The existence and the uniqueness of weak solutions to a degenerate parabolic equation with variable exponents u_t=div(ρ^α|a(u))|^p(x)-2a(u))+g(x)div(b(u)) is considered, where ρ(x)=dist(x,Ω) is the distance function from the boundary, a(s) is a strictly monotone increasing function. By choosing a suitable test function, the uniqueness of weak solution of the equation is proved under the condition of no boundary value.

We proved the existence of positive solutions for boundary value problems of fractional differential equations in Banach spaces by using the estimation technique of noncompact measure and the fixed point index theory of condensing mappings.

Using the new truncation function technique and the method of upper and lower solutions, we discussed the existence of solutions for the fully third-order boundary value problem:{u(t)=f(t,u(t),u′(t),u″(t)),t∈［0,1］,u(0)=u′(1)=u″(1)=0,where f: ［0,1］×3→was a continuous function. Under the condition that the nonlinear term f satisfied some inequalities, we gave the existence of solutions to the problem. In particular, we obtained the existence of the positive solutions to the problem when the nonlinear term f was not required to be non-negative.

We considered a class of stochastic SIR epidemic model with saturated incidence and psychological effect by white noise  in the environment. By constructing Lyapunov function and applying Ito formula, the global existence and uniqueness of the positive solution was obtained. We prove that when stochastic basic reproduction number R*≤1, the disease-free equilibrium is stochastically asymptotical stability, which means the disease will be extinction; if R*>1, the disease will be existence stochastically. The numerical simulation results verify the correctness of the theoretical results.

Firstly, the explicit new travelling wave and group invariant solutions of the Liouville equation were given by using the methods of extended tanh-function and Lie group analysis, respectively. Secondly, the ψ(ξ) expansion method for solving nonlinear partial differential equations was constructed by using the reduced transformation equation of the Liouville equation and its exact solutions. Finally, some explicit new travelling wave solutions of the Kawahara equation and (3+1)-dimensional Kadomtsev-Petviashvili equation were given by using ψ(ξ) expansion method.

The double module of  semi-associative 3-algebras was defined, and the structure of double modules and regular double modules of semi-associative 3-algebras were studied. We prove that for any semi-associative 3-algebra (A,{,,}),  the cycle sum ［,,］_c of the multiplication  {,,} is a 3-Lie multiplication on A, and study  the relation  between derivations of (A,{,,}) and (A,［,,］_c).

Let T=((A 0 U B)) be a triangular matrix ring, where A and B are rings and U is a (B,A)-bimodule. We use the isomorphism of modules tensor on the ring T as a bridge to give the equivalent condition that a module on the ring T is a projectively coresolved Gorenstein flat module: if fd(_BU)<∞,fd(U_A)<∞ or id(U_A)<∞, then a left T-module M=((M₁ M₂))_φ^M is projectively coresolved Gorenstein flat module if and only if M₁ is projectively coresolved Gorenstein flat left A-module, Coker φ^M=M₂/Im(φ^M) is projectively coresolved Gorenstein flat left B-module and φ^M: U*_AM₁→M₂ is a monomorphism.

A construction  method of algebraic preconditioner was given, and the proposed preconditioner and block diagonal preconditioner were analyzed theoretically by using the Weyl inequality. Both theoretical analyses and numerical examples show that the performance of the proposed preconditioner is better than that of the block diagonal preconditioners.

We consider the nonlinear autoregressive model X_i=r_θ(X_i-1,…,X_i-s)+ε_i,, where θ is a q-dimensional unknown parameter, {ε_i} is an independent and identically distributed random error with a mean of zero, and a variance of σ². We give the Berry-Esseen bound for error density estimators in nonlinear autoregressive models under appropriate assumptions.

We considered a nonlocal problems of a class of fractional differential inclusions with nonlinear growth conditions. Applying to the Leray-Schauder fixed point theorem, we first verified the existence and uniqueness of solutions for fractional nonlinear differential equations, and then proved the existence of solutions for a class of fractional differential inclusions by using set-valued fixed point theorem.

We generalized the dual representation of n-ary multiplicative Hom-Lie algebras to n-ary multiplicative Hom-Lie superalgebras, gave the definition of n-ary multiplicative Hom-Lie superalgebras, and gave necessary and sufficient conditions that representation of n-ary multiplicative Hom-Lie superalgebras was a dual representation.

