Based on the properties of the matrix structure, we used the block matrix techniques to give the specific form for the Moore-Penrose generalized inverse of the adjacency matrix of caterpillar trees with any number of vertices and any diameter length, which provided theoretical support for further study of the algebraic properties of caterpillar trees.

By using graph transformation, we give the lower bounds for the Mostar index and the weighted Mostar index of unicyclic graphs  when the cycle length of unicyclic graphs is even, and characterize the extremal graphs that achieve the lower bounds.

Based on the generalized strictly α-diagonally dominant matrices and its related concepts and properties, by dividing the matrix index set, forming corresponding positive diagonal factors and setting new parameters, we gave  a set of practical new criteria for nonsingular H-matrices,  expanding the judgment range of nonsingular H-matrices. Finally, numerical examples were used to illustrate the effectiveness of the new criterion.

Let R<M be a trivial ring extension, where R be a ring, M be an (R,R)-bimodule. We prove that (X,α) is a strongly Ding projective left R<M-module，and coker(α) is a strongly Ding projective left R-module under certain conditions.

Let (A,B) be a duality pair in the category of modules. Firstly, the concepts of Cartan-Eilenberg-A and Cartan-Eilenberg-B complexes are introduced. Secondly, it is proven that (C-E(A),C-E(B)) is a duality pair in the category of complexes, where C-E(A) and C-E(B) denote the class of Cartan-Eilenberg-A complexes and Cartan-Eilenberg-B complexes, respectively. Finally, the application of duality pairs to complexes is given.

A class of measures is considered on homogeneous trees whose distance to the origin is exponentially decreasing. The definitions of Lebesgue spaces, BMO (bounded mean oscillation) spaces, maximal operators and their commutators for this type of measure on homogeneous trees are given. By using the decomposition theory of homogeneous trees, the boundedness of maximal operators and their commutators in Lebesgue spaces and some equivalent properties are proved.

By using  the eigenvalue theory of differential equations, Poincare-Bendixson ring theorem and Hopf bifurcation theory, we  analyzed the predator-prey model of Holling-Ⅱ with fear effect and modification, gave the stability of the equilibrium point of the model, and proved that the model had stable limit cycles and Hopf bifurcations appeared at coexistence equilibrium points. The results show that the fear effect and the modified Holling-Ⅱ function have significant effects on the stability of the system.

We considered a platelet derived growth factor (PDGF) driven reaction-diffusion glioma mathematical model. Firstly, we gave the stability analysis of the equilibrium point for the ordinary differential system. We took the  rate m generated by chemoattractant as  the bifurcation parameter, gave the existence of the Hopf bifurcation near the positive equilibrium point, and then gave a formula to judge the stability of the periodic solution produced by the Hopf bifurcation through the gauge type theory and the central manifold theorem. Secondly, for reaction-diffusion systems, we obtained that the equilibrium point  did not occur Turing instability  when diffusion was involved. Finally, the  theoretical analysis results were verified through numerical simulation. The results show that the rate m generated by chemoattractant can be used to distinguish the types of glioma.

Using the Hopf bifurcation theory, we studied a class of Leslie-Gower predator-prey models with time delay. Firstly, taking time delay as the bifurcation parameter, we discussed the stability of the positive equilibrium point of the model and the existence of Hopf bifurcation. Secondly, according to the normal form theory and center manifold theorem for partial differential equation, we derived the direction of Hopf bifurcation and the stability of bifurcation periodic solutions. Finally, we used MATLAB for numerical simulations.

The critical point theory and the variational method were used to study the existence of the solution for the Caputo type fractional differential equation with the Sturm-Liouville boundary condition in Banach space. By defining the appropriate fractional derivative space, the existence of the solution to the boundary value problem of fractional differential equation was transformed into finding the critical point defined as the corresponding functional in a certain space, and a series of unbounded generalized solutions to the boundary value problem were obtained.

We proved  the uniqueness and existence of solutions for a class of singular boundary value problems of fractional impulsive differential equations with p-Laplacian operators by using Banach contraction mapping principle and Krsnoasel’skii fixed point theorem.

By using the continuation theorem, we discussed a class of periodic boundary value problems for Caputo-Hadamard type fractional implicit differential equations, obtained the existence result of solutions, and provided specific example for explanation.

One of the essence of  bounded operators  is that the  image set must be bounded when the original  image set is bounded, we propose  the inverse problem of operator boundedness: how to determine the boundedness of   the original image set of an operator T  when its image set is bounded. We first introduce the concept of operator reverse boundedness, and then use weight  function method and real analysis techniques to discuss  the equivalent parametric conditions for  reverse boundedness of integral operators, and give  a construction theorem for reverse boundedness of  integral operators. Finally, some special cases are given.

