Ganoderma lucidum spore powder was used as raw material,  ethanol  with a volume fraction of  70%  as extractant.  We adopted a combination of enzymatic  hydrolysis and ultrasound assisted extraction method,  set different liquid-solid ratios,  ultrasound time,  enzymatic hydrolysis time,  and enzyme dosage  as  four factors for a one-way test and designed a response surface experiment to  determine the optimal extraction method and its influencing factors. The   Ganoderma triterpene were separated and purified by using macroporous resin chromatography. By optimizing the  separation and purification process, the optimal elution resin,   eluent volume fraction,  flow rate of the upper sample solution and the mass ratio of the upper sample solution were determined. The compositional differences of the total  Ganoderma triterpenes were analysed by high performance liquid chromatography (HPLC). Though the pre-experimental analysis, the results show that the enzyme + ultrasound assisted extraction is more efficient compared to the single extraction method. Ethanol is used as an extractant to extract triterpenoids from Ganoderma lucidum can enhance the purity of triterpenoids. Under optimal conditions, the  rapid and accurate determination of the triterpene content can be achieved, providing a theoretical basis for the separation and purification of Ganoderma triterpenes.

We considered a  class of tumor-immune model, discussed the existence  conditions  of their equilibrium points, and used characteristic equations to analyze the local kinetic stability of each equilibrium point,  proving that the model underwent Hopf bifurcation under the corresponding conditions. By calculating the first Lyapunov coefficient, it can be concluded that if the coefficient is not zero, the model undergoes Hopf bifurcation,  the bifurcation is supercritical if the coefficient is less than zero, and the bifurcation is subcritical if the coefficient is greater than zero. Finally, numerical simulations are used to validate the theoretical analysis results.

Aiming at the problem that the traditional causality extraction in natural language processing was mainly based  on  pattern matching methods
 or machine learning algorithms, and accuracy of the results was low, and only explicit causality with causal cue words could be extracted, we proposed an algorithm BERT-GCN using large-scale pretraining model combined with graph convolutional neural network. Firstly,  we used BERT （bidirectional encoder representation from transformers） to encode the corpus and generate word vectors. Secondly,  we put the generated word vectors into the graph convolutional neural network for training. Finally, we put them into the Softmax layer to complete the extraction of causality. The experimental results show that  the model obtains good results on the SEDR-CE dataset, and the effect of implicit causality is also good.

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.

We discuss  the existence of positive 2π-periodic solutions of the second-order ordinary differential equation with nonlinear derivative term by using positive operator perturbation method and fixed point index theory in cones. Under certain inequality conditions of the 
nonlinear term f(t,x,y), we obtain the existence of positive 2π-periodic solutions of the equation.

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.

Firstly, we established a class of SEI₁I₂QR infectious disease models that included  transmission mode of asymptomatic infected individuals. Secondly, by using the next generation matrix method, we calculated the basic reproduction number of the model, performed the dynamic analysis of the model, and gave the threshold conditions for the extinction and outbreak of infectious disease. Finally, combined with  epidemic data, the sensitivity of the model parameters were analyzed through numerical simulations.

By using the method of upper and lower solutions, we discussed a class of elliptic equations with nonlinear terms of supercritical growth. We first proved the existence of solutions of the Dirichlet problem in the restricted region, and then proved that the local solutions in the restricted region could be extended to the whole region by combining a new  variational principle.

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 complexity and diversity of current network intrusion, the traditional model was insufficient to extract traffic characteristics, and had low accuracy, we proposed an intrusion detection method based on CR-BiGRU hybrid model improved by merging residual network. Firstly, the dataset was normalized and one-hot encoding treatment in the model. Secondly, the convolutional neural network based on the residual network was used to extract the spatial features. Finally,   the bidirectional gated neural network was used to extract the temporal features,  complete the training of the model and realize the intrusion detection of the abnormal network. In order to illustrate the applicability of the model, comparative analysis experiments were conducted based on NSL-KDD and UNSW-NB15 datasets. The results show that the accuracy of the method based on the above datasets is 99.40% and 83.79% respectively, which is obviously superior to the classical network intrusion detection algorithm, and can effectively improve the accuracy of network intrusion detection, so as to  better ensure the  communication security of network data.

