We considered the lower bound of VC (Vapnik-Chervonenkis) dimension for concept classes induced by general Bayesian networks where each random variable took any finite values. By analyzing the relationship between the number of parameters that could be freely set in a network and the corresponding VC dimension, we proved that adding 1 to the number of parameters that could be freely set in any discrete non-full Bayesian network was a lower bound of corresponding VC dimension.

With the help of the boundedness of the Lebesgue spaces, by applying the decomposition method of function and real variable
 techniques, the boundedness of Marcinkiewicz integral with rough kernel was proved on Morrey-Adams spaces. Meanwhile, the corresponding result of its commutator with Lipschitz and BMO functions was given.

By using Leray-Schauder degree theory and Banach contraction mapping principle, we studied the existence and uniqueness of solutions for boundary value problems of conformable fractional delay differential equations when the nonlinear term satisfied the growth condition and the Lipschitz condition, we obtained the results of existence and uniqueness of solution for the boundary value problem respectively, and gave an example to illustrate the applicability of the obtained results.

By using the Leray-Schauder fixed point theorem, we discuss the solvability of the fourth-order boundary value problem.  The existence and uniqueness of solutions to the problem are obtained under the condition that the nonlinear term f(x,u,v) is allowed to grow superlinearly with respect to  u,v.

By using Mawhin’s coincidence degree theory, we  study the existence of  solutions for the φ-Hilfer fractional order Riemman-Stieltjes integral boundary value problem. The results show that the solutions of φ-Hilfer fractional differential equation exist under the Riemann-Stieltjes integral boundary value conditions in suitable Banach spaces.

Let T be a formal triangular matrix ring. Using Hom functors and adjoint isomorphism  theory, we describe the structure of the F-Gorenstein flat modules over formal triangular matrix ring T.

By using the method of contradiction,  the method of constructing concrete coloring and distributing the color sets in advance, we discussed the general total colorings of complete 4-partite graph K_n1,_n2,_n3,_n4n₁≤n₂=n₃<n₄ or n₁=n₂=n₃=n₄) that were vertex-distinguished by multisets. We gave an  optimal coloring scheme and determined the chromatic numbers of the corresponding colorings.

We considered the extreme problem of the Randic energy of unicyclic graphs C_g∪S_t composed of sticking a star graph S_t at a certain vertex on the circle C_g. Using the definition and properties of the Randic energy, and combined with graph transformations, we found the graph that obtained the minimum Randic energy in this class of unicyclic graphs C_g∪S_t.

We used the differential complex to calculate the standard cohomology of 4-dimensional even centers and 3-dimensional odd centers Heisenberg Lie superalgebras with coefficients in the 1-dimensional trivial modules. Firstly, we calculated the differential operators of these two classes of Heisenberg Lie superalgebras. Secondly, we calculated the standard cohomology of these two types of Heisenberg Lie superalgebras with coefficients in the 1-dimensional trivial modules. In particular, we obtained the basis and dimension of the standard cohomology for these two types of Heisenberg Lie superalgebras.

We used the adaptive penalized likelihood method to solve the structure learning problem of Gaussian graphical models with latent variables. The simulation results show that the adaptive penalties are significantly superior to the non-adaptive penalties, which can effectively reduce the estimation bias and more accurately estimate the conditional independence relationships among observed variables given latent variables.

We used  finite element method to numerically solve the viscous Cahn-Hilliard equation. Firstly, the equivalent form of the viscous Cahn-Hilliard equation was obtained by introducing the Lagrange multiplier r of the auxiliary variable. Secondly, the second order linear finite element numerical scheme for the viscous Cahn-Hilliard equation was given by using the mixed finite element approximation  in space and the implicit backward differentiation formula (BDF)  for discretization in time, and the unconditional stability in energy and error estimation of the given scheme were analyzed in detail. Finally, a series of numerical examples were used to verify the accuracy and effectiveness of the given scheme. The results show that the proposed numerical scheme is ideal and has the characteristics of simultaneously satisfying linear, unconditional stability in energy and second order accuracy.

