method performs excellently in terms of effectiveness, superiority, and generalizability, providing a valuable technical path for Chinese implicit sentiment analysis and helping to improve sentiment understanding and decision-making support capabilities in scenarios such as social media and user reviews.

Aiming at the problems of insufficient accuracy of pathological image recognition and semantic gaps in feature fusion process caused by the diversity of lesion morphology, we proposed an improved U-Net architecture that integrated Transformer and attention mechanisms. Firstly, we designed a boundary-aware module to enhance the expression of lesion edge features in pathological images, thereby improving the model’s ability to perceive complex structures. Secondly, we introduced a regularized large-kernel attention module at the bottleneck layer to model long-range dependencies, and mitigated overfitting risk through a layer-wise regularization strategy. Finally, we further introduced a learnable visual center module to strengthen the complementarity between global and local features. Experimental results on the MoNuSeg and GlaS datasets show that the proposed method outperforms current mainstream models in terms of segmentation accuracy and boundary clarity.

Aiming at the problems of small-object recognition difficulty, sparse point clouds at long distances, and insufficient multimodal feature fusion in three-dimensional object detection for autonomous driving scenarios, we proposed an improved algorithm based on a multimodal three-dimensional object detection framework. The algorithm enhanced the ability  to preserve foreground information and suppress background noise interference by constructing a class and centroid-aware foreground point sampling strategy. By introducing  a dynamic convolutional image feature extraction mechanism,  the quality of image feature representation was improved. By designing a multi-stage interactive feature attention fusion module,  the deep collaborative modeling ability between point cloud features and image features was improved. Experimental results on a public dataset show that the proposed method achieves average detection accuracies of 83.49%, 46.98% and 68.28% for three types of objects: cars, pedestrians and cyclists, respectively, and outperforms current mainstream methods in overall performance. The proposed method can effectively improve the accuracy and robustness of three-dimensional object detection in complex traffic scenarios and has certain reference value  for promoting the development of autonomous driving environment perception technology.

Aiming at  the challenge of balancing model accuracy and inference speed in metal surface defect detection, we proposed an improved SWE-YOLOX detection algorithm based on the YOLOX model. Firstly, in order to solve the problem of large  interference of complex backgrounds and significant variation in defect scales, we introduced a channel shuffle attention module to enhance feature expression ability  and suppress irrelevant information. Secondly, aiming at the problem of unclear defect edges and weak texture features, we incorporated wavelet convolution to  improve the extraction ability of frequency-domain features, thereby enhancing the expression of  detailed information. Finally,  the original intersection over union (IoU) loss function was replaced with an enhanced intersection over union (EIoU) loss function to optimize  the regression accuracy between predicted boxes and ground truth boxes. Experimental results show that the proposed method achieves a mean average precision (mAP) of 76.3% 
on the NEU-DET dataset, which is 3.86 percentage point higher than that of YOLOX model. It also maintains a fast inference speed without increasing the number of parameters and  computational complexity.

Aiming at the problem that current artificial neural network methods could not  accurately forecast the Madden-Julian oscillation (MJO), a seasonal climate phenomenon, we proposed a domain prior knowledge-based spatio-temporal neural network model. Firstly, we integrated domain prior knowledge into data preprocessing according to the characteristics of climate circulation data. Secondly,  a pretraining-finetuning architecture was adopted, model data from the subseasonal-to-seasonal scale were used for pretraining model, and we completed  finetuning by using the ERA5 reanalysis data. Finally, through spatio-temporal modeling, a framework  combining convolutional neural networks and long short-term memory networks  was selected to embed the prior knowledge into the pretraining process and optimize the forecasting. Experimental results show that the proposed model can achieve accurate MJO forecasting for  23 d, and its performance is superior to other artificial neural network methods and domestic numerical forecasting methods.

Aiming at the problem that it was difficult to accurately represent and process  uncertain knowledge in a single way due to its ambiguity,  randomness or  incompleteness, we proposed an uncertainty knowledge representation algorithm based on resource description framework (RDF) and probabilistic reasoning. Firstly,  RDF graph was used to describe uncertain knowledge data samples, and uncertain knowledge meta statements and their hierarchical relationships were constructed to obtain uncertain knowledge RDF graph patterns and standard statement patterns. Secondly, fuzzy Petri nets were used to represent uncertain knowledge and define fuzzy Petri net octets.  The probabilistic soft logic reasoning was used to construct fuzzy inference rules and constrain the logical inference rules. Finally, through specific operator inference, we output uncertain knowledge representation results when the library credibility value was stable. The experimental results show that the semantic richness values of the standard sentences constructed by proposed method are all higher than 0.8. When the number of logical rules increases to 220, 
there are only 3 occurrences of logical contradictions, with a probability of 1.36%. The certainty of different uncertain knowledge representations is all above 0.9, indicating that the algorithm has high accuracy in representing uncertain knowledge and can effectively capture and describe the logical relationships of variables within the knowledge.