By using k-order Poisson dependent-driven random coefficient mixed thinning integer-valued autoregressive model, we analyzed data with the counting of elements of variable character, gave  statistical properties of the model and conditional maximum likelihood estimation of parameters, and proved the asymptotic normality of the estimators. The numerical simulation results show that as the sample size increases, the parameter estimation gradually converges to the true value. The actual data analysis results  show  that the effectiveness of the proposed model.

Firstly, we uesd the quadratic B-spline finite element method to solve the Fisher-Kolmogorov (FK) equation, and proved the stability and convergence of solutions for the semi-discrete scheme and the fully discrete scheme. Secondly, the time variable was discretized by using the Crank-Nicolson method and the convergence order of the approximate solution was O((Δt)²+h³). Finally, the numerical example verified theoretical analysis results and the effectiveness of the B-spline finite element method.

Aiming at the problems of dense detection targets, occlusion, missed detection caused by inconsistent morphology in various regions and weak generalization ability of the model in the wheat ear dataset, we proposed a wheat ear detection algorithm based on improved YOLOv7. Firstly, we introducd a mixed attention mechanism into the backbone feature extraction network of YOLOv7 network to strengthen the extraction of location features and alleviate the missed detection problem caused by dense detection targets. Secondly, switchable atrous convolution (SAC) which could combine different sizes was introduced into the backbone feature extraction network, and the feature information of different scales was extracted by increasing the receptive field, which could effectively improve the missed detection problem caused by occlusion. Finally, an incremental learning module example vector correction (EVC) was introduced into the feature fusion part to improve the robustness and generalization ability of the model. The experimental results show that the average target detection accuracy of the improved wheat ear recognition algorithm in the global wheat ear dataset is 2.11 percentage points  higher than that of the original YOLOv7.

In order to effectively solve  the problem of facial super-resolution feature recovery in complex environments, we proposed a novel facial super-resolution network. By integrating 3D rendering prior knowledge and a dual attention mechanism, the network enhanced the understanding of the facial spatial position and overall structure while improving the ability to recover detailed information. The experimental results on the CelebAMask-HQ dataset show that  the proposed algorithm achieves peak signal-to-noise ratio and  structural similarity of 28.76 dB  and  0.827 5 for  downsampled faces magnified by 4 times, and  26.29 dB and 0.754 9 for downsampled faces magnified by 8 times.   Compared with the similar SAM3D algorithm, the proposed algorithm improves the peak signal-to-noise ratio and  structural similarity by  4.09 and 1.93 percentage points when dealing with  4 times  downsampling, and by 2.02 and 4.54 percentage points  when dealing with 8 times downsampling, respectively.  This proves the superiority of the proposed  algorithm and  also indicates that  facial super-resolution recovery can achieve more realistic and clear visual effects in practical applications.

We proposed a new classification of rock thin section images based on mixture of expert model by using  five common  rock thin sections as the research object to construct a dataset. The model learned the characteristics of each rock image from the thin section images and classified them. Firstly, multiple image classification models based on convolutional neural network(CNN) and Transformer (such as ResNet50, MobileNetV3, InceptionV3, DeiT, etc.) were used to train the data. Secondly, models with better performance were selected,  a mixture of experts model was built to obtain the final prediction result. The  ACC and AUC of lithology recognition reached 85.33% and 96.69% on the validation set and 87.16% and 96.75% on the test set. Finally, by combining a mixture of experts model with  multiple models, combining  advantage of each model,  balancing their contributions between each model, we improved the accuracy and robustness of classification results, making the obtained classification results more reliable and stable.

Aiming at the limitation of the simplifying the processing of homophily relational classifiers based on first-order Markov assumption, when constructing the class vector and reference vector in the class-distribution relational neighbor classifier, we introduced the activation spreading algorithm of local graph ranking, combined with the relaxation labeling collective inference method. By appropriately expanding the range of neighboring nodes during classification, we increased the homophily of nodes to be classified in network data, thereby reducing the error rate of classification. The comparative experimental results show that this method expands the  neighborhood of nodes to be classified, and has good classification accuracy  on network data.

Aiming at the problem of low efficiency and failure of dependent task offloading  in the cloud-edge-end architecture, we proposed a two-stage  dependent task offloading algorithm based on preference and virtual fitness. In the first stage, based on the proposed two-dimensional offloading preference factor,  direct offloading decisions were made for some sub-tasks of the dependent tasks, thus effectively reducing the size of the initial population of the genetic algorithm. In the second stage, we proposed a heuristic crossover method based on virtual fitness  to improve the crossover operator of  the fast non-dominated sorting genetic algorithm Ⅲ(NSGA-Ⅲ) based on reference points, which preserved the diversity of population and improved the convergence speed of the algorithm. Finally, we used  the improved algorithm to search for the optimal offloading decision set  for the subtasks of all dependent tasks. The experimental results show that compared with other algorithms, the proposed algorithm 
optimizes task completion time, task energy consumption and edge cloud cluster cost by 10.2%—18.3% on average and reduces the task failure rate by 10.7%—25.6% on average.

