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.

By constructing the cohomologies complexes of Rota-Baxter Lie algebra homomorphisms, we discuss the formal deformation of Rota-Baxter Lie algebra homomorphisms and prove that Rota-Baxter Lie algebra homomorphism is rigid when the 2th-cohomology group of the deformation complex is zero.

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.

In order to suppress the transformation of amyloid β polypeptide (Aβ)  from random curling or α-helix to β-folding structure, we studied the conformational changes of wild type Aβ and its array mutants. Combining Markov model and molecular dynamics simulation, we studied the conformational change precess  of the wild type,  A4 type and D7N type Aβ, and identified the  conformational transformation path of three Aβ types. The experimental results show that one region of β-folding is found in the wild type Aβ, and the conformation of the A4 type Aβ is almost unchanged, while two regions of β-folding are found in the D7N type Aβ, indicating that the D7N type mutant has the characteristic of promoting β-folding. The results provide a theoretical baisis for exploring treatment methods for Alzheimer’s disease.

We discussed the E-total coloring of complete bipartite graphs K_4,n which were vertex-distinguished by multiple sets by using
 the method of proof by contradiction, the method of pre-assignment of color sets and the method of constructing specific coloring, and determined E-total chromatic numbers of K_4,n which were vertex-distinguished by multiple sets.

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.

Let R S be a Frobenius extension of rings and M be an S-module. We prove that if R S is a separable Frobenius extension, then _SM is a projectively coresolved GorensteinFI_n-flat module (GorensteinFI_n-flat module) if and only if _RM is a projectively coresolved GorensteinFI_n-flat module (GorensteinFI_n-flat module).

Aiming at the problem of insufficient feature extraction resulting in low classification accuracy of the traditional encrypted traffic classification model, we  proposd an encrypted traffic classification model based on an improved convolutional neural network combined with Transformer by using deep learning techniques.  In order to improve the classification accuracy, firstly, we cut and filled the dataset,  and completed standardization processing. Secondly, the multi-head attention mechanism in the Transformer network model was used to capture long-distance feature dependencies, and the convolutional neural network was used to extract local features. Finally, the Inception module was added to achieve multi-dimensional feature extraction and feature fusion, and the model training and encrypted traffic classification were completed. The experimental verification was conducted on the 
ISCX VPN-non-VPN 2016 public dataset, the experimental results show that the classification accuracy of the proposed  model reaches 98.5%, with the precision rate, recall rate and F₁ value  all exceeding  98.2%, which show better classification effect compared with other models.

Aiming at the problem that the current data compression algorithm of sensor network had the defects of low compression ratio and serious data deformation, in order to improve the realtime performance of data transmission of sensor networks, we proposed a data compression algorithm based on spatiotemporal correlation. Firstly, the original data of sensor network was collected, and the spatial transformation technology was used to analyze the correlation between the data of sensor network in space, and then the noise was removed to reduce the spatial resource occupied by noise. Secondly, according to the temporal correlation of the data of sensor network, the compression sensing algorithm was introduced to compress the spatial coefficient to reduce the data redundancy of sensor network. Finally, the performance of data compression algorithm of sensor network was analyzed by simulation experiment. The simulation results show that compared with other sensor network data compression algorithms, the proposed algorithm can improve the data compression ratio of sensor network without losing the data information of sensor network, obtain faster data compression speed of sensor network and reduce the communication pressure of sensor network.

Aiming at the problem that the traditional neural network proportionalintegraldifferential (PID) controller and linear quadratic regulator (LQR) optimized PID controller had long recovery time and poor antiinterference for speed control of brushless direct current motor， we proposed a BP neural network PID controller optimized by LQR for speed control of brushless direct current motor. Firstly, BP neural network was used to adjust the PID gain to improve the dynamic adaptability and robustness of the controller. Secondly, LQR was used to optimize the optimal output of BP neural network, which was closer to the target PID gain. The simulation results show that the controller can effectively improve the response speed, reduce the steadystate error and enhance the antiinterference ability.