By using Rosenthal’s inequality, we discussed almost sure convergence of weighted sums for m-END (m-extended negatively dependent) random variable sequence. Almost sure convergence of weighted sums for END sequence in the classical probability space was extended to the almost sure convergence of weighted sums for m-END random variable sequence under the sub-linear expectations.

The ADCBAR(1) model was extended to case of the random coefficient,  we proposed a class of first-order random coefficient binomial autoregressive model RCADCBAR(1) with dependent thinning operator, which could be used to characterize the finite-range integer-valued time series data with dependence and zero stacking properties. Firstly, some statistical properties of the model were derived. Secondly, the unknown parameters in the model were estimated by the conditional maximum likelihood method, and the asymptotic properties of estimators were discussed. Finally, the model was applied to a group of real data to illustrate the applicability of the model.

By using the fixed point theorem on expansion and  compression of cones, we study the existence of positive solutions for a class of periodic boundary value problems of third-order ordinary differential equations. The  results show that there exists  at least one positive solution to the above problem when the nonlinear term f satisfies appropriate conditions.

Aiming at the redundant relations and entity overpalling problems in  the task of relational triple extraction,  we proposd a 2D entity pair tagging scheme based on the relation filter (RF2DTagging).  RF2DTagging model consisted of two parts: 1) A relation filter for filtering redundant relations, and 2) a 2D entity pair tagging scheme that could effectively solve various entity overlapping problems. To further validate the RF2DTagging model, we conducted experiments on three public Chinese relation extraction datasets CCKS2019-Task3, CMeIE and DuIE2.0. The experimental results show that the  model can effectively solve the above two problems,  and the overall performance is better than the comparison model.

Aiming at the time-consuming and labor-intensive problem of obtaining large-scale multi-hop question and answer training dataset, we  proposed a multi-hop question generation model based on the contrastive learning idea. The model was divided into the generation phase and the contrastive learning scoring phase. In the generation phase, candidate multi-hop questions were generated by executing the inference graph. In the contrastive  learning scoring phase, candidate questions were scored and sorted through a candidate question scoring model without reference question based on the contrastive learning idea, and the best candidate question was selected. This model had to some extent narrowed the gap between unsupervised methods and manual annotation methods, effectively alleviating the problem of lacking a multi-hop question and answer dataset. The experimental results on HotpotQA dataset show that the multi-hop question generation model based on contrastive learning can effectively expand the training data and greatly reduce the cost of manually labeling data.

In order to realize the effective precipitation of power transformer operation and maintenance knowledge, taking the operation and
 maintenance text as the research object, we proposed a framework for deep construction of power transformer operation and maintenance knowledge graph with fusion rules. We  first constructed the concept layer of the knowledge graph from top to bottom according to the guidance of experts, and then  integrated rules and deep neural network models to extract knowledge and construct the data layer of the knowledge graph. Aiming at the blurred boundaries of entities and insufficient utilization of contextual information in operation and maintenance texts, we proposed a method for obtaining extended Span lables by extending contextual information and bidirectional encoder representations from transformers  for entity and relation extraction. The example analysis shows that  the proposed method performs well in  knowledge extraction from  power transformer operation and maintenance data.

Aiming at the problem of location privacy leakage of workers in traditional mobile crowd sensing, we proposed a two-stage location privacy protection method. Firstly, a system model combining blockchain and edge computing was designed to replace the third-party platform. Secondly, a ciphertext time worker selection algorithm based on homomorphic encryption was proposed in the task allocation stage, which efficiently completed the task allocation through the cooperation of edge nodes. Finally, in the data upload stage, a two disturbance local differential privacy algorithm was given, workers perturbed location data locally, and the interference factor ω was added to balance the protection strength and the quality  loss. Simulation experimental results show that compared with the existing algorithms, the proposed method improves the task completion rate, reduces the  service quality loss, and effectively protects the location privacy of workers.