The author considered a class of delayed predator-prey model with fear effect. Firstly, by using the characteristic equation and Lyapunov-LaSalle invariance principle, the global asymptotic stability of the boundary equilibrium was proved when R(τ)≤1. Secondly, by using the Hopf bifurcation theory of delay differential equation, the author discussed the stability of the coexistence equilibrium point and the existence of the global Hopf bifurcation when R(τ)>1, and obtained the results that fear effect and delay affected the stability of the system. Finally, the correctness of the theoretical results was verified by numerical simulations.

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%.

We discussed a class of Schnakenberg models with homogeneous Neumann boundary conditions in view of the periodic oscillation phenomenon in biochemical reactions. By using the  methods of Hopf bifurcating theory, center manifold theory, normal form method and perturbation theory, we gave  the existence, stability and Turing instability of the Hopf bifurcating periodic solutions of the reaction-diffusion Schnakenberg system.

We used the Faedo-Galerkin method to investigate the three-dimensional magnetofluid equations with nonlinear damping terms and  delay terms on a bounded domain  and solved the problem of well-posedness of the solutions. Firstly, the existence of strong solutions was proven when α≥16/5. Secondly, the uniqueness of strong solutions was proven by using the Gagliardo-Niernberg inequality.

By using the Schauder fixed point theorem and topological degree theory, the author studies the existence of positive solutions of Neumann boundary value problems for second order ordinary differential systems with variable coefficients, where f,g: [0,1]×R→R are continuous functions, and f(x,0)<0, g(x,0)<0; a,b∈C([0,1],[0,∞)) are not always 0 on any subinterval of [0,1]. The result shows that under suitable conditions, there exists λ₀>0 such that the problem has at least one positive solution for 0<λ<λ₀.

We considered the finite time blow-up to  a strongly damped  wave equation with variable-exponent nonlinear term. With the help of concave method and appropriately selected  parameters, we gave a new  blow-up criterion  for this problem and estimated the upper and lower bounds on  the blow-up time. The results show that the blow-up criterion contains special  implications for any high initial energy, and  the problem has a finite  time blow-up solutions.

We considered the coexistence solution problem of a class of Lotka-Volterra competitive systems with nonlinear cross-diffusion under homogeneous Dirichlet boundary conditions. Firstly, the stability of trivial solutions and semi-trivial solutions of the problem was analyzed by using spectral theory of linear operators. Secondly,  sufficient conditions for the existence of coexistence solutions of the problem were given by using the fixed point index theory on positive cone.

By applying mathematics induction and combinatorial analysis, we gave D(2)-vertex-distinguishing total colorings of cactus graphs G_T with maximum degree of 3, and then obtained χ_2vt(G_T)≤6. The result shows that D(β)-VDTC conjecture holds for cactus graphs with maximum degree of 3.

Aiming at  the blurring problem of remote sensing images, we designed an image restoration algorithm based on non-subsampled shearlet  transformation and sparse prior. Firstly, the image recovery model was created by setting the sparse a priori condition of remote sensing image under non-subsampled shearlet decomposition of the high-frequency image. Secondly, the model was solved by using the alternating direction multiplier method. Thirdly, the high-frequency image was restricted by the soft thresholding method, and the guided filtering was conducted in the low-frequency image to maintain the detailed information of the image as much as possible. Finally, the high-frequency image and the low-frequency image were reconstructed, the  
 reconstructed image was subjected to deep denoising by  using  convolutional neural networks, ultimately restoring a clear image. The deblurring algorithm was compared with H-PNP, GSR, and L2TV algorithms through experiments. The experimental results show that the algorithm can effectively remove  blurring and noise in remote sensing images, preserve the edge details of the image, and  the objective evaluation indexes are higher than the other three comparative experimental algorithms.

By using the fixed point theorem on expansion and  compression of cones, we study the existence of positive solutions for a class of periodic boundary value problems of third-order ordinary differential equations. The  results show that there exists  at least one positive solution to the above problem when the nonlinear term f satisfies appropriate conditions.

