Let R be an associative ring with an identity, and let R=Mn(R) be the ring of all n×n matrices over R. For 1≤r Related Articles | Metrics

We considered a class  of 3-ary algebra: the semi-associative 3-algebra, which did not satisfy completely skew-symmetric and associative law, studied  the derivation structure and centroid structure of semi-associative 3-algebras, and  proved that for any m-dimensional semi-associative 3-algebra A with dim A≤6, the derived algebra A¹ was contained in the center Z(A).

Firstly, by using group theory and congruence theory, the author calculated the number of endomorphisms and automorphisms between a class of non commutative inner cyclic groups, and gave the quantity relation of the number of homomorphisms from such inner cyclic groups to finite groups. Secondly, the author verified that the conjectures of Asai and Yoshida were true for the above cases.

By using Darboux transformation method, we discussed a class of discrete integrable systems. Starting from a new initial solution, the exact solutions of the equation were given by using Darboux transformation, and then the 1-bell-shaped soliton solution, 1-kink-shaped soliton solution, 2-anti-bell-shaped soliton solution and periodic solutions of the equation were given by choosing the appropriate parameters, and the images of these solutions were given. We analyzed their structures, elastic and inelastic collisions of these solutions through these images.

When the internal nonlinearity and boundary nonlinearity adhered to polynomial growth of arbitrary order as well as the balance condition, and the forcing term was only translation bounded rather than translation compact, we considered the asymptotic behavior of solutions for the non-autonomous classical reaction-diffusion equation with nonlinear boundary condition and weak fading memory. By using the contractive function method and the new prior estimate technique, we proved the existence and gave topology structure of uniform attractors on topological space L²(Ω)×L²_μ(R⁺;L²(Ω)).

We gave the continuous dependence and convergence results of solutions of Brinkman-Forchheimer equations with temperature dependence in porous media on the boundary coefficients by using the method of energy inequality and with the aid of some a priori estimates. The results show that these equations are structurally stable for the boundary coefficients.

Aiming at the problem of the numerical solution of higher order convolution integro-differential equation. Firstly, the discrete numerical scheme of higher order convolution integro-differential equation was constructed by using barycentric rational interpolation collocation method, and the global convergence theorem was given. Secondly, by selecting equidistant nodes and corresponding configuration parameters, the effectiveness of the method was verified by numerical examples.

The lattice Boltzmann method (LBM) was used to study the problem of numerical simulation of the ion-acoustic wave in quantum plasma controlled by KPB (Kadomtsev-Petviashvili-Burgers) equation. The results of propagation and evolution of ion-acoustic wave in KPB equation were obtained.

Let {X_n, n≥1} be a sequence of identically distributed positive negatively superadditive dependent (NSD) random sequence. Under some suitable conditions, by using the central limit theorem of weighted sums and the law of large numbers of NSD random sequence,  and we discuss similar conclusion for the strictly stationary case.

We discussed the convergence and stability by using the fully implicit numerical method—balanced methods for a class of stochastic variable delay differential equations. Firstly, we proved that the numerical solution of the equation converged to the exact solution in 1/2 order mean-square. Secondly, we proved that the method could keep the mean-square stability of the analytical solution. Finally, the correctness of the theoretical results was verified by numerical experiments.

Aiming at the problem of  the position and shape of inverse obstacles with  phaseless far-field data, we proposed  a two-layer gated recurrent unit (GRU) neural network to gated recurrent unit neural network (MGNN) method, and gave the convergence analysis of the proposed  method. Firstly, using the phaseless far-field data and the obstacle boundary curve equation parameters as input and output, through GRU neural network control gate idea and long-term memory function, the network states were selectively updated and the  data characteristics were saved. Secondly, we applied the gradient descent algorithm to update the weights and bias of the model, and  solved the difficulty of  the position and shape of inverse obstacles with phaseless far-field data. Finally,  the effectiveness of the proposed  method was demonstrated by numerical experiments.

Using the idea of the discontinuous Galerkin algorithm, we calculated a class of quasi-periodic scattering problem with a mixture of media and obstacles. The fundamental solution functions and Rayleigh-Bloch expansion were used to approximate behavior of the scattering field in the bounded regions and unbounded regions， respectively. The effectiveness of the algorithm was verified by numerical example.