Aiming at the problems that device-free sensing technology had high parameter dependence in practical applications and existing low-parameter-dependent solutions based on optimization algorithms tended to fall into local minima, we proposed a low-parameter-dependent device-free sensing method based on the differential evolution algorithm. The proposed method optimized the parameter configuration of the sensing system through the differential evolution algorithm, combined iterative search and performance evaluation of multi-parameter combinations to gradually approach the global optimal solution, and introduced multiple classifiers to verify the effectiveness of the method.  The experimental results show that this method can effectively overcome the problem of parameter dependence, improve the accuracy of data collection and target detection, with a classification accuracy of 97.06% on the human behavior recognition dataset and 94.02% on the brain nerve dataset. It  has good practicability and robustness, and  effectively solves the defects of parameter dependence and local optimal solutions of traditional sensing methods, providing a new  parameter optimization idea for the engineering application of device-free sensing technology.

Aiming at the problem that existing incremental least mean square algorithms, which relied solely on the local data at each node to perform local estimation, suffered from low estimation accuracy under limited information exchange, we proposed an incremental recursive least squares algorithm based on cyclic network estimation. The algorithm performed  exponentially weighted summation of local loss functions node by node in the cyclic network, and recursively solved  the local estimate at each node by using only the local estimate of parameter and intermediate process matrix estimate from the immediately preceding node. It featured low demand for information exchange and high estimation accuracy. Through theoretical analysis of the mean and mean-square error of proposed estimation method,  the simulation experimental results are highly consistent  with the theoretical analysis. In different application scenarios, the  estimation accuracy of proposed algorithm is superior to the current comparative  incremental least mean square algorithms, providing an efficient and practical solution for parameter estimation in distributed cyclic networks.

Aiming at the problem that the peak density was usually chosen as the cluster head in the wireless sensor networks, and these nodes might not have the optimal energy state or network location, and might fail prematurely due to energy depletion, forming energy holes that affected the stability of network operation, we proposed  an optimization algorithm for multi-level circular clustering in wireless sensor networks. Firstly, we divided the network area equally based on the distance from the boundary of the wireless sensor network area to the base station to obtain multiple circular areas. Secondly, within each circular region, the clustering by fast search and find of density peaks （CFSFDP） algorithm was used to cluster nodes based on their density and distance to balance the distribution of nodes within the cluster and optimize communication load. Thirdly, after determining the optimal number of clusters within each layer of the circular region, we calculated the weight values of each node and selected the node with the higher weight value as the clustering center to complete node clustering. Finally, we considered the remaining energy and relative density of nodes,  dynamically selected cluster heads, and established a multi-level clustering structure.  At the same time, we sorted data transmission according to the remaining energy ratio of cluster heads to balance the energy consumption of each node, avoid premature failure of some nodes, ensure connectivity and transmission efficiency, and achieve multi-level circular clustering optimization in wireless sensor networks. The experimental results show that the number of surviving nodes of the proposed method remains above 280, and the maximum and minimum remaining energy of the nodes are both above 3.5 J.  The load balancing value is the highest, which can be maintained above 0.8. This can avoid the energy hole caused by energy depletion and ensure the stable operation of the wireless sensor networks.

Aiming at the problem that traditional encryption methods for  sensitive information in  communication network terminals often failed to balance the high sensitivity of signals and robustness in complex environments, making encrypted information vulnerable to cracking or tampering, we proposed a chaotic encryption solution based on parallel interference cancellation technology and evolutionary hypernetwork model. Firstly, by constructing a weight vector matrix with minimum mean square error, the estimation and ranking of interference signals from each user could be achieved, and interference could be subtracted from them to improve the quality of the target signal. Secondly, an evolutionary hypernetwork model was introduced to determine the sensitivity of information samples by using hyperedge association rules, construct a decision classification model, and achieve mining of sensitive data. Finally, by using Lyapunov exponent to measure the sensitivity of chaotic sequences, combined with feedforward 
stream cipher mechanism and scrambling processing, a high security sensitive information key stream was generated to ensure high sensitivity and robustness in complex environments during the encryption process, thereby improving the security and anti cracking ability of encrypted information. The experimental results show that the proposed method can improve the anti-interference ability of encryption methods, and enhance the transmission efficiency of information while ensuring information security.

We studied the characteristics of interface states of photonic crystals with inverted symmetric composite structures, where the
 media composing the crystals were functional media with refractive index that was a function of spatial position. The results show that when the refractive index of the medium is a constant, photonic crystals composed of two different composite structures (PC1+PC2 and PC1+PC2+PC1) exhibit different interface state characteristics. The composite structure composed of PC1+PC2 can only generate one interface state, while the composite structure composed of PC1+PC2+PC1 can generate at most two interface states. When the refractive index of the medium is a function of spatial position, the photonic crystal with the composite structure composed of PC1+PC2 can realize the regulation of a single interface state and multiple interface states. As the two endpoint values n_b(0) and n_b(b) of the refractive index of the functional medium increase, the single interface state undergoes an obvious red shift, and its peak intensity is significantly attenuated. The position and number of multiple interface states remain unchanged, while the peak intensity is significantly enhanced.

