By using a fixed-point index theorem in cone, we investigated the existence of radially k-admissible solutions for a class of k-Hessian equations and obtained several new results for the existence of radially k-admissible solutions of k-Hessian equations.

By using the method of energy analysis, firstly, we considered the wave equation defined on a three-dimensional semi-infinite cylinder. When the spatial variable approached infinity, we proved that the solution of the equation either grew exponentially or decayed exponentially. Secondly, we considered the wave equation defined on the exterior region of the sphere, and proved the alternative result of its solution with radius. Finally, we proved that the alternative theorem was still valid for nonlinear elastic equations.

Firstly, by using the weight function method, we considered how to determine the matching parameters so that the Hilbert-type integral inequalities with non-homogeneous kernel G(x^λ₁y^λ₂)(λ₁λ₂>0) had the best constant factor. Secondly, we gave the necessary and sufficient conditions for the best matching parameter and the discriminant for fast determination of the best constant factor. Finally, we discussed applications of the best matching parameter in the integral operator theory.

By using the theory of matrix factorization and generalized inverse, we gave the calculation formulas of the polar factorization and generalized inverse for universal extended matrix, and deduced  some perturbation bounds for the polar factorization of universal extended matrix. The results show that the method not only keeps the numerical accuracy, but also reduces the calculation amount and storage capacity.

Firstly, by using the basic properties of generalized quadratic matrices, we studied the existence of the nontrivial solution (ρ,σ) for the linear combination ρA+σP of  generalized quadratic matrix A and an idempotent matrix P expressed as A²=αA+βP. The results show that when η²=4β+α²≠0, ρA+σP has only two nontrivial solutions, and the matrix A can be uniquely expressed as a linear combination of idempotent matrix generated by these two nontrivial solutions. Secondly, we discussed the case for nontrivial solution of ρA+σP when η²=4β+α²=0.

The author considered the influence of the complementability of minimal subgroups and Sylow subgroups on the structure of finite groups. Let F be a formation containing all finite supersolvable groups, and G be a finite group, M>1 be a normal subgroup of G with G/M∈F. The author prove if for any minimal subgroup H of M, H∩F*(G^F) is complemented in G, then G∈F.

Firstly, the approximation theorem and basic properties of one-dimensional Bernstein polynomial were introduced, and two-dimensional or even n-dimensional Bernstein polynomials were introduced, and then a three-layer forward neural network was constructed by using the difference values of Bernstein polynomials in the adjacent equidistant points as the back connection weights. Secondly, the operation process of the algorithm was given through coding mechanism, simulation selection, genetic duplication, crossover and mutation. Finally, the error function and fitness function were used to iterate and update the front connection weights and threshold to design a genetic algorithm for the network. The experimental result shows that the algorithm is effective.

By constructing a matrix which was composed of color sets and empty set as the elements, using the distributing method of color sets in advance and specific coloring scheme, we gave the best vertex\|distinguishing Ⅰ-total colorings (VDITC) and the best vertex-distinguishing Ⅵ-total colorings  (VDVITC) of graph mC₈. Thus vertex-distinguishing Ⅰ-total chromatic numbers and the vertex-distinguishing Ⅵ-total chromatic numbers of graph
mC₈ were determined. The results show that the VDITC conjecture and VDVITC conjecture are valid for graph mC₈.

By using the method of analysis and introducing the concepts of (f,g)-type-Ⅰ and (f,g)-pseudo quasi-type-Ⅰ generalized convexity, we studied the problem of robust approximate solutions for a class of multiobjective programming, and obtained the optimality conditions and saddle point theorems of approximate quasi weak efficient solutions for robust multiobjective programming problems.

We considered a class of semi-infinite multi-objective optimization problems with uncertain data. We first introduced a robust approximate Pareto weak efficient solution of the uncertain semi-infinite multi-objective optimization problem. Then, by means of a robust-type subdifferential constraint qualification and a class of generalized convexity assumptions, we gave necessary and sufficient optimality conditions for the robust approximate quasi Pareto weak efficient solution of the multi-objective optimization problem.