Aiming at the problem of unstable clustering results and low solving accuracy of  I-k-means-+ algorithm, we proposed I-k-means-+ clustering algorithm based on min-max criterion and region division. Firstly, the min-max criterion was proposed to calculate the distance from each data point to the nearest center, and the data point with the largest distance was preferentially selected as the new clustering center to avoid multiple initial centers gathering in the same cluster. Secondly, the data points in the split cluster were divided into different regions, and a data point was selected as the candidate center in each region to increase the diversity of the candidate center. Finally, for the clusters that failed to pair, the new split cluster was re-selected by gain to pair with the original deleted cluster again, so as to improve the pairing success rate and further reduce the objective function value. The experimental results show that compared with the I-k-means-+ algorithm, the proposed algorithm improves the accuracy of the solution by 6.47% on average while maintaining similar operational efficiency, and the clustering results are more stable. Compared with k-means and k-means++ algorithms, the proposed algorithm has higher solving accuracy.

Aiming at the problem of unreasonable traffic-path allocation and elephant flow collision in data center networks, we proposed a 
software defined network (SDN) flow scheduling algorithm based on discrete partical swarm optimization. The algorithm redefined the search  process within the partical swarm with the goal of optimizing  network performance,  dynamically allocated optimal paths for  data center traffic to reduce elephant flow collision, and introduced Metropolis to design  diversified optimal  scheduling scheme to ensure reasonable scheduling of data center traffic. The experimental results of  comparing and verifying with other flow scheduling algorithms show that the algorithm improves network quality, reduces  elephant flow delay, and achieves a better
 load balancing of network.

Aiming at the problem that the initial number of clusters and cluster centers derived from the clustering layer in the original deep embedding clustering (DEC) algorithm had  strong randomness and thus affected the effectiveness of the  DEC algorithm, we proposed a review text clustering algorithm based on improved DEC for unsupervised clustering of category-free labeled e-commerce review data. Firstly, we  obtained a vectorized representation of the BERT-LDA dataset incorporating the sentence embedding vector and the topic distribution vector.  Secondly, we improved DEC algorithm, reduced the dimensionality by the autoencoder, and stacked the clustering layers  after the encoder, where the number of clusters in the clustering layers was selected based on the topic coherence. Meanwhile,  the topic feature vector was used as the custom clustering center, and then the joint training of encoder and clustering layers was performed to improve the accuracy of clustering. Finally, the visualization tool was used to visually  display the clustering effect. In order to verify the effectiveness of the proposed algorithm, unsupervised clustering  training was conducted  on an unlabeled product review dataset by using the algorithm and six comparison algorithms. The results show that the algorithm  achieves the best results of 0.213 5 and 2 958.18 in the contour coefficient  and Calinski-Harabaz (CH) index, indicating that the algorithm  can effectively handle ecommerce review data and reflect users’ attention to the products.

Aiming at the problem that the diagnosis of pleomorphic adenoma completely relied on manual labor, we proposed a computer
-assisted diagnostic method. Firstly, by  collecting data and constructing a pleomorphic adenoma dataset, the current dense connection nertwork was improved and fused with the channel attention mechanism for disease tissue classification feature extraction to obtain tissue categories and probabilities. Secondly, by using classification and regression trees (CART), we obtained diagnostic results and  provided manual assistance in the selection of difficult categories, thus achieving  computer-assisted work on pleomorphic adenomatous diseases. The experimental results show that the method  achieves  classification extraction accuracy of 97.7% in the classification recognition module, and decision tree inference diagnostic accyracy of 100%. In addition, the accuracy of classification recognition module  achieves 98.6%  in the field of blood cell classification, and the method has certain transferability and validity.