By using T-weak continuous operator method and classical Galerkin technique, we discussed the initial boundary value problem of a class of incompressible magneto-micropolar fluid equations in a two-dimensional bounded smooth region, and obtained the existence and uniqueness theorems of the global weak solutions for the problem,   further improving the regularity of the weak solutions.

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.

Firstly, by using the fractional order concentration-compactness principle, we proved the compactness conditions for a class of nonlinear Kirchhoff equations with electromagnetic fields and critical Hardy-Littlewood-Sobolev term in the whole space to overcome the problem of lack of compactness conditions caused by unbounded regions and critical term in this equation. Secondly, combined with the symmetric mountain path theorem, we proved that the equation satisfied the mountain path structure, and proved the multiplicity of the solution to the equation by using genus theory.

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 Leray-Schauder degree theory and Banach contraction mapping principle, we studied the existence and uniqueness of solutions for boundary value problems of conformable fractional delay differential equations when the nonlinear term satisfied the growth condition and the Lipschitz condition, we obtained the results of existence and uniqueness of solution for the boundary value problem respectively, and gave an example to illustrate the applicability of the obtained results.

By using topological degree theory, the author studies the existence of positive radial solutions of 2m order semipositone elliptic equations in the annulus, where λ>0 is a parameter, m≥1 is a positive integer,  Ω={x∈Rⁿ; a<|x|<b}(n>2m), 0<a<b<∞, f∈C(［a,b］×［0,∞),R).  The results show that there exists λ₀>0, so that the above problem 
has at least one positive radial solution when λ₀ under suitable conditions.

We considered the existence of solutions of differential equations for fractional Choquard type Kirchhoff critical problems. Firstly, Hardy-Littlewood-Sobolev embedding theorem was introduced, and combined with Nehari manifold method and fibbing maps of energy functional related to the problem, the existence of nontrivial solution of the equation was proved when the parameter λ was small enough. Secondly, the functional had (PS) sequence was obtained by Ekeland variational principle, and then the appropriate parameter λ was selected. Combined with the truncation method and mountain pass theorem, the compactness 
condition was proved to be true. Finally, the existence of nontrivial solutions of the above equations was established by using the fractional concentration-compactness principle.

We studied  the antioxidant active components and mechanism of  dandelion based on  high performance liquid chromatograph (HPLC) method and network pharmacology method.   The effective components of Chinese herbal medicine dandelion were extracted by  organic reagents,  such as petroleum ether,  ethyl acetate,  dichloromethane and n-butanol,  and their antioxidant effects were studied. Multiple online databases of network pharmacology were used to obtain  common targets of dandelion antioxidant construct PPI network,  and conduct GO enrichment analysis and KEGG signal pathway enrichment analysis. The results show that the  extracts of each phase of dandelion have a certain scavenging ability to hydroxy radical (.OH),  superoxide anion radical (O^2-.) and 1,1-diphenyl-2-picrylhydrazyl radical (DPPH.),  the ethyl acetate phase extract of dandelion and the dichloromethane phase extract of dandelion have better scavenging effects,  and the main antioxidant active components are isorhamnetin and oleanolic acid. There are 137 dandelion antioxidant targets screened from the online database. The common targets are mainly concentrated on membrane rafts,  which are resistant to the response of cells to inorganic substances,  nitrogen compounds,  and nutrient levels oxidation. The common targets are closely related to cancer signal pathway,  NF-kappa B signal pathway,  and PPAR signal pathway. 

Aiming at the  characteristics of  subtle, uneven, imperceptible inter-class differences between classes and real-world data distribution in  fine-grained image classification, we proposed a fine-grained image classification model based on attention mechanism. Firstly, the preliminary feature extraction of the image was carried out  by introducing the fusion of a two-way channel attention and residual network. Secondly,  the multi-head self-attention mechanism was applied to extract fine-grained relationships between  deep feature data. Thirdly, the training of loss function measurement system was designed by combining cross entropy loss and center loss. The experimental results show that the test accuracy of the model on two standard datasets 102 Category Flower and CUB200-2011 is  94.42% and 89.43%, respectively. Compared with other mainstream classification models, the classification effect is better.