We proposed a new inexact nonmonotone smoothing Newton method for the linear weighted second-order cone complementarity problem. Firstly, based on a new smoothing function with parameters, the linear weighted second-order cone complementarity problem was transformed into a system of smooth equations. Secondly, we gave a new inexact nonmonotone smoothing Newton method for solving the equations. Finally, under the assumption of positive semidefinite matrix, we proved the global convergence and local superlinear convergence of the algorithm. Some numerical results show that the algorithm is stable and effective.

By using research methods different from probability spaces, we gave the complete integral convergence of the dependent linear process with random coefficients under the sublinear expectation when C_V|ε|^p<∞. Thus, the complete moment convergence of the dependent linear process with random coefficients in the probability space was extended to the sublinear space.

We considered the problem of the sampling stability of function f in the Sobolev space subset V_α by means of sampling inequality，and gave the characterization condition of the sampling set X={x_j: j∈J}, which proved that the sampling inequality held under this condition, in other words, for any function f∈V_α could be stably reconstructed from the sample {f(x_j): j∈J}. Finally, the explicit expressions of the upper and lower bounds of the sampling inequality were given.

We considered inclusion properties of generalized inverses in an idempotent reflexive *-ring, and proved that a=b if and only if a{1,3}=b{1,3} for two {1,3}-invertible elements a and b of an idempotent reflexive *-ring.

By using the specified method and constraint criteria for local interpolation, and the idea of transferring from part to whole in order to solve the problem efficiently, the general framework of the accumulated average arc length parameterization method was given, and three concrete accumulation average arc length parameterization methods and corresponding numerical algorithms were given under the framework. The objective of the accumulated average arc length parameterization method was to reduce the objective function value of the curve with respect to the smoothness obtained by the traditional method, and make the method have the flexibility to generate the curve satisfying the conditions according to designer’s requirements. Examples show that under the same constraint criterion, the objective function values of global interpolation curves obtained by the method can be less than that corresponding to chord length parameterization and centripetal parameterization.

Aiming at the problems that the fracture occurred randomly, it was difficult to segment the boundary of the broken bone in contact with each other, and the loss of the small broken bone led to the difficulty of the broken bone splicing, we proposed a three-dimensional broken bone repair method based on template-guided and data-driven. Firstly, the neural network was used to train initially and extract the external surface of broken bone, and calculate the external surface features of the broken bone and the template. Secondly, based on the features, the external surface of each broken bone was matched with the bone template. Finally, the fracture boundary was determined according to the distance between the broken bone and the template and the curvature information of the broken bone surface, and the broken bone repair and splicing were realized.
 The experimental results show that the method can effectively segment and splice the broken bone. The segmentation accuracy is 98.44%, the splicing translation error is 9.218 mm, and the splicing rotation error is 1.298°.

Aiming at the problem that dynamic range expansion of brightness did not match saturation in the process of using a single low dynamic range image to generate high dynamic range (HDR) images, which resulted in image whitening after expansion. We proposed a method of generating HDR image from a single image combined with saturation adjustment. This method converted the image into HSV color space. Firstly, the new brightness component was obtained by inverse tone mapping and high-light region correction, and the saturation component was linearly stretched. Secondly, the correlation coefficient between original brightness and saturation was calculated, and then the new saturation component was obtained by fine-tuning the saturation component after stretching through correlation coefficient and new brightness component. Finally, the processed components were fused to get the high dynamic range image. The experimental results show that the method can produce high dynamic range images with bright colors, which is more in line with the visual characteristics of human eyes.

Aiming at the problem of accuracy of vehicle logo recognition, we proposed a vehicle logo recognition algorithm based on improved residual network of ResNet-18 model. Firstly, the residual network was used and improved, and the improved linear correction unit Leaky ReLU activation function was used to replace the original activation function. Secondly, we adjusted the traditional residual network structure, put the batch standardization and activation function before the convolution layer, and reduced the network parameters to speed up the network training. The experimental results show that the recognition accuracy of the improved residual network model is 99.8%.

