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.

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.

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 the quantum Bernoulli noise method, we investigated the one-dimensional space-time inhomogeneous open quantum walk, and gave the evolution properties and limit probability distribution of the walk. It was also shown that the one-dimensional space-time inhomogeneous open quantum walk based on quantum Bernoulli noises had the same limit probability distribution as the classical random walk when the localized ground state was used as the initial state.

Let G=G(A,M,N,B) be a generalized matrix algebra, and a:G→G be a map (without the assumption of additivity). Using the  method of algebraic decomposition, we proved that if  a(XY)=a(X)Y+Xa(Y) held for any X,Y∈G and  at least one of X  and Y was idempotent, then a was an additive derivation on G.

We used taking condition method, probability method and moment generating function method to research the lifetime problem of Yule-Furry classical δ shock model, and gave the explicit expressions of the lifetime properties such as reliability, moment generating function and moment of lifetime of the model. The mean lifetime of the model was applied to the problem of cell carcinogenesis and numerically verified.

We used the methods of conservative energy estimation and characteristic line estimation to solve the Sobolev norm growth estimation problem of the solution of the (1+1)-dimensional Maxwell-Chern-Simons-Higgs model, gave the L^∞ estimation of the first derivative of the finite energy solution of the model, and obtained the polynomial growth of the H² norm of the solution by improving the exponential growth.

By using the techniques of dealing with sublinear neutral terms, generalized Riccati transformation and integral averaging techniques, firstly, the author gave an analytical method for estimating Riccati transformation inequality. Secondly, the author considered a class of third-order damped differential equations with sublinear neutral terms and distributed delays, and obtained some sufficient conditions for the solution to oscillate or converge to zero. Finally, the results were verified by some examples.

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.

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.

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.

Aiming at the problems of the limitations of  data sparsity and “cold start” on collaborative filtering and the inapplicability of the existing collaborative multi-armed Bandit algorithm to nonlinear reward functions, we proposed a neural Bandit recommendation algorithm COEENet, which combined collaborative filtering. Firstly, it adopted a dual neural network structure to learn expected  rewards and  potential gains. Secondly, we considered the collaborative effect of neighbors. Finally, a decision-maker was constructed to make the final decision. The experimental results show that the proposed method is superior to the four baseline algorithms in cumulative regret, and has a good recommendation effect.

Aiming at the problem of the difficulty in collecting noiseless point clouds and the low generalisation performance of  training on synthetic datasets using simulated noise,  we proposed a self-supervised denoising method that only required  noisy point clouds to complete  training in order  to achieve point cloud denoising in different environments. The method first performed downsampling on  the noisy point cloud by designing and implementing a special sampler to obtain the paired point cloud required for training the network, and then the problem of noise perturbation in network training was solved by designing a lightweight multi-scale denoising network. The experimental results on multiple datasets show that the method is effective and can obtain the same effect as supervised training in different scenarios.

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.

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.

With the development of deep learning technology,  the number of parameters in automatic speech recognition task  models was becoming  increasingly  large, which gradually increased  the computing overhead, storage requirements and power consumption of the models, and it was difficult to deploy on resource-constrained devices. Therefore, it was of great  value to compress the automatic speech recognition models based on deep learning to reduce the size of the modes while maintaining the original performance as much as possible. Aiming at the above problems,  a comprehensive survey was conducted on  the main works in this field in recent years, which was summarized as several methods, including knowledge distillation, model quantization, low-rank decomposition, network pruning, parameter sharing and combination models, and  conducted a systematic review  to  provide alternative solutions for the deployment of models on resource-constrained devices.

The stochastic stability and stochastic bifurcation behavior  of Van der pol vibration damping system constructed based on fractional-order viscoelastic material was studied under external broadband noise excitation. Considering the influence of constraints condition, a non-smooth Zhuravlev transformation was introduced to transform the collision system into a collision-free dynamic system. A set of quasi-periodic functions was used to replace the fractional-order differential element approximately, the stochastic average method was used to obtain the Ito stochastic differential equation of the system. The stochastic stability of the system was classified and discussed based on the maximum Lyapunov exponent method and singular boundary theory. The stochastic bifurcation behavior of the system under the linear Ito equation was analyzed by using the pseudo Halmiton system stochastic average method, and the critical condition for D-bifurcation was obtained. Furthermore, the stationary probability density function related to the amplitude of the system was obtained. Using the steady-state probability density curves drawn by MATLAB to visually display the changes of steady state that occurred in the system. The results show that the system can generate P-bifurcation behavior when the fractional-order and noise intensity change within a certain threshold.

Based on scalar diffraction theory, the aberration function was constructed by using Zernike polynomial method, and the aberration function was applied to ZEMAX to study the spherical aberration of Gaussian laser beam in Fraunhofer circular aperture diffraction imaging when the distance between lens and circular aperture was large. The experimental and theoretical simulation results show that the lens and the distance between lens and circular aperture have significant effects on spherical aberration. When selecting optimized aspheric lens, lens materials with higher refractive index and small field-of-view, it can effectively reduce the spherical aberration caused by large  distance between lens and circular aperture, thereby effectively improving the diffraction imaging quality.

