By using the estimation of A(p,q) and A_p and the function decomposition method, and with the aid of to the weighted estimation on the L^p spaces, we proved the weighted boundedness of the Riesz potential and Marcinkiewicz integral on mixed Morrey spaces, and obtained the weighted boundedness of BMO commutators of Marcinkiewicz integral.

By using the time-weighted energy method, we discussed  the global existence and the asymptotic behavior of solutions near the constant equilibrium state of  the Cauchy problem on a hyperbolic-parabolic model for vasculogenesis. The results show  that the density, the velocity and the chemical attractant concentration converge to the constant equilibrium state with the decay rate (1+t)^-3/4 in the sense of L² norm when  the pressure P and the far field state ρ of initial density satisfy that bP′(ρ)-aμρ>0.

By using Leray-Schauder fixed-point theorem, we discuss the existence and uniqueness of solutions for the boundary value problems of nonlinear second-order integro-differential equation, where f: ［0,1］×R²→R is continuous, S is a Fredholm type integral operator. Under proper inequality conditions of the nonlinear term f(t,x,y), the existence and uniqueness of solutions of the problem are obtained, and the results are applied to bending elastic beam equation.

By using the upper and lower solution method and monotone iterative method, the author gave the existence of solutions for periodic boundary value problems of a class of second-order iterative differential equations.

By using upper and lower solution method and topological degree theory, the author studies the existence of multiple positive solutions for clamped beam equation with inhomogeneous boundary conditions, where f∈C(［0,1］×［0,∞),［0,∞)), b>0. The results show that when f satisfies certain conditions, there are countable multiple positive solutions for the problem.

By using the method of upper and lower solution and topological degree theory, the author considered the existence and multiplicity of positive solutions of a class of first-order nonlinear boundary value problems. The results show that  there is  a positive number b*, so that there are  at least two positive solutions to the problem when  0<b<b*, there is exactly one positive solution to the problem when b=b*, there is no positive solution to the problem when b>b*, where b is a positive parameter, a∈C(［0,1］,［0,∞)) and is not always 0 on any subinterval of ［0,1］, f∈C(［0,+∞),［0,+∞)).

Firstly, we proved the existence of  traveling wave solutions for Klein-Gordon equations with complex nonlinear source terms by using the mountain pass lemma. Secondly, we proved that the  traveling wave solution of the equation had asymptotic  stability  by using the perturbation function method and the weighted  energy estimate method under the initial conditions.

The author considered  nonexistence of global solutions to a class of dissipative generalized Tricomi equations with nonlinear memory terms of derivative type and variable coefficients. By constructing energy functionals and using Bessel equations and iterative techniques, the author gave the result of blow-up of energy solutions to the Cauchy problem in the subcritical case. Furthermore, the author gave the nonlocal effect of nonlinear memory terms of derivative type on the solution of Cauchy problem and the estimation of the lifespan for the solutions.

Using the properties of determinant, firstly, we gave the normalized Laplacian and normalized signless Laplacian characteristic polynomials based on  the characteristic polynomial of the Randic matrix of a graph G. Secondly, we gave the characteristic polynomials of Randic matrix, normalized Laplacian matrix and normalized signless Laplacian matrix by means of the characteristic polynomials of the induced subgraphs. Finally, we gave the characteristic polynomial of the Middle graph of a graph G.

Using exponential  pair theory, we discussed the  mean value problem of a class of general arithmetic functions, and gave an asymptotic formula of  for a class of arithmetic functions f.

We considered  the pricing of American put options under  regime-switching model. Firstly, we designed a semi-implicit difference scheme to solve this kind of option pricing problem according to the characteristics of the problem. Secondly, based on the structure of discretized nonlinear systems, we constructed the projection and contraction methods for solving discretized systems. Finally, we verified the correctness and effectiveness of the algorithm through numerical experiments.

Aiming at the problem  of the imperfect tagging mechanism in the open source npm (node package manager) community, we proposed a method to automatically recommend tags for open source third-party library npm packages. Firstly,  according to the association relationship between existing tags in the npm community, the tags were clustered  and a tag library was  established  while solving the problem of tag synonyms. Secondly,  the word vector technology was used to calculate the semantic correlation degree between the Readme document of the npm package and the tags in the tag library. Finally, the tags were sorted according to  the degree of correlation to generate a tag recommendation list and complete the tag recommendation. The experimental results show that this method can effectively recommend tags for npm packages, and the accuracy rate of Recall@3 is 49.1%, Recall@5 is 56.3%, and Recall@10 is 66.9%.