Based on the Black-Scholes-Merton option pricing model, we first gave a simplified algorithm of European option pricing equation under Vasicek model by using the method of conversion of valuation units, and then based on the simplified equation, we gave the iterative scheme for the numerical solution of the European option price by using the explicit difference method and the Crank-Nicolson difference method, and verified the stability of the iterative scheme.

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.

Aiming at the parameter optimization problem of deep learning network in the process of network traffic prediction modeling, in order to improve the network traffic prediction results, we proposed a network traffic prediction model based on improved gray wolf algorithm to optimize the deep learning network. Firstly, the historical data of network traffic was collected and preprocessed by phase space reconstruction and normalization. Secondly, gray wolf algorithm was introduced to quickly search the relevant parameters of the global optimal deep learning network, the preprocessed historical data of network traffic was learned according to the optimal parameters, and a prediction model that could mine the change law of historical data of network traffic was established. Finally, the network traffic prediction model of deep learning network optimized by other algorithms was compared and analyzed. The experimental results show that the network traffic prediction accuracy based on improved gray wolf algorithm to optimize deep learning network is more than 90%, which is much higher than other comparison models, and the modeling time of prediction modeling process is less than that of comparison model, which can meet the requirements of high accuracy and real-time of network traffic management.

We proposed a fractional-order Lü chaotic system with nonlinear delay term according to the fractional-order Lü chaotic system. Firstly, the fractional-order Lü chaotic system was numerically solved by Adomian-decompositio-method (ADM). Secondly, the phase trajectory diagram of the system was drawn by MATLAB software. Finally, by using simulation technology and dynamic analysis tools such as bifurcation diagram, complexity and phase trajectory, the effect of system parameters on the system was analyzed. The numerical simulation results show that the system has rich dynamic characteristics.

We considered a class of fourth-order thin-film equation with singular term and logarithmic source. Firstly, we obtained the local existence of weak solutions to the equation by  combining truncation function and  Galerkin approximation. Secondly, by virtue of the potential well method and Rellich inequality, we proved the global existence and decay estimate of weak solution to the equation under certain conditions. Finally, we proved the blow-up result of the  solution to the equation at a finite time by using the convex method, and gave the lower and upper bounds for blow-up time.

Aiming at  the problems that  the whale optimization algorithm was prone to getting stuck in local optima and had drawbacks such as slow  speed control response and large overshoot of brushless DC motor, we  proposed an improved whale optimization algorithm (IWOA) for optimizing proportional integral derivative (PID) parameters in brushless DC motor speed control. The algorithm combined Gaussian mutation factor, adaptive weight factor, and dynamic threshold to optimize the whale optimization algorithm. The simulation experiment results show that the  improved whale optimization  PID speed control algorithm of brushless DC motor has faster  convergence rate, smaller overshoot phenomenon, and better robustness.

A novel fuzzy clustering algorithm which uses the merits of the global optimizing and higher convergent speed of Particle Swarm Opt imization(PSO) algorithm and combines with Fuzzy C-means(FCM) is proposed. The iteration process is replaced by the PSO based on the gradient descent of FCM, which makes the algorithm have a strong global searching capacity and avoids the local minimum problems of FCM. At the same time, FCM is no longer a large degree dependent on the initialization values. Numerical experiments show that the proposed algorithm is more accurate and efficient than FCM.

Effect of Al₂O₃ doped on the high permeability MnZn ferrites was researched by means of comparing experiment data of different samples. The results show that a suitable amount of Al₂O₃ doped can inhibit ZnO evaporation so as to increase the initial permeability of MnZn ferrites, reduce the relative temperature coefficient, and increase the permeability range.

We considered the American put option pricing problem under Black-Scholes model. Firstly, based on the Black-Scholes model, we designed a neural network algorithm for the model, and gave the numerical approximation of the American option price. Secondly, the effectiveness of the algorithm was proved by comparing with the traditional binomial tree method.

Let the strong product graph of path P_m and star graph S_1,n-1 be G=P_m*S_1,n-1. Firstly, by inducing assumptions and constructing internally vertex or edge disjoint paths, combined with the centrality of star graph, the vertex fault diameter D_w(G) and edge fault diameter D′_t(G) of the graph G were given. The results show that for any vertex or edge fault in the graph G, there holds D_w(G)≤d(G)+2 and D′_t(G)≤d(G)+1. Secondly, through the unequal relation between the number of vertices and the number of edges, the upper bound of the vertex fault diameter of the strong product graph of two maximally connected graphs and the 
upper bound of the edge fault diameter of the strong product graph of two nontrivial connected graph were given.