We studied the one-dimensional non-Newtonian fluid model with gravitational potential and damping terms. The singularity and strong nonlinearity were solved by using the method of regularization equations and constructing  approximate solutions. The existence of the positive density solution was obtained by assuming the compatibility condition. Furthermore, the existence and uniqueness of local solutions for coupled equations under vacuum conditions were obtained.

In order to solve the environmental pollution caused by the stacking of furfural residue and expand the high-value utilization of waste resources, the furfural residue based lignin/cellulose composite was prepared through the pretreatment processes such as ultra-fine grinding and high-pressure homogenization. The sample morphology was characterized by using scanning electron microscopy (SEM) and atomic force microscopy (AFM), the composition and elemental content of the composite were analyzed by using normal form washing method and elemental analysis, the surface functional groups of the composite were analyzed by using Fourier transform infrared spectroscopy (FTIR) and ultraviolet spectroscopy (UV), and the thermokinetic analysis was performed by using multiple heating rate thermogravimetry (TG) under non-isothermal conditions. The results show that the mass fraction of C in furfural residue based lignin/cellulose composite is high (55.95%), which can be used as an ideal carbon source. The material contains abundant lignin (53.18%) and cellulose (39.48%), and has high utilization value. The overall apparent activation energy is low (30 kJ/mol), and the half-wave potential (E_1/2=0.83 V) in 0.1 mol/L KOH alkaline electrolyte reaches 96.5% of commercial Pt/C (E_1/2=0.86 V). Therefore, carbon materials prepared by using furfural residue based lignin/cellulose composites as biomass precursors can be used as ideal oxygen reduction catalysts for fuel cells.

We investigated the adsorption and dissociation behaviors of NO molecules on the surface of TM-MoS₂ (TM=Fe,Ir) doped systems by  using the PW91 method under the generalized gradient approximation in density functional theory in combination with periodic plate model. The results show that,  unlike the physical adsorption  on the intact MoS₂ surface (-0.05 eV),  the adsorption energies of NO on the surface of Fe and Ir doped MoS₂ are -3.30,-3.17 eV respectively,  indicating  that  the doped  surface exhibits more excellent adsorption performance for NO.  Differential charge density analysis shows that after adsorption of NO molecules,  there is an increase in charge  between the N atoms and the doped atoms Fe and Ir,  covalent bonds are formed,  and the charge around the doped atoms decreases.  The  calculation results of the density of states show that the adsorption of NO on the surface of doped TM-MoS₂ (TM=Fe,Ir) is mainly consisted of strong interactions between2p_y and 2p_x of N atoms, and 3d_xy,3d_yz,3d_xz of doped atom Fe as well as 5d_xy,5d_yz, and 5d_xz orbitals of Ir.  Comparative analysis of the activation energy of the dissociation reaction, the results show that, compared to the noble metal Ir,  the activation energy of NO dissociation on the Fe-MoS₂ surface  is smaller than that on the Ir-MoS₂ surface after doping with inexpensive Fe,   and the adsorption energy on  the Fe-MoS₂ surface is nearly close to the activation energy,  with only a difference of   0.08 eV,  indicating that there is a mutual competition between the adsorption and dissociation of NO in this system. 

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 designed and screened  αvβ6 polypeptide ligands with new structure by using computer-aided drug design strategy and solid-phase synthesis method,  and determined  the binding affinity between  the polypeptide ligands and αvβ6 by using enzyme-linked immunosorbent assay (ELISA) to establish a screening scheme for αvβ6 polypeptide ligands.  Firstly,  Sybyl-X 1.3 was used to perform molecular docking of the  αvβ6 polypeptide ligands and natural ligands. Secondly, Amber 16 was used to perform molecular dynamics simulation to determine the binding mode between the polypeptide ligands and αvβ6 protein,  and RGDLXXL (X was any amino acid) was used as the core structure of the polypeptide ligand, the virtual peptide library was constructed by gradual extension of amino acids,  polypeptide ligands with a length of 7—10 amino acids were screened， and new polypeptide ligands different from the core of RGDLXXL were designed and screened by similar amino acid substitution method. Finally,  the newly designed polypeptide ligands were synthesized by solid-phase synthesis method, and  the binding affinity of polypeptide ligand-αvβ6 was determined by indirect ELISA method.   The molecular docking and molecular dynamics simulation results of polypeptide ligands and natural ligands show that the binding of αvβ6 to the ligand is mainly achieved through the hydrogen bond formation between Asp218 and the polypeptide ligand,  and the metal chelation between Mg²⁺ and the polypeptide ligand. Combined with virtual combination screening and similar amino acid substitution,  we find that polypeptides such as GRTDLGTLLFR，GRRTDLATIHG，RTDVGRVRGRG and RGDVGRVGR all meet this binding pattern, and  the affinity between  RTDVGRVRGRG and αvβ6 is 10.76 μmol/L. Therefore,  RTDVGRVRGRG  and αvβ6  have a good affinity and are a new   αvβ6 polypeptide ligand.