In order to effectively solve large-scale numerical calculation  problems, make full use of machine resources and improve computational efficiency, based on the linear element finite volume scheme, we proposed a parallel scheme suitable for computing on multi-core machines or parallel systems on triangular meshes by domain decomposition method. The results of numerical experiments show that the scheme can not only achieve the best convergence speed, but also have good parallel efficiency on various distorted meshes.

We considered the 3-block varibles convex optimization problem with linear constraints. In the partial parallel splitting algorithm (APCM), on the basis of selecting different step parameters in the correction step,  we proposed a proximal partial parallel splitting method (PAPCM), and proved the convergence of the proposed  algorithm. On the basis of selecing different step parameters in APCM, adding a proximal term to the objective function of a sub-problem, and a new parameter condition was established. Compared with  APCM, the parameter condition of the proposed algorithm was  greatly relaxed, making the algorithm more practical. Numerical results show that, compared with the existing algorithms, the iteration number and computation time of the proposed algorithm are both significantly reduced.

By using the Hopf bifurcation theory, we studied an arbitrary order autocatalysis reaction-diffusion model with saturation effect. Firstly, the stability of the positive equilibrium points for the ordinary differential system was given, and the existence and stability of Hopf bifurcation were given by taking a as the bifurcation parameter. Secondly, the Turing instability caused by  diffusion was established for diffusion system, and the existence of Hopf bifurcation was given. Finally, some numerical simulation examples were used to verify the correctness of the theoretical analysis results.

Firstly, we proved the existence of positive solutions for a class of nonlinear Riemann-Liouville conformable fractional differential equations by using the properties of Green’s function and Guo-Krasnosel’skii’s fixed point theorem, and obtained that there were at least two positive solutions to the problem. Secondly, based on a comparison principle, we proved the existence of extremal solutions to the problem by using the monotone iterative technique and the method of upper and lower solutions.

The Riemann problem of a simplified chemotaxis model with Dirac initial value was discussed  by using phase-plane analysis method and generalized Rankine-Hugoniot conditions. According to the relationship between the initial values q_±,q₀ and 0, we divided the Riemann problem into five cases and obtained the global solutions of the problem constructively. Finally,  numerical simulations were used to verify the correctness of the theoretical results.

We gave the existence of the optimal control function for the initial  boundary value problem of evolution p-Laplace equations by taking the limit of the minimizing sequences of the cost functional. Firstly, we studied the existence and uniqueness of the solution to the problem by using the energy estimate method. Secondly,  we analyzed convergence of the minimizing sequences of the cost functional by using compact estimates and compact imbedding theorem. Finally, we proved  the existence of the the optimal control function.

We studied  the local derivations of Schrodinger algebras  by using the derivation structure of Schrodinger algebras and the theory of solutions of linear equations, and  proved  that all the local derivations of Schrodinger algebras were derivations by calculation.

By using the relevant properties of  matrix factorization and generalized inverse, some calculating formulas of the polar factorization, generalized inverse and perturbation bounds for universal extended matrix were given. The results of numerical examples show that this method can greatly reduce the calculation amount and storage capacity without changing the numerical accuracy.

Let (R,m,k) be Cohen-Macaulay local ring and M,N be finitely generated R modules. Let N∈ΩCM(R) and Ext1≤i≤dR(M,N)=0. We prove that HomR(M,N)∈ΩCM(R) and give some  conditions that the finitely generated module N is  the canonical module.

By using the basic knowledge of elementary number theory, we studied the element characteristics of a class of metacyclic groups, calculated the number of homomorphisms between H and  metacyclic groups and verified that the number of homomorphisms between the two groups satisfied  the conjecture of Asai and Yoshida.

Firstly, we introduced the definition of Gorenstein AC flat dimension for complexes and gave some characterizations of GFacdim M≤n for any complex M. Secondly, we proved that if the complex M had finite Gorenstein AC flat dimension, then M had a complete AC resolution.

The graceful labels of graphs were given by the construction method, and it was proved that these five kinds of graphs were all graceful graphs. When n≤5, were all extremely minimal graceful graph, from which the 15 groups of scale values with the least number of scales for the corresponding length ruler were given.

We considered the r-hued chromatic number of Cartesian product of complete graph K_n and complete bipartite graph K_n□K_m,s. Firstly, we classified the positive integer r according to its different values, and combined with the properties of K_n□K_m,s, we characterized a lower bound of the r-hued chromatic number of the graph. Secondly, we found a specific (k,r)-coloring of K_n□K_m,s, so we characterized an upper bound of the r-hued chromatic number of the graph. Finally, we determined the r-hued chromatic number of K_n□K_m,s.