Aiming at the problem that the traditional recurrent neural network (RNN) structure in  image Chinese caption was not conducive to long sentence generation and lacked detailed semantic information, we proposed a Transformer multi-head attention (MHA) network, which  fused the coarse-grained global features and fine-grained regional target entity features.  Through the fusion of multi-scale features,  the method made it easier for image attention to focus on fine-grained target regions and an image representation with more fine-grained semantic features was obtained, thus effectively improving image caption. A variety of evaluation indicators were used for verification on the ICC dataset, the results show that the model achieves better image caption effects in all indicators.

Firstly, aiming at the problem of low efficiency of traditional ontology construction methods, especially large-scale ontology construction methods, we provided  a fast ontology construction method based on XML Schema partition. Secondly, taking the Web service schema of  open geospatial consortium standard as the research object, we  analyzed the mapping rule generation between XML Schema and Web ontology language model, ontology model construction, ontology instance generation, instance verification and rule feedback technology. Finally, the effectiveness of the method was verified by the Web coverage service schema transformation experiment.

Aiming at the problem of multi\|unmanned aerial vehicle (multi-UAV) task allocation, we proposed a multi-UAV task assignment method based on adaptive salps swarm algorithm. On the basis of the classic salps swarm algorithm, the leader’s position updating formula was redesigned to improve the defect that salps swarm algorithm was easy to fall into local optimality. At the same time, adaptive operators were added during  iterative process of the algorithm to dynamically adjust the number of leaders and followers, so as  to improve the global search  in the early stage and the ability to jump out of local extremes in the later stage. Through the comparative experiments with genetic algorithm, particle swarm optimization algorithm and the classical salps swarm algorithm, the experimental results show that the proposed algorithm has better effect on solving the problem of multi-UAV task assignment, and has better adaptability and convergence.

Aiming at the problems that how to fuse the rich information of multi-views into the consensus graph and avoid the sub-optimal performance caused by the spectral embedding in the subsequent processing, we proposed a multi-view clustering algorithm based on diversity consensus spectral embedding learning. In order to learn the consensus graph better, the algorithm automatically learnt the consensus spectral embedding matrix and the discrete clustering label matrix under the consideration of the diversity of views. By comparing with other algorithms on real data sets, the superiority of the proposed algorithm in improving clustering performance was proved.

Aiming at the problem that most traditional methods for multidimensional time series analysis relied on manually establishing temporal dependencies to explore the  implicit rules  in historical data, we proposed  an autoregressive neural network method. Firstly, the neural network composed of convolution neural network (CNN) and bidirectional long short-term memory (LSTM) was used to capture the complex dependencies existing in multidimensional input features and time series, and the linear relationship was extracted by combining the traditional autoregressive method. Secondly,  compared with several classical models on two datasets in different domains, the experimental results showed that the model had the best prediction performance and could  successfully capture the repeated patterns in the data. Finally, the  ablation experiments verified the efficiency and stability of the model framework.

Aiming at the problem of the loss of semantic information in the feature extraction process of U-shaped network, which affected the accuracy of liver image segmentation, we  proposed a liver image segmentation method based on multi-scale feature fusion, introducing embedded spatial attention and improved channel attention. Firstly,  multi-scale convolution modules were used  to extract semantic information of different scales and stitch them together in the encoding stage of the network. Secondly,  spatial attention and improved channel attention were introduced into the whole network model to strengthen the weight of meaningful semantic information from the perspectives of spatial and channel domains. Finally, the liver segmentation results were output through a convolutional layer. The experimental results show that the segmentation method has a better segmentation effect on the liver image data set, improves the liver segmentation accuracy, and effectively improves the difficulty of small-area liver segmentation.

Aiming at the problem of low  embedding rate of dynamic graph software watermarking data,  we proposed a new dynamic graph software watermarking algorithm: enhanced dynamic graph watermarking algorithm. The algorithm combined dynamic graph watermarking with static data watermarking, by adding a data field to each node of the watermarking graph structure to store watermarking information,  the watermarking protection was not affected by the watermarking graph structure coding. The graph structure could be  randomly selected to  generate  intermediate code instead of directly generating the target code, so that the algorithm could support watermarking protection for software developed in multiple languages. The experimental results show that the enhanced dynamic graph software watermarking algorithm has higher data embedding rate than conventional dynamic graph watermarking algorithm, and has higher invisibility, anti-attack ability and robustness than static data watermarking algorithm.

Aiming at the problem of network anomaly cause analysis in communication networks, we proposed  a method of alarm data feature analysis based on decision trees.  Firstly, the alarm data generated by network devices were mostly untagged data, and the alarm data was analyzed based on the correlation analysis of geographical and temporal features to obtain root  information and add tags, and  then the  alarm data  features were multi-dimensional. Secondly, the importance of various features and their impact on accuracy were analyzed by the decision tree method, and  the computational burden on time was reduced by pruning.  The experimental results of alarm data in each region show that the alarm compression rate is about 70% and 90% after pre-processing and correlation analysis, respectively. The impact of alarm object type and alarm logic classification features on network anomalies is stable, and  the importance degree is above 0.25, among them,  the root alarm mostly belongs to communication alarm in the alarm logic classification. This method can help network managers to identify the main alarm data features to a certain extent, and  recover the network first according to  the data features.