Aiming at the problems of low accuracy, under-detection, and missed detection in the vehicle target detection algorithm at traffic intersections, we proposed a target recognition algorithm of traffic intersection based on improved YOLOv7.  Firstly, the algorithm  used the feed-forward convolutional attention mechanism CBAM to enhance the network’s  attention to key features from both channel attention and spatial attention, improve the network’s running  speed, and optimize the network’s feature extraction capabilities. Secondly, a new learning module was formed by connecting the  spatial layer to depth  layers to form a  full-dimensional dynamic convolution, which improved the YOLOv7 feature learning method and enhanced the feature expression ability. Finally, the experiments were conducted on the actual collected traffic intersection dataset. The experimental results show that the proposed method  achieves an average accuracy of 96.1% on the corresponding dataset, and the training time is reduced to 16.71 h. Therefore, it has obvious recognition advantages  for small target detection at traffic intersections.

Chromatographic peaks of different concentration of Nigella sativa L.extacts were characterized by HPLC. B16 murine melanoma cells were used as an in vitro cultured model. MTT was used to study the effect of Nigella sativa L.ethanolic extracts on the proliferation of B16 murine me
lanoma cells. Oxidation rate of LDOPA was measured to estimate the effect of Nigella sativa L.ethanolic extracts on tyrosinase activity of B16 murine melanoma cells. NaOH cleavage method was performed to study the effect of Nigella sativa L.ethanolic extracts on the melanogenesis of B16 murine melanoma cells. Statistical analysis to the chromatographic peaks of different concentration of Nigella sativa L.extacts and pharmacodynamic data for correlation analysis. Results show that 50% ethanolic extract of Nigella sativa L.enhances me lanogenesis and growing rate of B16 murine melanoma cells. Componenteffect relationship shows that there is no significant difference in the 6 chromatographic peaks on pharmacodynamic effect. Pharmacodynamic effect is due to the multiplecomonents of Nigella sativa L.

Firstly, a mixture solution of Fe₃O₄ nanoparticles and graphene oxide was prepared by solutionblending method. Then, 
Fe₃O₄/rGO composite film was prepared by stepbystep thermal reduction method from room temperature up to 160 ℃. X-ray diffraction, Fourier transform infrared spectroscopy and scanning electron microscopy were used to characterize the structure and morphology of the films with different mass fractions of Fe₃O₄. We used vector network analyzer to test electromagnetic parameters of the composite film. The results show that when the mass fraction of Fe₃O₄ is 40%, the absorbing wave performance of the composite film is 17.30 dB at frequency of 1072 GHz with a matching thickness of 2.0 mm, and the effective absorption bandwidth less than -10 dB is 3.28 GHz.

Firstly, we selected the world ocean atlas 2013 (WOA13) ocean data  as the experimental data, the unequal distance differential method and vertical gradient method were applied to the preprocessing of ocean data, the division of ocean area and analysis of thermocline. Through the performance analysis of various neural networks based on the threedimensional WOA13 ocean data in the binary classification experiment, we chose the residual network as the network model of the binary classification experiment, and added the Dropout retention layer on the basis of the threelayer residual network model to prevent over-fitting. Secondly, the residual network model was used for thermocline analysis and determination, and the comparative tests such as the super parameters optimization, the residual unit improvement and  the retention rate adjustment were carried out for the improved model. The experimental results show that the improved ResNet26 network is effective for the thermocline data classifica
tion of WOA13 ocean area data, and the classification accuracy is more than 94%.

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.

The effects of different linear functional forms of dielectric column dielectric constant of two-dimensional functional photonic crystals on transverse electric (TE) wave and transverse magnetic (TM) wave band structures were studied by using plane wave expansion method. The results of numerical calculation show that the band gaps of two-dimensional functional photonic crystals are wider than that of two-dimensional conventional photonic crystals. By changing the different functional forms of dielectric column dielectric constant, the number, position and width of band gaps of the two-dimensional functional photonic crystals can be changed, so as to adjust the band gap of two-dimensional functional photonic crystals.