In order to improve the accuracy of the target tracking and achieve real-time tracking, we proposed a new method based on improved siamese fully convolutional networks: siamese squeeze and excitation fully convolutional networks (Siam-SEFC). Siam-SEFC fused spatial channel information by adding squeeze and excitation networks structure with a small number of parameters, added spatial information for the tracking object, and adjusted the training data scale for variable-scale data enhancement to extract multi-scale features, which effectively improved the accuracy of target tracking. Compared with the three algorithms of MDNet, SENet and DAT, Siam-SEFC has real-time performance while ensuring the accuracy of target tracking. Compared with Siamese-FC, the tracking accuracy of Siam-SEFC is improved by 2.2%, the number of parameters is only increased by 1.01%, and there is no loss of real-time performance, which verifies the effectiveness of the improved scheme.

Aiming at the problem of poor positioning accuracy and real-time in robot servo positioning and grasping, we proposed a feature matching  and  target location algorithm based on Harris-Hist. Firstly, Harris detection algorithm was adopted to extract the image feature points. Secondly, we proposed a new method to define descriptor of feature points. The  gray histogram of pixels in the circular neighborhood of the feature points was calculated to describe the feature points. The feature matching was realized by calculating the distance between the descriptors of each feature point in two images. Finally, according to the matching results, the homography matrix was estimated to locate the target in the scene image. Experimental results show that the  algorithm has fast  matching speed and high positioning accuracy, which can  meet the requirements of positioning accuracy and real-time in robot servo positioning and grasping.

Aiming at the problem that the position scale orientation-scale invariant feature transform (PSO-SIFT) algorithm was difficult to find enough correct corresponding relations for oilfield remote sensing images in the case of obvious differences in gray levels, and it took a long time, we proposed an
image matching algorithm based on improved PSO-SIFT algorithm. Firstly, we adopted the idea of “backing” character block to construct feature descriptors, which reduced the dimension of the feature descriptors. Secondly, we used a matching strategy that combined the bilateral functions for global motion modeling (BF) algorithm and the fast sample consensus (FSC) algorithm to eliminate mismatches from the obtained matching pairs and increase the number of correct matches. Finally, we compared the proposed algorithm with four similar algorithms and the original PSO-SIFT algorithm. The experimental results show that the proposed algorithm is more accurate than similar algorithms. Compared with the original algorithm, the proposed algorithm not only guarantees the accuracy of image matching, but also increases the number of correct matching pairs by about three times, and shortens the matching time by about 20 s.

Aiming at the problem of the loss of features and precision degradation in the analysis process of neural network classifier prediction model based on dimension reduction, we proposed a multi-layer perceptron (MLP) regression prediction model optimized by random forest algorithm. The optimization model added an optimization mechanism between the full connection layer and the logistic regression layer of MLP regression network, the random forest algorithm was used to optimize the state of hidden layer, so as to solve the problem of losing some data features in the process of dimension reduction of neural network. The experimental results on the information data set of the borrowing customers show that the model can guarantee the main features and greatly improve the prediction accuracy, which proves that the model has high practicability in feature engineering.

Aiming at the problems of large delay and low efficiency of industrial Ethernet communication link scheduling, we proposed a real-time periodic message task scheduling method based on an improved firework algorithm (CVFWA). In order to achieve the goal of reducing the network transmission delay. Firstly, the continuous solution space of the traditional firework algorithm was mapped to the discrete solution space of the real-time periodic sequence scheduling problem. Secondly, in order to increase the diversity of population, the coefficient of variation was introduced in the process of Gaussian variation. Finally, the selection strategy based on the median tournament was adopted instead of Euclidean distance selection strategy. Simulation results show that the proposed method can make real-time periodic message sequence complete queue scheduling in the shortest time, effectively reduce network delay and improve global search efficiency.