By coupling the total energy convective upwind and split pressure (E-CUSP) scheme with the WENO-η scheme, we gave a new scheme (E-CUSP-WENO-η） to solve the one-dimensional shock tube problem. The numerical simulation results show that the new scheme is more accurate in capturing contact discontinuities and shock waves, among which the new scheme (E-CUSP-WENO-η(τ^opt₇)) with higher order optimal global smoothness factor has the least numerical dissipation. The coupled new scheme can capture shock wave more steeply, and the calculation results are accurate and stable.

By using the unique continuation of conjugate equations, we discussed the coupled parabolic equations with boundary degeneracy, and gave approximate controllability of the problem. The result shows that for any objective function, there exists a control function such that the solution of the problem can be sufficiently close to the objective function in a finite time.

Aiming at the evaluation index of iris quality was single or too many, we proposed a sequential iris quality evaluation algorithm based on GA-BP neural network. Firstly, the rough quality of iris image was evaluated, and most of the unqualified images with poor quality were screened out. Secondly, we evaluated the fine quality of iris image and selected three important indexes to obtain the index value. Finally, the final evaluation of image quality was carried out by combining BP neural network with precise quality evaluation index. It was verified in JLU-6.0 iris library, and compared with other algorithms, the results show that the algorithm can retain more effective iris images and has higher classification accuracy.

Aiming at the problem that the recognition rate of gender and age using facial features was low, we proposed a new method based on improved high-resoultion network (IHRNet). Firstly, we integrated the MobileNetV3 structure with a small number of parameters and a high recognition rate in IHRNet, and combined with the advantages of multi-scale feature extraction of the high-resolution network, which effectively improved the accuracy of facial feature recognition. Secondly, in order to reduce the risk of overfitting, the network first used the IMDB-WIKI face data set for pre-training, and then loaded the pre-training model for training and testing on the Adience face data set. Finally, compared with three similar algorithms such as ResNet50, HRNet and MobileNetV3. The experimental results show that the accuracy of IHRNet in age and gender recognition is as high as 82% and 95%, respectively, which are an average of 9% and 3% higher than similar algorithms, respectively, and the number of parameters is reduced by 36% compared with the previous one. The effectiveness of the improved algorithm is verified.

We combined the traditional two memory-based collaborative-filtering methods and proposed a data-based personalized mixed recommendation method for GitHub projects. The method could not only calculate the similar users dynamically to ensure the personalized recommendation, but also obtain the recommendation quality comparable to the item-based method with only small scale of similar users. At the same time, the method solved the data sparsity and cold boot problems of the original method in the face of GitHub, a data set of users and projects of an order of magnitude but with low degree of crossover to some extent by establishing inverse table and using K-means classification. By comparing with the
traditional method, we verified the effectiveness and superiority of the proposed method.

In order to realize cooperative control of underwater imitation box fish group, reduce the energy loss caused by the load imbalance among the network nodes, and improve the group endurance, we proposed a load balancing clustering control algorithm based on logical partition. Firstly, local fast clustering was realized to reduce the number of maintenance messages between nodes and the overall cost of the system. Secondly, based on the logical partition strategy within the cluster, it realized multi-regional cooperative control of monitoring, support and reconnaissance, integrated scattered fish schools with minimum response time, optimized the network control system and improved the flexibility of networking. Finally, in the process of maintenance,  the role transformation mechanism of regional nodes was used to realize the network load balance. The effectiveness of the algorithm was verified by simulation clustering experiments, and the feasibility of the algorithm was verified by combining the three indicators of network energy consumption, network life cycle and energy balance.

Aiming at the problem of oscillation caused by excessive selection of learning rate in the learning process of traditional BP neural network, we proposed a new adaptive tuning algorithm for PID (proportional-integral-differential) parameters of BP neural network. BP neural network was used to adjust and optimize PID parameters adaptively, and momentum factor was used to optimize learning rate and increase momentum term to restrain oscillation phenomenon in BP neural network training, so as to accelerate convergence speed. The experimental results show that the proposed algorithm can effectively alleviate the oscillation phenomenon and accelerate the convergence speed of the algorithm.

A genetic algorithm based fuzzy PID (proportional-integral-differential) controller genetic algorithm based fuzzy PID controller (GFPC) was designed to improve the stability of brushless DC motor. GFPC used fuzzy controller to adjust the proportional, integral and differential coefficients of PID, and an improved genetic algorithm was used to optimize the membership function and fuzzy rule of fuzzy controller to improve the control effect of brushless DC motor. The method was tested by contrast experiment. The experimental results show that GFPC has good steady-state performance and dynamic quality, and has stronger adaptive ability and robustness.