Aiming at  the problems that graph attention networks were weak in handling noisy and temporal data, as well as gradient explosion and oversmoothing after stacking multiple layers, we proposed an improved graph attention network model. Firstly, we used  the Squeeze-and-Excitation module to pay different levels of attention to the feature information of the sample input data to enhance the model’s ability to handle noise. Secondly, the temporal sequence of the data was extracted by using the multi-head attention mechanism, which weighted and summed each sequence in the sequence data relative to the other sequences. Thirdly,  the node features extracted from the graph attention network were spliced with the degree centrality of the nodes to obtain the local features of the nodes, and the global features of the nodes were extracted by using global average pooling. Finally, the two were fused to obtain the final feature representation of the nodes, which enhanced the representational ability of the model. In order to verify the effectiveness of the improved graph attention network, the improved graph attention network model was compared with LSTM, GRU and GGNN models. The experimental results show that the prediction effect of the model has been effectively improved, with higher prediction accuracy.

Aiming at the problem of low accuracy and poor robustness of speech recognition in complex noise environment, we proposed  a speech recognition method based on Mel cepstrum fusion feature of increasing and decreasing residuals.  This method first used the increase and decrease component method to screen the key speech features, and then mapped them to the Mel domain-residual domain spatial coordinate system to generate the increase and decrease residual Mel cepstral coefficients. Finally, these fusion features were used to train the end-to-end model. The experimental results show that the proposed method significantly improves the  accuracy and performance of speech recognition under different noise types and signal-to-noise ratio conditions. Under the low signal-to-noise ratio condition of -5 dB, the speech recognition accuracy reaches 73.13%, while the average speech 
recognition accuracy under other noise conditions reaches 88.67%, which fully proves the effectiveness and robustness of the proposed method.

Aiming at the problems of missing key information and difficult control of content in the original text during the generation process of existing generative summary models， we proposed a generative text summarization method guided by extraction methods. This method first obtained key sentences from the original text through an extraction model, and then adopted dual encoding strategy to encode key sentences and news text respectively, so that key information was guided to generate a summary during the decoding process. Finally, expert network was introduced to screen information during decoding to further guide the  generation of summary. The experimental results on CNN/Daily Mail and XSum datasets show that the proposed model can effectively improve the performance of abstractive text summarization. This method improves the content of key information in the original text for generating summary to a certain extent, while alleviating the problem of  difficult  control of generated content.

In order to solve the problem of cementing quality evaluation, we proposed a cementing quality evaluation method based on CNN-SVM and integrated learning. Firstly, the method adopted improvement measures such as reducing the number of network layers, adding multi-scale convolutional layers, and embedding convolutional attention modules for the DenseNet model to improve the training speed and evaluation accuracy of the model. Secondly, the InceptionV1 module and dilated convolution were used to construct an Inception-DCNN model with relatively small model complexity and relatively high evaluation accuracy. Thirdly，three classic convolutional neural network models (ResNet50, MobileNetV3-Small and GhostNet) were selected. By utilizing the powerful feature extraction capabilities of convolutional neural networks and the structural risk minimization capabilities of support vector machines, the above  models were combined with a support vector machine to synthesize a new CNN-SVM model to improve the generalization ability of the model. Finally, the Bagging method was used to integrate the five new CNN-SVM models into a strong learner, thereby improving the accuracy of the evaluation results and enhancing the anti-interference ability of the model. The experimental results show that the accuracy of  the method for 3 types of evaluation samples in the test set is 97.69%, which is 1—9 percentage points higher than that of  a single model and other methods, thus verifying  the feasibility of using  methods based on CNN-SVM and ensemble learning for cementing  quality evaluation.

Based on the chaotic Rulkov neuron model, the two-parameter bifurcation analysis of the coupled Rulkov neuron model was carried out through numerical calculations  by considering the situation of two identical neurons under electrical coupling, and the bifurcation mode was further validated by using the one-parameter bifurcation diagrams and the maximum Lyapunov exponent diagrams. The results show that the coupled Rulkov neuron model exhibits three classic chaotic paths: period-doubling bifurcation path, quasi-periodic bifurcation path, and intermittency path. The model presents a period-adding bifurcation phenomena accompanied by chaos. The coupled Rulkov neurons model exhibits more complex dynamical behavior as the coupling strength increases.