Aiming at the problem of multi-channel distribution during the handover of high-speed trains, we proposed a channel selection algorithm based on the multi-armed bandit (MAB) model. Firstly, the model was based on the upper-confidence bound (UCB) algorithm, and the algorithm converged to the optimal channel quickly by setting the channel idle difference factor. Secondly, the satisfactory communication probability (SCP) was introduced to measure the communication quality of the mobile train, and the relationship between the communication quality and the bit error rate during the analysis and handover process was analyzed. Finally, the optimal channel selection rate, successful transmission rate and cumulativ
e access loss were used as the evaluation criteria to analyze the performance of the algorithm. The simulation results show that the cumulative access loss of the algorithm is about 18.5% less than the original UCB algorithm, compared with the random selection algorithm and the original UCB algorithm, the successful transmission rate is increased by about 30.2% and 3.3%, and the optimal selection ratio is increased by about 88.3% and 13.5%.

Aiming at the problem that semantic features of source code were not fully used in the process of software defect prediction and class overlap in training data set, we proposed a cross-version software defect deep feature learning method for class overlap. This method used a hybrid nearest neighbor cleaning strategy to alleviate class overlap problem in deep learning semantic features. The test results on open data set PROMISE show that this strategy can improve the performance of software defect prediction based on deep semantic learning, and the classification performance can be improved by 14.8% at most in the median value. The experimental results show that a hybrid nearest neighbor cleaning strategy can be used to alleviate the class overlap problem in the cross-version deep defect prediction problem.

We gave the relativistic expression of Lagrangian function and Hamiltonian of particles in the external field. Let rest mass m₀=0, we further gave the Hamiltonian of photons and the potential energy of photons in the medium. On this basis, we gave the quantum wave equation of free and non-free photons, which could be used to study the quantum dispersion relation and quantum transmission of light in photonic crystals.

We studied adaptive sliding mode synchronization of fractional-order Sprott-F chaotic systems with uncertainties and outer disturbances. By constructing appropriate fractional-order sliding mode surfaces and control laws and adaptive rules, we obtaind two sufficient conditions for adaptive sliding mode synchronization of fractional-order Sprott-F uncertain chaotic systems. The  results show that adaptive sliding mode synchronization of
fractional-order Sprott-F uncertain chaotic systems can be  achieved under certain assumptions.

Using B3LYP method of density functional theory (DFT), the geometry of methionine (Met) was optimized under the gas phase condition at the level of 6-311+G(2df) basis set, and under the PBE0/def2-TZVPP, using the method of time-dependent density functional theory (TDDFT), we obtained the molecular orbital (MO) characteristics, and hole-electron distribution isosurface maps of the chiral conversion reactants of Met and H₂O molecules with 1∶1,1∶2 mixed system in the implicit methanol solvent,  compared and analyszed electronic excitation characteristics with diagrams. The results show that the three qualitative analysis results are basically consistent, and the qualitative results of excitaed state S9 of S-Met-CH₃OH are inconsistent with those of S-Met-CH₃OH+1H₂O and S-Met-CH₃OH+2H₂O, the qualitative results of excited state S7 of S-Met-CH₃OH+2H₂O and S-Met-CH₃OH+1H₂O are inconsistent, and the water chain has a certain effect on the electronic excitation characteristics of S-Met-CH₃OH molecular system.

Firstly, we reviewed the latest research and application progress of several main types of nano-ferrite based core-shell structured composite absorbing materials, introduced the corresponding preparation methods and their advantages and disadvantages. Secondly, we summarized the main problems in the research field of nano-ferrite based core-shell structured composite absorbing materials. Finally, we looked forward to the future research and development direction.

Ferrocene porphyrins with different substituents were designed and synthesized，   thier structures were characterized by ¹H nuclear magnetic resonance (¹H NMR)，ultra-violet-visible (UV-Vis) and infra-red (IR)  spectra，  and the effects of substituents on fluorescence，  electrochemical and Raman spectra of ferrocene porphyrins were discussed. The experimental results  show that the electron donating substituents make the fluorescence spectra of porphyrin red shift,  increase   quantum yield, and have a great influence on   the vibration of benzene ring in Raman spectrum. Porphyrins connected with electron donating substituents are more likely to lose electrons and be oxidized, while those connected with electron withdrawing substituents are on the contary. Therefore,   the spectra and electrochemical properties of ferrocene porphyrins can be controlled  by changing the  substituents around porphyrins.