Aiming at the problem that the construction of the current metamorphic relationship mostly depended on the tester’s knowledge in the domain of the test program, which had limitations and high cost, we proposed a method of new generating metamorphic relationship. The method combined the construction of the transformation relationship with the gradient descent algorithm, and generated the corresponding transformation relationship by analyzing the numerical relationship between a large number of test cases and their outputs. The experimental results show that the method can effectively reduce the dependence of testers on knowledge in related fields.

Aiming at the problem that traditional convolutional neural network relied heavily on the amount of data, we proposed an image recognition algorithm based on mean iterative threshold segmentation method and convolutional neural network. The image background was filtered by means iterative threshold segmentation method, and a new convolutional neural network was constructed based on AlexNet. Compared with other commonly used convolutional neural networks, the experimental results show that the recognition effect of the proposed algorithm is ideal in image recognition tasks with insufficient samples, and it has higher recognition accuracy, lower recognition error and faster convergence rate than that of other convolutional neural networks.

Aiming at the problem that the cultural shuffled frog leaping algorithm was easy to fall into local optimal solution when solving high-dimensional functions, we proposed a cultural shuffled frog leaping algorithm, which used the individuals in group space and belief space to complete information exchange and global optimization through reception function and influence function. Firstly, belief space individuals searched for better individuals around the superior individuals by spiral updating and random walk. Secondly, the worst individuals in group space balanced the relationship between local optimization and global exploration by learning from different knowledge, so as to improve the accuracy of optimization and speed up convergence of the algorithm. Finally, compared the proposed algorithm with 12 intelligent algorithms, the test results of typical high-dimensional benchmark function show that the algorithm has good convergence accuracy and calculation speed.

Aiming at the problem of the conflict between fine-grained and coarse-grained chunk recognition models in parsing, in order to solve the problem of multiple collocation rules in parsing and reduce the influence of collocation priority changes, we proposed a hierarchical parsing model which combined conditional random field (CRF) with multiple rules. First, CRF algorithm was used to identify the chunk tag sequence of the fine-grained sentence, and then the coarse-grained chunks were identified by combining statistics and multiple rules, and binary and ternary rules of different priorities were introduced into the identified chunks. The model realized the identification of fine-grained and coarse-grained chunks at the same time, which could better serve parsing. On the Chinese TreeBank8.0 corpus, the 5-fold cross-validation method was used for experimental verification. The results show that it is compared with the parsing using only binary and ternary rules, as well as the use of binary rules and CRF, the accuracy of the model is improved by nearly 12%,3%,5%, respectively, which verifies the effectiveness and stability of the model.

Aiming at the problem that the fast image feature region detection was affected by noise and scale space, which resulted in low detection accuracy, large delay and unreliable detection results, the author proposed a fast image feature region detection method based on scale invariant feature transformation. Each pixel in the image was weighted and smoothed by weighted kernel function to realize image denoising. On this basis, image feature points were determined by constructing image Gaussian scale space, low contrast pixels and edge pixels were deleted, and image feature points were quickly extracted and the detection of location of feature points was the image feature region. The simulation results show that the method can achieve fast and comprehensive detection of image feature region with high efficiency and precision.

The geometric structure, electronic structure and optical properties of Fe/Ni mono-doped (co-doped) sphalerite CdS were studied based on the first-principles calculation method. The results show that the band gap is narrowed by Fe/Ni mono-doped (co-doped), more impurty leves appear in the band gap due to (Fe,Ni) co-doped, these impurities are mainly provided by the Fe 3d, Ni 3d and S 3p state electronic mutual hybridization effect. The light absorption intensity of (Fe,Ni) co-doped CdS is much higher than that of mono-doped CdS. The synergistic effect of (Fe,Ni) co-doped can greatly improve the ability of the CdS to visible light and light catalytic activity.

RC sine wave oscillation circuits with different structures were equivalent to LC parallel resonance circuits by changing the parameters of components，and the memristor with nonlinear characteristics was used to replace the Chua’s diode in Chua’s circuits，four equivalent Chua’s memristive chaotic circuits were designed， and the equivalent conditions were given theoretically. The simulation results show that the experimental results are consistent with the results of theoretical analysis and numerical calculation. The circuits are easy to adjust and have better robustness.

Based on the optimized R-threonine (R-Thr) molecular structure, the method of the time-dependent density functional theory (TDDFT) was used to calculate the wave functions of excited states in the process of electronic excitation of R-Thr molecular system in gas phase, implicit H₂O and methanol solvents at the PBE0/def2-TZVP， and the excitation types of valence shell electrons in R-Thr mol-ecular system was studied by identifying the molecular orbital type method. The results show that the implicit solvent environment is more suitable for studying the electronic excitation characteristics of R-Thr molecular system than the gas\|phase environment, and the analysis results of molecular orbital (MO)  type and the Δr index are ideal, most excitation types of excited states are in good agreement with excitatin mode identification.