Fourier transform infrared spectroscopy was used to analyze five groups of light-roasted coffee bean samples from different producing areas and different altitudes. The main components of the samples were analyzed according to the infrared spectral characteristic peaks of functional groups. In order to further analyze the compositional differences of the five groups of samples， the original spectra were subjected to second-order derivative processing. The average deviation analysis method was established based on the theory of cluster analysis, and the average deviation between the five groups of samples was calculated and analyzed. The results show that the infrared spectral characteristic peaks of the five groups of samples have similar peak shapes, that is, the main components are the same, the average deviation from the infrared spectrum is positively correlated with the altitude difference of the producing area. The research results provide identification basis for analyzing producing areas and the altitude of the coffee bean, and provide certain reference value for the study of infrared spectrum.

In order to investigate the effects of Ag doping concentration on the photoelectric performance of In₂O₃ thin films, such as bandgap width, optical switching ratio and optical detectivity, Ag doped In₂O₃ (In₂O₃∶Ag) thin films with different concentrations were prepared by magnetron sputtering method on quartz (SiO₂) substrate. The crystal structure, elemental content and valence state, surface morphology, bandgap width and photoelectric performance of In₂O₃∶Ag thin films were analyzed by using X-ray diffraction, X-ray photoelectron spectroscopy, scanning electron microscopy and ultraviolet-visible spectrophotometer. The results show that with the increase of Ag doping concentration, the transmittance of In₂O₃∶Ag thin films gradually decreases, the bandgap width decreases from 2.47 eV to 2.08 eV, and the optical detectivity and optical switching ratio increase. The spectral response range increases with the increase of doping concentration.

Using  5,5′-(5,5-half dioxide  [b,d] thiophene-3,7-digroup) diphthalic acid (H₄DTPA) as an organic ligand,  we constructed a new metal-organic framework compound [NH₂(CH₃)₂][Zn₃(DTPA)₂]xsolvent  through solvothermal synthesis method. This compound is a novel topological network structure with a  {4,8}-connected anionic framework, with good chemical and thermal stability, and good selective  adsorption performance for organic dye methylene blue (MB).

Aiming at the problem that   the visible light absorption and active site exposure capacity of graphitic phase carbon nitride (g-C₃N₄ or CN) were limited,  and the photogenerated carriers were easy to recombine,  which  limited the activity of CN-based photocatalytic materials. A new type of diphenylaminourea doped CN (BCN) photocatalyst was  prepared by a  one-step thermal polymerization method using urea as a precursor and diphenylaminourea as dopant. The BCN photocatalyst was characterized by using nitrogen adsorption-desorption test,  Fourier-transform infrared spectroscopy (FT-IR), X-ray diffraction (XRD), ultraviolet-visible spectroscopy (UV\|Vis DRS), photolumine-scence spectroscopy (PL),  electrochemical impedance spectroscopy (EIS). The results show that compared with CN, the BCN photocatalyst can significantly improve visible-light absorption capacity and separation efficiency of photogenerated electron-hole pair,  and the specific surface area is about twice that of the original.   The hydrogen production rate of the BCN photocatalyst under visible light irradiation is 588.7 μmol/(h·g),  which is about  twice that of  the original CN,  and the photodegradation rate is 74% for tetracycline,  corresponding  to rate constant of about  1.5 times that of the original CN. This research results can provide useful references  for the development of novel CN photocatalysts,   hydrogen energy production and antibiotic pollution remediation.

In view of the environmental characteristics of low temperature,  low oxygen and oligotrophic groundwater polluted by oil in a certain area of Northeast China,  an experiment on microbial degradation of alkanes was carried out. We determined the nutrient matrix components that stimulated the degradation of indigenous microorganisms through batch static experiments, and investigated the effects of vitamin B (VB),vitamin C  (VC) and vitamin H (VH) on the growth of indigenous functional degrading bacteria and microbial degradation of alkanes.  The experimental results show that VB₁,VB₃,VC and VH have inhibitory effects on the growth of indigenous microorganisms,  VB₆ and VB₁₂ promote the growth of indigenous microorganisms.  The main effects ofvitamins on microbial degradation of alkanes are that VB₆,  VB₁₂ and VH have a promoting effect on the degradation of alkanes to a certain extent,  the degradation rate of alkanes is 73.91%—89.60% after the optimization ofvitamin components, among them,  VB₁₂ has the most obvious promoting effect, and 5 μg/L VB₁₂ has the best  promoting effect on the growth of microorganisms. When the mass   concentration of alkane in  groundwater is 10 mg/L,   the degradation rate of alkanes can reach 91.17% after 7 d of adding  the optimal nutrient matrix of high-efficiencyvitamins under 10 ℃ and low oxygen conditions. The degradation law of alkanes conforms to the second-order degradation kinetic equation, R² is above 0.900. Compared to the non nutrient matrix stimulation,  the relative abundance of alkane-dominant bacteria is significantly increased when the optimizedvitamins effectively stimulate the degradation of alkanes by indigenous bacteria.