Aiming at the problem of inaccurate information collected by a single sensor, we proposed a data fusion algorithm for confined space detection based on Bayesian estimation. Firstly, by analyzing the composition structure of the detection signal,  filtering, amplitude limiting, step signal removal and other methods were used to solve the problem of signal interference and improve the significance of characteristic parameters. Secondly, based on  the dynamic characteristics of the data fusion architecture, reasonable assumptions were given, and a dynamic Bayesian network model was jointly established by combining a prior network and the transfer network to obtain the fusion objective function. Finally, by introducing  normal distribution  to study the uncertainty of detection value, the detection node was regarded as the likelihood function, and the maximum a posteriori probability after fusion was deived. Taking the fusion weighted average error ratio as the index, multi type detection data fusion was realized by “two-two encounter”. The results of simulation experiments show that the proposed algorithm solves the problem of signal redundancy, the data fusion effect is better, the overall number of fire missed reports is less, and the highest value of the data fusion time is only 2.4 s.

By using the compactness method, we gaved the existence of solutions to the Cauchy problem of the energy-critical fractional  nonlinear Schrodinger equation and proved the existence of global solution to the Cauchy problem. By constructing the approximation equation and taking the limit of the solution sequence satisfying the approximation equation, the obtained limit function was the global weak solution of the energy-critical fractional nonlinear Schrodinger equation, and it was proved that the weak solution satisfied the energy inequality and mass conservation property.

Firstly, based on the Black-Scholes stock price model,  the neural stochastic differential equation (NSDE) model was established by parameterizing the asset return rate and volatility as a drift network and a diffusion network, respectively. Secondly, in the empirical analysis, the underlying asset as a single stock option was used as the research object, and real stock data was used for  the network training  and testing. The experimental results show that the NSDE model can overcome the defects of the constant assumption of the Black-Scholes model. Finally, for the case where the price of the underlying asset of the option was unobservable, we  proposed that the price of any target option and the price of a known option could be constrained within the Wasserstein distance of their risk-neutral equivalent martingale measure, and theoretically  proved the method.

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.

By using the method that the determinant of the adjacency matrix of the singular graph was equal to zero, we discussed the singularity of the generalized θ-graphs and the generalized plum blossom φ-graphs, and gave the necessary and sufficient conditions for the generalized θ-graph θ(a₁,a₂,…,a_k) and the generalized plum blossom graph φ(a₁,a₂,…,a_k) to be a singular graph, respectively. The probability values of singular graph occurring in these two types of graphs were calculated.

By studying  a class of three-species cooperating models on periodically evolving domain, we discussed  the effect of periodic evolution of domain on the persistence and  extinction of species. The existence and stability of the positive periodic solution of the model were studied by using the upper and lower solutions method, the comparison principle, the theory of quasi-monotone system and the priori estimates of parabolic equations. We recorded  ρ as the domain evolution rate. The results show that the effect of periodically  evolving domain on the persistence of species is negative when ρ^-2>1, it is positive when ρ^-2<1, and  there is no effect when ρ^-2=1.

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.

Aiming at the problem that the pre-training model would cut off part of text when dealing with long text such as news, which led to the loss of text infomation, we  proposed a  method to build a model by combining  TextRank algorithm, implicit Dirichlet distribution topic model and pre-training model on the basis of integrating news title information, and  compared the model with other  semantic similarity calculation methods. The results show that the accuracy rate of the model is 82.46%, the recall rate is 87.43%, the accuracy rate is 82.68%, and the F₁ value is 84.99%,  the optimal results are obtained, which effectively improves the performance of semantic similarity calculation between news texts and comments.

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.

We used an ideal convergence structure to solve the characterization problem of directed topology, and provided necessary and  sufficient conditions for the topological transformation of ideal S limits and ideal generalized S limits. The results show that the directed topology, the ideal S limit topology and the ideal generalized S limit topology are the same  in T₀ topological spaces.  The ideal S convergence in a directed space is topological if and only if it is a c-space. The ideal generalized S convergence in a directed space is topological if and only if it is a locally strongly compact space.

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.