Aiming at the problem that the hybrid Gaussian model using the traditional expectation-maximum algorithm for parameter estimation was too dependent on the initial probability density center for the final clustering effect, we proposed an improved expectation-maximum  algorithm based on the fuzzy C-means algorithm for parameter initialization. The  experimental results show that compared with the traditional unsupervised clustering algorithms (the fuzzy C-means algorithm, the K-means algorithm and the unmodified expectation-maximum algorithm),  the improved expectation-maximum algorithm has better clustering performance metrice and  better global clustering effect than  the traditional clustering algorithm in a practical user knowledge level clustering task.

Three schemes were used to study the adaptive sliding mode synchronization of financial uncertain fractional-order chaotic systems. Three sufficient conditions for financial uncertain fractional-order chaotic systems to achieve sliding mode synchronization were obtained according to the fractional-order sliding mode control theory. The three control schemes were compared, and the obtained conclusions were verified.

Taking  JSM-7900F type field emission scanning electron microscope as an example, the application of secondary electron and backscattered electron in the morphology characterization was discussed, three kinds of probes equipped with this instrument were used to observe the morphology of nano-scale samples by optimizing experimental conditions, and the influencing factors of various experimental conditions were analyzed and discussed. The results show that the backscattered detector combined with electron beam deceleration mode can be used to image several nanometers of particle on the glass surface, the signal-to-noise ratio of image is high, and the imaging effect is better than that of the high-resolution mode, that is, the upper electron probe, which expands the application of backscattered electron in high-resolution imaging.

In order to enhance the photochromic effect of polyacid composites,   a protonated complex  film was prepared by combining polypyrrole with phosphomolybdic acid. The structure,  photochromic properties and discoloration mechanism were studied by atomic force microscopy,  Fourier transform infrared spectroscopy,  X-ray photoelectron spectroscopy and ultraviolet-visible absorption spectroscopy. The results show that phosphomolybdic acid maintains a stable Keggin structure in the complex film,  and the basic structures of phosphomolybdic acid and polypyrrole are not destroyed. The interaction between active group of polypyrrole and phosphomolybdic acid through non chemical bond lactam bond promotes the protonation,  improves the photochromic properties and broadens the light absorption range of the complex film. Under visible light irradiation,  the colorless and transparent polypyrrole and phosphomolybdic acid  complex film turns blue,  showing strong photochromic response. The discolored material is heated in air, showing good reversibility.  The appearance of MO⁵⁺ in X-ray photoelectron spectroscopy after discoloration shows that there is a photoreduction reaction between phosphomolybdic acid particles and polypyrrole matrix,  and the photochromic process proceeds according to the proton transfer mechanism.

We used molecular dynamics (MD) method based on OPLS-AA (optimized potentials for liquid simulations all atom) force field to investigate the hydrophobic properties of cysteine-rich protein from soybean and  the weak interactions between protein and solvent,  and   studied  the free energy changes of the protein at different λ from the aspects of  thermodynamics and  dynamics. The results show that the cysteine has a decisive effect on the protein properties,  and the solvent  mainly affects  the protein conformations. 

In order to clarify the relationship between the resistance to root rot of Panax ginseng and the activities of antioxidant and secondary metabolism related enzymes,  fresh P.ginseng was used as the material to conduct artificial infection with Fusarium solani to study the changes of physiological and biochemical indexes of P.ginseng after infection treatment. The experimental results show that the activities of cell wall degrading enzymes in the bacterial invasion group are basically higher than those of the blank control group,  and the activity of polygalacturonase (PG) is the highest. The pectinases that play the main roles are PG and polymethylgalacturonase (PMG). The activities of superoxide dismutase (SOD) and catalase (CAT) in the bacterial invasion group reach the peak at 14 d,  and the activity of peroxidase (POD) in the bacterial invasion group reach the peak at 28 d,  indicating that P.ginseng increased the activity of plant defense enzymes in order to resist bacterial invasion. The activities of phenylalanine ammonia-lyase (PAL) and polyphenol oxidase (PPO) in the bacterial invasion group are higher than those in the control group,  indicating that the invasion of pathogenic bacteria may induce the increase of PPO and PAL activities. The mass molar concentration of malondialdehyde (MDA)  in the bacterial invasion group is lower than that in the control group,  indicating that P.ginseng can inhibit the invasion of pathogenic bacteria. The mass fraction of soluble sugar  in the pathogen invasion group is always higher than that in the control group,  which may be a self-protective reaction of P.ginseng against pathogen invasion.