Aiming at the problems of overfitting and low classification accuracy in brain tumor magnetic resonance image classification, we proposed a brain tumor classification method based on an improved EfficientNetV2 network. The method  introduced the coordinate attention mechanism in the EfficientNetV2 network, which simultaneously obtained the feature information of brain tumor from both vertical and horizontal directions and accurately identified the lesion features of brain tumor. It helped the model to locate and identify the lesion area information more comprehensively and accurately, and effectively suppressed the influence of background information on the detection results, so that the model had higher classification accuracy. The problem of low classification accuracy caused by  insufficient acquisition of feature information was solved. In order to further improve the classification accuracy, the Hard-Swish activation function was introduced, which could not only improve the computational speed of the brain tumor classification network model, but also effectively improve the classification accuracy. Meanwhile, the improved model was equipped with Dropout layer and normalization layer, which could better suppress the occurrence of overfitting, accelerate the convergence speed of the model, improve the robustness of the model, and significantly improve the classification accuracy. The experimental results show that the improved model obtains classification accuracy of 98.4% in the validation set, and the effectiveness of the improved model in brain tumor classification task is verified by comparison experiments and ablation experiments.

Aiming at the shortcomings  of gradient-domain tone mapping methods in subjective display performance, we proposed a luminance-gradient co-guidance tone mapping algorithm based on Retinex theory by  using the perceptual ability of the human visual system  and the gradient-domain method. Firstly, a domain-aware adaptive  normalization  method was proposed to construct normalized mappings for different domain algorithms. Secondly, a Retinex luminance guidance term was introduced to estimate the background luminance, and the dynamic range of the image was compressed based on the gradient guidance term. Finally, the luminance and gradient guidance terms were combined for unified modeling, and the exponential mean local variance weight was used to suppress halos. The experimental results show that the algorithm suppresses oversaturation and artifacts while compressing the dynamic range, and  has good visual effects and robustness.

Aiming at white Gaussian noise in remote sensing images, we proposed a remote sensing images denoising algorithm based on shearlet transform and goodness of fit test. Firstly, the noisy remote sensing image was decomposed into different sub-bands through shearlet transform at multiple scales, and  the denoising threshold was estimated using the statistical relationship of white Gaussian noise coefficients in the shearlet domain. Secondly, we calculated the goodness of fit test statistics of high-frequency sub-bands  and compared it with the denoising threshold for denoising. Finally, shearlet  inverse transform on the coefficient matrix was performed to reconstruct the denoised  images. The simulation experiment results show that this algorithm can effectively remove Gaussian noise in remote sensing images, maintain the edge texture information of images, and achieve  high peak signal-to-noise ratio under different noise levels, among which the  average increase is  0.33 dB compared with  the shearlet threshold denoising algorithm.

Aming at  the problem that traditional clothing classification algorithms based on convolutional neural networks could not meet the needs of massive and diverse clothing classification, we  proposed a clothing classification network based on convolutional attention fusion.  The network adopted a parallel structure, including a ResNet branch and a Transformer branch, and  fullly utilizing  the local features extracted by the convolution operation and the global features extracted by the self-attention mechanism to enhance the representation learning ability of the network, thereby improving the performance and generalization ability of the clothing classification algorithm.  In order to verify the effectiveness of the method, we conducted comparative experiments on the Fashion-MNIST and DeepFashion datasets.   The results show that on the Fashion-MNIST dataset, the method achieves an accuracy rate of 93.58%, and on the DeepFashion dataset, the method  achieves an accuracy rate of 71.1%, which is superior to the  experimental results of other methods.

In order to grasp the phase transformation mechanical behaviour of shape memory alloy beam with variable cross section during bending deformation, based on the bending deformation theory, the non-linear control equations of shape memory alloy beam with variable cross section was derived by combined with constitutive relationship of shape memory alloy,  the phase transformation process of variable cross section beam was analysed by using a step-by-step method,  the effects of mechanical load, the tension-compression asymmetry coefficient and the variable cross section coefficients on neutral axis displacement, 
curvature and phase boundary were studied and compared them with the finite element results. The results show that the effect of the variable cross section coefficient on the phase boundary and curvature is more obvious, the larger its value, the smaller the maximum value of neutral axis displacement, and the position of each phase boundary is further away from the section edge. The effects of the tension-compression asymmetry coefficient on the maximum displacement of the neutral axis is greater than that of load and variable cross section coefficient, but it has the smallest effect on the position of the cross section where the maximum value occurs. The tension-compression asymmetry coefficient has a greater effect on the phase boundary of compression side than on the tension side. The larger the tension-compression asymmetry coefficient, the more likely the phase transformation occurs on the compression side of the cross section.