Aiming at  the problem that when the semantics of the input text were relatively complex, traditional end-to-end models generated questions with incomplete semantics,  we proposed a text encoder architecture based on semantic feature extraction. Firstly, we constructed bidirectional long short-term memory network to obtain  basic contextual information. Secondly,  self-attention mechanism was used to extract global features of semantics and bidirectional convolutional neural network model was used to extract local features of semantics respectively. Finally, we designed a hierarchical structure to merge the features and input their own information  to obtain the final text representation for question generation. Experimental results on the SQuAD dataset show that the question generation based on semantic feature extraction and hierarchical structure are significantly effective, and the results are better than the existing methods. Moreover, semantic feature extraction and hierarchical structure are improved  in each evaluation index of the task.

Aiming at the problem that the deep embedding clustering method only considerd the intra-class relationship and multi-view clust
ering had insufficient feature representation, we proposed a deep embedding clustering method based on inter-class loss and multi-view fusion. The method introduced a new regularization term into the loss function of deep embedding clustering to improve the class discrimination. Firstly, the feature representations of multi-view data were extracted by the auto-encoder, and the feature representations of different views were fused to obtain the public representation. Based on this, the soft allocation distribution and auxiliary target distribution of data were obtained. Secondly, the final clustering result was obtained by jointly optimizing the public representation and cluster allocation. The experimental results on multi-view datasets show that this method can effectively improve the clustering performance.

Aiming at the problems existing in few-shot learning at present, we designed a new network structure and its training method to improve the few-shot learning. The  convolution network and multi-scale slide pooling method were used to enhance feature extraction in the feature embedding part of the network. The main structure  of the networks was the Siamese network  to facilitate learning semantics from small sample data through comparison between samples. The training method  of the framework adopted nested level parameter updating to ensure the stability of convergence. Compared with the common visual model and 
few-shot learning methods, the experimental results  on two classical few-shot learning datasets show that the method significantly improves the  accuracy of  few-shot learning, and  can be used as a solution  under the condition of insufficient sample.

Aiming at the problem of mixed noise in hyperspectral images, we proposd a method based on subspace representation and weighted low-rank tensor regularization to remove mixed noise from hyperspectral images. The subspace representation used the correlation between spectral bands to select an appropriate orthogonal matrix and project the hyperspectral image into a low-dimensional subspace, so that  the proposed algorithm had lower complexity and simplified the denoising process while  removing part of the noise in the image. The denoising process was based on the low-rank tensor extracted from the simplified image. The regularization term of the weighted low-rank tensor was introduced to represent the prior information of the simplified image subspace. A reasonable weighting mechanism was constructed based on the physical meaning of the nuclear norm in the Tucker decomposition, and the intrinsic structural correlation of the hyperspectral image was preserved. We designed  a method based on  iterative minimization to solve the proposed non-convex denoising model. The experimental results on simulated and real datasets show that the proposed subspace representation and weighted low-rank tensor regularization method achieve high denoising performance in both quantitative and qualitative analysis.

Aiming at the problems that the traditional  hierarchical matching algorithm of visual image for mobile robot could only complete rough matching, resulting in low final matching accuracy and long matching time, we proposed a  hierarchical matching algorithm of visual image for mobile robot based on deep reinforcement learning.  Firstly, the strategy network and value network in the deep reinforcement learning network structure were used to guide the floating image to move to the reference image in the correct direction. Secondly, in the process of rough matching, the reward function was designed to realize the rough matching of color features. Finally, on the basis of rough matching, the improved scale invariant feature transformation algorithm was used to extract  the local features of the image to be matched, and the mobile robot visual image was graded matched according to the similarity. The experimental results show that the algorithm can effectively realize the coarse matching and fine matching of images. The stability of feature detection is high under different viewing angles and scales. The matching accuracy is high, the time is short, and the matched image quality is good, which improves the actual application effect of mobile robot.

Aiming at the problem of false segmentation caused by the  significant changes in target size due to glaucomatous lesions in the optic disc and optic cup segmentation task, we proposed a lighter encoder-decoder network and introduced pyramid pooling modules to capture more context features, enrich the scale features and make full use of the global information through  more receptive fields of the network.  A number of comparative experiments and evaluations were carried on  the RIM-ONE v.3 dataset, the experimental results show that the mean intersection over union of optic disc segmentation is 0.908, the Dice coefficient is 0.958, and the mean square error is 0.002. Compared with the existing algorithms, the performance of each index is improved.