The redox reaction of anions in zinc ion batteries was tested and analyzed. Taking the MnO₂ as the research object, the cyclic voltammetry, galvanostatic charge-discharge method and ex situ X-ray photoelectron spectroscopy were applied to analyze the redox reaction of oxygen of MnO₂ in water-in-salt electrolyte. The results show that the oxidation reaction of oxygen exists at high potential when using the 30 mol/kg ZnCl₂, but it does not happen in the diluted electrolyte.

A flexible stretchable antenna working at 2.45 GHz was designed based on flexible conductive fabric, and the influence of different stretchable strains on the performance and radiation properties of the proposed flexible fabric antenna were studied. The simulation and measurement results show that the simulated and measured values of return loss are -40,-26 dB respectively at central frequency of 2.45 GHz, and the simulated and measured gain patterns have good consistency at the central frequency.

Expanded graphite was prepared by natural flake graphite as raw material, phosphoric acid and nitric acid as intercalating agent, potassium permanganate as oxidant.  The chitosan/expanded graphite composite adsorbent was prepared by expanded graphite and chitosan in a certain proportion. The chitosan/expanded graphite was characterized by Fourier transform infrared spectroscopy(FT-IR), scanning electron microscopy(SEM), X-ray diffraction(XRD). The effects of adsorption conditions such as the mass ratio of chitosan and expanded graphite, the dosage of adsorbent, the mass concentration of Congo red, and the adsorption time on the adsorption performance of Congo red wastewater by chitosan/expanded graphite were investigated.  The experimental results show that chitosan is successfully combined with expanded graphite, the adsorption performance is best when the mass ratio of chitosan and expanded graphite is 3∶1, the dosage of adsorbent is 1.75 g/L, the mass concentration of Congo red is 250 mg/L, and the adsorption time is 40 min at room temperature. The adsorption process is more in line with Lagergren pseudo-second-order kinetic equation. The experimental data fit well with the Langmuir isotherm adsorption model. The adsorption process of Congo red on chitosan/expanded graphite is monolayer adsorption.

The biomass charcoal from poplar leaves was added to the aeolian sandy soil with simulated fertilization， we studied effects of biomass charcoal from poplar leaves on distribution of nitrogen forms in aeolian sandy soil. The results show that compared with the traditional fertilization mode and soil testing formula fertilization mode, the prepared biomass charcoal can increase the mass ratios of ammonium nitrogen, nitrate nitrogen, available nitrogen and total nitrogen in aeolian sandy soil. The mass ratios of ammonium nitrogen, nitrate nitrogen and total nitrogen are directly proportional to the amount of biomass charcoal added in the growth cycle of maize. When the mass fraction of biomass charcoal addition is 0.2%, it is fully mixed with the soil, the mass ratios of ammonium nitrogen, nitrate nitrogen and total nitrogen are 36.43 mg/kg,35.02 mg/kg,5.76 g/kg, which are the highest in the traditional fertilization mode, when the mass fraction of biomass charcoal addition is 0.5%, the mass ratio of available nitrogen is the highest under the soil testing formula fertilization mode, and the mass ratio is 79.52 mg/kg.

Using static experiment method, considering the research cost and environmental protection requirements, six kinds of low-cost and biodegradable leaching agents of citric acid, oxalic acid, fulvic acid, water, rhamnolipid, and tartaric acid were elected to leach and repair high mass ratio Cr contaminated soil. Firstly, the effects of different aging time of Cr in soil on the leaching efficiency were investigated. Secondly, the leaching agent was screened and the leaching conditions were optimized. Finally, a variety of mixed leaching combinations were investigated to determine the best leaching agent combinations. The results show that the Cr aging time has little effects on the total Cr removal rates, but  has significant effects on the removal rates of Cr（Ⅵ）. Different leaching agents have different leaching effects on total Cr and Cr（Ⅵ）, but oxalic acid and citric acid can effectively remove total Cr and Cr（Ⅵ）. The optimal leaching condition of removing total Cr and Cr（Ⅵ）is 0.5 mol/L of oxalic acid or citric acid, m(solid)∶V(liquid)=1∶10, and leaching one time. Under the optimal leaching condition, the removal effect on Cr in  soil is better.