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.

Aiming at the problem that the cellular Internet of Things involved large-scale device connection and identity authentication management, and attackers cuold use various methods  to forge identity information, which made the difficulty of  anonymous access  user identity authentication increase, the author proposed  an  anonymous access user identity authentication algorithm for cellular Internet of Things. Firstly, the 5G network was used as the dynamic application scenario of the cellular Internet of Things system, and the system parameters were preseted. Secondly, according to the user’s identification number and public key, the forged name was used to generate the user’s anonymous access information, and the registration was anonymously saved to the local. Finally, based on the concept of decentralization, the decryption results of the unit public key and the adjacent group key, the random number encryption information and the unit Hash value were compared to authenticate the user identity. The experimental results show that the proposed algorithm effectively shortens the time required for identity authentication and batch message authentication, reduces the number of bytes required for data transmission, with a time cost of only 13 ms, a computational cost of only 4 ms,  and a communication cost of only 210 bytes. Moreover, it can successfully resist 15 types of identity authentication attacks.

We calculated the contributions of the natural atomic orbital (NAO) of the molecular orbital S-Leu system under different implicit solvents by using the Gaussian natural bond orbital (NBO) analysis program. The results show that the implicit solvent methanol and chloroform have great influence on the molecular orbital of S-Leu system according to the contribution of NAO. The contribution of NAO of implicit solvent methanol is closer to the calculation result of the implicit solvent H₂O. The total contribution value of NAO of carboxyl fragment under implicit solvent methanol is closer to 
the calculation result of the implicit solvent H₂O. The effect of contribution of NAO of carboxyl fragment under implicit solvent chloroform is different from implicit solvents methanol and H₂O.

Aiming at the problem that the path planning methods based on the shortest path only focused on path length, while trajectory-based path planning methods excessively depended on users’ preference, we proposed a path planning method based on both routing preferences and path length. Firstly, the long short-term memory model was used to extract users’ routing preferences from the historical routing trajectory. Secondly, Markov chain Monte Carlo sampling technology was used to introduce the users’ routing preferences into the heuristic search algorithm A* to search for the shorter path in line with users’ routing preferences in the road network. Finally, taking Beijing road network and taxi trajectories as test data, the method was compared with the shortest path based planning method and the trajectory based path planning mehtod. The experimental results show that the path planning method is more stable, and the path planning has higher accuracy, shorter travel distance and travel time.

Aiming at the problem that the current convolutional neural networks usually  obtained multi-scale image features on the conditio
n of reducing receptive fields, and it was difficult to capture the important relationship between channels.  Combined with the features of cycle-generative adversarial networks structure, we proposed a new cycle-generative adversarial networks with multi-scale and self-attention mechanism. Firstly, VGG16 module was used to form U-Net structure in the generator to enhance the extraction of image feature information. At the same time, the down-sampling  and up-sampling  in the network were improved to improve the feature resolution and obtain more detailed information. Secondly, a multi-scale feature fusion block was designed. The multiple parallel dilated convolutions with different sampling rates were used to integrate the spatial information on different scales, and capture image information in multiple proportions while maintaining  a large receptive field of the image. Finally, in or
der to capture the feature dependencies in the spatial dimension and channel dimension, the pixel self-attention module was designed to model the semantic dependencies in the spatial dimension and channel dimension, so as to enhance the representation ability of image features and improve the quality of the generated sketch images.

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.

Based on the polynomial feature generation method for one-dimensional feature data, we proposed a data augmentation algorithm that used the polynomial feature generation method to generate feature data for high-dimensional feature data. At the same time, we proposed an  algorithm  that combined the generated polynomial feature data with the neural network model during convolutional neural network training, which could organically combine the  generated polynomial feature data with the convolutional neural network model, and  improve the low recognition accuracy  and the limited generalization performance of model caused by data limitations such as limited data samples, fixed total number of data samples, and differences in available data samples  when modeling convolutional neural network models. Experimental results show that the accuracy of the convolutional neural network model using this method achieves significant improvement.