By using the definition and properties of the coherence measure, we studied the state ordering of the pure state and the mixed state respectively in a single quantum system, and gave the state ordering results between C_max,C_vmax and C_r,C_I,C_l1 The results show that C_r,C_Ι, and C_H provide the same state ordering for pure states, but this state ordering result is not formed for mixed states. Unlike entanglement measures, the order relationship between two coherence measures in a pure state may not necessarily have the same result for any state.

We proposed an adaptive method for calculating the sensitivity of the system eigenvector. Firstly, the mid-modes to be calculated were determined adaptively. Secondly, an iterative algorithm was constructed to adaptively approximate the unknown low-order modal and high-order modal contributions. Finally, the effectiveness of this proposed method was verified by numerical example. The results show that this method only needs to decompose the shifted stiffness matrix once, and does not need to decompose other matrices.

We studied crushing performance and its analytical formula of the 3D printed Kagome honeycomb thin-walled stiffened structure, which was made of acrylonitrile butadiene styrene (ABS) plastics, and verified the crushing performance of isotropic Kagome honeycombs through experiments. According to the effective elastic modulus formula of orthogonally anisotropic Kagome honeycomb with plane structure, we gave the relationship among elastic modulus, relative density and shape anisotropy ratio of 3D printed Kagome honeycomb structure. Through analytical formulas and experimental results, we obtained the Kagome honeycomb structure with the best crushing performance. The method could be used to guide the design and processing of the stiffened structure of the rocket body.

Sunflower straw was used as a biological template, a novel graded porous structure of nickel oxide doped zinc oxidenanocomposite (Bio NiO/ZnO) was synthesised.  The composition and structure of the composite were characterised by using X-ray diffraction (XRD),  scanning electron microscopy (SEM),  transmission electron microscopy (TEM) and X-ray photoelectron spectroscopy (XPS). The experimental results show that the synthesised Bio NiO/ZnO preserves the original graded porous structure of the sunflower straw material,  which consists of a large number of hexagonal crystalline fibrillated ZnO-type structures of uniform size and shape stacked with spherical particles of nickel oxide in a cubic crystalline aragonal phase structure.  Compared with the undoped ZnO material,   a gas sensor made of Bio NiO/ZnO composite  material has enhanced gas sensitivity to formaldehyde.  The response of the gas sensor to formaldehyde of 10^-4   is 42 at an operating temperature of 240 ℃， the response time and recovery time are 7 s and 6 s respectively. The lower limit of detection is 1.48×10^-4, which is  related to the increased concentration of oxygen vacancies in the complex and the existence  of p-n type heterojunctions between the two phases.

M2-like macrophages induced from human macrophages THP-1 were used as the model, we studied  inhibitory effects of β-1,6-glucan   isolated and purified from Armilla melariella (AAMP-A70) on its polarization and analyzed the role and mechanism of AAMP-A70 in inhibiting DLD-1 proliferation of colon cancer cells by regulating macrophage polarization.   The enzyme linked immunosorbent assay (ELISA) and quantitative real-time PCR (qRT-PCR)  were used to detect the expression of M1-like and M2-like macrophage markers in M2 macrophages induced by THP-1 before and after AAMP-A70 treatment, DLD-1 cells were treated with cell culture medium of each treatment group, and the proliferation of DLD1 cells was detected by MTT assay and crystal violet staining assay, and the expression of apoptosis protein in DLD-1 cells was detected by Western-blot test.  The experimental results show that AAMP-A70 can significantly inhibit the expression of M2-like macrophages markers including VEGF,Arg-1 and TGF-β, and promote the expression of M1-like macrophages markers including TNF-α,IL-1-β and CCR7. The  culture medium of AAMP-A70 treated cells can significantly inhibit the  proliferation of DLD-1 in a concentration-dependent manner.  The supernatant of AAMP-A70 treated cells can induce up regulation of cleaved-PARP and cleaved-Caspase-3 expressed in DLD-1 cells.

Aiming at the problem  of nitrate pollution in water, we synthesized a novel polymer vinylimidazole/dibromodecane/ethylene glycol dimethacrylate (VDE),  its structure was characterized by scanning electron microscopy (SEM),  Fourier transform infrared spectroscopy (FT-IR),  X-ray photoelectron spectroscopy (XPS),  and its optimal dose ratio,  pH value,  adsorption temperature,  and reusability in aqueous solutions containing nitrate were investigated. The results show that the adsorption capacity of nitrate nitrogen on VDE at 15 ℃ and pH=4 is 28.31 mg/g by Langmuir model,  and this adsorption process can reach the equilibrium in 10 min,  and it is in accordance with the quasi-primary and quasi-secondary kinetic fitting model,  and its adsorption capacity can still reach 95.5% of the first use after five adsorption/desorption experiments,  which indicates that this material can effectively  purify  nitrate wastewater with low mass concentration.