With the help of auxiliary N-donor ligand 3-(2-methyl-1H-imidazol-1-yl)-5-(5-methyl-1H-imidazo-1-yl)pyridine (MIMIP)，  a pair of novel homochiral coordination polymers (HCPs) [Cd((R)-CBA)(MIMIP)]·H₂O (1-R) and [Cd((S)-CBA)(MIMIP)\]·H₂O (1-S) were  synthesized by solvothermal reaction of  lactic derivatives (R)-4-(1-carboxyethoxy) benzoic acid ((R)-H₂CBA) and (S)-4-(1-carboxyethoxy)benzoic acid ((S)-H₂CBA)  with Cd(Ⅱ) ions, and the powder X-ray diffraction (PXRD), thermostability, UV-Vis absorption spectra and photoluminescent properties of two complexes were tested.   The results show that both 1-R and 1-S crystallized in the monoclinic  P2₁2₁2₁ space group and have 3D supramolecular framework enantiomers. In complex  1-R，  (R)-CBA^2- and MIMIP are linked by Cd(Ⅱ) ions to form two kinds of right-handed helical chains along b-axis，  respectively，   the enantiomeric left-handed helical chains exists in complex  1-S.   (R)/(S)\|CBA^2- and   MIMIP are linked by  Cd(Ⅱ) ions  to form the third helix in complexes 1-R and 1-S along b-axis.

Titanium-doped BiFeO₃  nanoparticles was prepared by using the sol-gel method. The effects of different calcination temperatures on the structure of Ti-BiFeO₃ and the photocatalytic performance were studied.  X-ray diffraction (XRD)，  scanning electron microscopy (SEM)，  energy dispersive spectromentry (EDS)，  ultraviolet visible (UV-Vis)  spectroscopy were used to test and analyze the  phase structure, morphology, atomic ratio and photocatalytic performance of the particles. Taking Rhodamine-B as the target degradation product，  the  photocatalytic performance of Ti-doped BiFeO₃ was studied.  The results show that there are Bi₂Fe₄O₉ phases at different calcination temperatures in Ti-doped BiFeO₃ samples. The calcination temperature can control the content of Bi₂Fe₄O₉.  There are appropriate amount of Bi₂Fe₄O₉ phase in the calcined sample at 650 ℃， which can effectively improve the photocatalytic activity of Ti-doped BiFeO₃ and degradation activity. The degradation efficiency is 85% within 60 min.

By comparing the digestion effects of hydrofluoric acid-nitric acid high pressure tank closed digestion method, hydrofluoric acid-nitric acid-perchloric acid-hydrochloric acid low pressure closed digestion method and hydrofluoric acid-nitric acid-perchloric acid-hydrochloric acid open digestion method on molybdenum ore samples, the low pressure closed digestion method was selected to prepare samples, the inductively coupled plasma mass spectrometry  (ICP-MS) method was used to determine the mass ratio of associated rare elements lithium，  gallium and other 15  rare earth elements in molybdenum ore. Through the analysis of interfering elements, the suitable isotope was selected and the correction coefficients of ¹⁵¹Eu，¹⁵⁷Gd，¹⁵⁹Tb mass spectrum interference was determined. The results show that the standard solution of 20 μg/L rhodium is used as an internal standard solution can effectively inhibit matrix effect and signal dynamic drift in the solution,  the detection limit of the method is  0.001—0.113 μg/g，  and the relative standard deviation （RSD, n=7） is  0.30%—3.92%，  which is verified by standard materials and actual samples. The method is reliable and suitable for the determination of associated lithium，  gallium and rare earth elements in molybdenum ore.