Based on the domestic simulation support platform vPower, we established a simulation model of the core system, primary circuit, secondary circuit, tertiary circuit and main instrumentation and control system of large sodium-cooled fast reactor. We simulated and analyzed the dynamic response characteristics of the main system under the emergency shutdown condition of a large pool-type sodium-cooled fast reactor, and compared and verified the simulation calculation results with the real reactor test data. The results show that the deviation between the simulation calculation results and the real reactor operation data under the full power steady-state condition is less than 1%, the simulation calculation results fit well with the real reactor data under the emergency shutdown transient state, and the change trend of the main variables is basically consistent, which can accurately reflect the dynamic characteristics of the main reactor system.

In order to study the effect of trace Ni-doping on the crystallinity, defect concentration and electrical properties of Cu₂ZnSn(S,Se)₄ thin films, without affecting other cations (Cu,Zn and Sn), we introduced trace Ni ions into the Cu₂ZnSnS₄ precursor solution, and prepared the Ni-doped Cu₂ZnSn(S,Se)₄ films through a spin-coating, sintering and selenization process. We conducted testing and analysis by using X-ray diffraction, Raman spectroscopy, X-ray photoelectron spectroscopy, inductively coupled plasma optical emission spectrometry, scanning electron microscopy, UV-Vis spectrophotometry, Hall effect and conductive atomic force microscopy. The results show that when the Ni-doping percentage is 0.5%，the film achieves optimal crystallinity and the concentration of deleterious Sn_Zn defect is minimized. The carrier concentration is 3.58×10¹⁶ cm^-3,  the average surface current is 4.67 nA, and the electrical properties of the film reach its optimum.

Prunella vulgaris polysaccharides (PVPs) were extracted by using ultrasonication extraction,  and polysaccharide component (PVP-2) was isolated and purified from PVPs. Physicochemical characteristics,  antioxidant,  hypoglycemic and antibacterial activities of PVP-2 and derivatives (Zn-PVP-2,Se-PVP-2,S-PVP-2 and P-PVP-2) modified by zinc,  selenium,  sulfonation and phosphorylation were compared. The results show that compared with natural PVP-2,  the contents of uronic acid,  total phenol,  total flavonoids,  sulfuric acid group,  glucuronic acid and galacturonic acid,  water solubility,  antioxidant,  hypoglycemic and antibacterial activities of the derivatives are significantly increased,  but the relative molecular weight and protein content are decreased. The modification leads to the degradation of the neutral side chains of PVPs,  and significantly changes the molar ratio of monosaccharides,  but does not change the backbone structure of PVP-2. P-PVP-2 has the highest antioxidant activity and hypoglycemic activity,  and Se-PVP-2 has the best antibacterial activity,  indicating that the chemical modification methods are effective in the modification of PVP-2, and chemical modification can enhance the potential application of PVPs in the food and pharmaceutical industries.

By using combination of  nonequilibrium Green’s function (NEGF) and density functional theory (DFT),  the spin transport properties of four molecular junctions (M1—M4) consisting of rhenium azulenocyanine isomers (m1—m4) bridged to zigzag graphene nanoribbon (ZGNR) electrodes were investigated. The research results show that the transport properties of different isomers vary significantly. Among them,  the device M1 constructed based on the m1 molecule has the best overall performance:  In the parallel (P) ferromagnetic electrode configuration,  the spin filtration efficiency (η_SFE) is consistently higher than 98% under bias voltages ranging from 0 to 0.6 V;  a significant negative differential resistance (NDR) effect is observed in the bias voltage interval from 0.4 V to 0.55 V;  and the magnetoresistance ratio (R_MR) is as high as 4  493% at a specific bias voltage of 0.20 V. It can be seen that the rhenium azulenocyanine/ZGNR molecular junctions can effectively integrate high η_SFE,  ultrahigh R_MR,  and significant NDR effects into a single junction,  which provides a theoretical foundation for designing novel multifunctional molecular spintronic devices.

Using 2-mercaptoisonicotinic acid (H₂mna)， Cu⁺ and Zn²⁺ as raw materials, a  novel heterometallic complex {\Cu₆Zn₃(mna)₆(en)₃H₂O\].solvent}_n(1)  was prepared by solvothermal  synthesis using a one-pot  method. Its structure and thermal stability were characterized by single crystal  X-ray diffraction,  infrared spectroscopy and thermogravimetric analysis. The experimental results show that the  interactions of Cu⁺  and (mna)^2-₆ in compound 1 form  two anionic \[Cu₆(mna)₆\]^6-  metal ligands through coordination bonds,  both containing pseudo\|hexagonal prismatical Cu₆S₆ clusters,  and Cu₆S₆ clusters are connected to  Zn²⁺  to form a three-dimensional network structure.  Compound 1 exhibits distinct red light emission in the solid state with a maximum emission wavelength of 664 nm. Compound 1 shows a sensitive fluorescence quenching response to 2-nitrotoluene,  with quenching constant (K_SV) and detection limit of  2.33×10³ (mol/L)^-1 and 1.20×10^-5 mol/L,  respectively. The quenching effect of 2-nitrotoluene is primarily due to photoinduced electron transfer.