Flower-like ZnO (ZnO-F) structure was prepared by chemical precipitation method. The sample structure was characterized by scanning electron microscope (SEM) and transmission electron microscope (TEM), the composition of sample was analyzed by X-ray powder diffraction (XRD), X-ray photoelectron spectroscopy (XPS) and energy dispersive spectroscopy (EDS), the photoelectric performance of the sample was analyzed by UV-visible diffuse reflectance spectroscopy (DRS) and fluorescence spectroscopy (PL), and the photocatalytic activity of ZnO-F was studied by photocatalytic degradation of methylene blue (MB). The results show that the product is ZnO with a diameter of about 1 μm, and its flower-like structure is formed by cross assembly of nanosheets with a diameter of about 17 nm. The sample has high photocatalytic activity, and the photocatalytic degradation efficiency of MB exceeds 90% within 240 min.

Nanoparticles of CoFe₂O₄ were prepared by thermal decomposition method. The crystal structure, microstructure and magnetic properties of samples were analyzed by using X-ray diffraction (XRD), scanning electron microscope (SEM) and vibrating sample magnetometer (VSM). The effects of different heating rates on the microstructure and magnetic properties of CoFe₂O₄ nanoparticles during the preparation process were investigated. The results show that increasing the heating rate can increase the growth momentum of crystal nuclei, which is beneficial for the grain growth of the sample, thereby increasing saturation magnetization and coercivity of the sample.

We designed and synthesized an inorganic-organic hybrid complex based on Keggin-type polyacids,  and obtained [SiW₁₂O₄₀][Ag(bpy)₂]₄·H₂O (1)(bpy=2,2′-bipyridine)  by using  hydrothermal in situ synthesis method. The bpy in complex 1 was obtained by in situ decarboxylation of 2,2′-bipyridine-6,6′-dicarboxylic acid. The structure of complex was characterized  by single crystal X-ray diffraction,  elemental analysis,  infrared spectrum and thermogravimetric analysis, and its   fluorescence,  photocatalytic degradation of organic dyes,  electrochemical and antibacterial properties were  studied.

We synthesized a   metal-organic framework complex  [Cu₃(L)₃·2DMF]·2DMF modified by isoquinoline. The  structure of the complex was characterized by elemental analysis,  thermogravimetric analysis,   infrared spectroscopy,   X-crystal diffraction and powder X-ray diffraction. The results show that this complex  has a new  topology network structure with {3,4,6}-connectivity, which can selectively separate carbon dioxide from methane and has good adsorption performance for iodine in solution with a   maximum adsorption capacity of 661.84 mg/g.

We designed and synthesized  a novel imidazole ionic liquid crystal compound containing azobenzene group,    its structure was characterized by  ¹H nuclear magnetic resonance,  mass spectrum and infrared spectrum,  and its thermal properties  were characterized by thermogravimetry and differential scanning calorimetry. The results show that compound  remains stable before 190 ℃,  the melting point is 142.96 ℃,  and the liquid crystal range is 124.37—134.04 ℃  upon cooling. The spherical texture of compound can be observed by using polarization microscope,  and confirmed to be the layered structure of compound by X-ray diffraction test. The photo-responsive time of compound  from trans to cis isomerization is 205 s when it is irradiated by ultraviolet light,   the photo-responsive time of compound from cis to trans isomerization is  595 s when it is irradiated by  visible light,  and the degree of trans-cis isomerization reaches 80.4%.