We used iso-geometric analysis method to solve the minimum compliance topology optimization for the thin plate porous structure, and the optimal characteristic parameter distribution was realized in the design domain of uniformly distributed materials, which improved the mechanical performance of the thin plate porous structure. The triply periodic minimal surface (TPMS) was presented to design the porous element, and the relationship between the porous element characteristic parameter and the material distribution was analyzed. The porous element characteristic parameters were taken as optimization variables to solve the optimization problem in the proposed method, which ensured the continuity of stress function in the process of static equilibrium analysis and improved the calculation accuracy. Meanwhile, the number of porous elements could be controlled by designing porous structure based on optimization results, and the porous elements were connected smoothly.

Aiming at the problem of the complexity of dark channel prior fog removal algorithm, and using guided filtering to refine the atmospheric transmittance layer for a long time, we proposed an algorithm to refine transmittance layer by the median filtering to improve the fog removal spe
ed of aerial image. The improved algorithm defined a simple median filter with edge protection effect, independent of the filtering window and time complexity of O(1).  The blocky processing result generated by calculating the dark channel layer was better blurred by the median filter for the uniform cloud input image. The effect of fog removal image before and after improvement of the algorithm was compared by computer encoding and objective image quality assessment method without reference. The quantitative analysis and experimental results show that the median filtering algorithm is easier to implement than the guided filtering when the original image is evenly distributed. It can not only save fog removal time, but also realize image smoothing.

Aiming at the problem that it was difficult to segment adhesive leukocyte accurately, we proposed an adhesive leukocytes segmentation algorithm based on deep learning. Firstly, the color space of the blood cell microscopic images of patients with acute lymphoblastic leukemia was transformed
 from RGB to HSV, in order to filter out red blood cells and extract leukocytes. Secondly, for the adhesive leukocytes in extraction results, the cell border was set as the third class, in addition to foreground and background. During the training process of deep learning segmentation model, a weighted cross-entropy loss function based on class weight was introduced to make the model learn more cell border features. The experimental results show that using the proposed method to segment the leukocytes in the dataset ALL_IDB1 can achieve an accuracy of 95.19%.

Aiming at the problems of high energy consumption, low communication resource utilization and low channel utilization of cellular communication systems, we proposed a network resource allocation strategy based on the joint optimization of energy efficiency (EE) and spectral efficiency (SE). Firstly, on the premise of ensuring the quality of service of communication users, a channel selection strategy based on a heuristic algorithm was proposed to allocate channel multiplexing resources for D2D users in the system. Secondly, under the constraints of the interference threshold and backhaul capacity of the communication system, the Lagrange dual decomposition iteration was used to realize the system power and spectrum resource allocation. Simulation results show that the algorithm can effectively expand the number of D2D users in the system, improve energy efficiency and channel utilization, increase spectrum utilization, allocate optimal power for D2D users, enhance the service carrying capacity, reduce the energy consumption of communication system  and reduce the waste of resources.

Aiming at the problem that the automatic epileptic seizure detection algorithm focused on the establishment of a detection model for single patient, and the generalization ability was weak, we proposed an automatic epileptic seizure detection algorithm for non-specific patient based on machine learning. The algorithm used the electroencephalography (EEG) data of multiple epileptic patients, analyzed the characteristics of EEG data after preprocessing the data, and then selected the characteristics to train an automatic epileptic seizure detection model for non-specific patients. The algorithm did not need to establish a separate detection model for each patient, it could detect epilepsy in different patients with only one detection model. The accuracy, sensitivity and specificity of the algorithm are 0.877 4,0.854 8 and 0.9, respectively.

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.

In order to improve the cluster cooperation ability of autonomous underwater vehicle, reduce the energy consumption of group network and further improve the network reliability, we proposed a bionic fish swarm ad-hoc network algorithm based on underwater electric field communication and considering the influence of actual water area electrical conductivity. The roles and functions of the nodes were determined by calculating the priority of the nodes based on the communication time between the nodes of the proposed algorithm, and generated the underwater cluster cooperation network model to realize the rapid networking of small-scale bionic fish swarm. The independent cruising function of sub node and scattered node guided by objective coordinates and the setting of backup function of the main control node could not only realize group scattered nodes retrieved, but also indirectly optimize network coordination model, reduce the routing maintenance information between network nodes, effectively save the network energy consumption and enhance the system security. Simulation results show that the algorithm is effective and practical.

In view of the skin lesions with different scales and irregular shapes, the traditional U-Net method lacked robustness to analyze targets from different scales, and lost some spatial context information when extracting high-level semantic features of the image, which affected the accuracy of subsequent segmentation, the author proposed a medical image segmentation method based on U-Net with multi-scale and multi-dimensional feature fusion. Firstly, the spatial context information from different scales was fused by atrous convolution. Secondly, the weight information of each channel of the feature map was extracted by the channel context information fusion module. Finally, the multi-scale and multi-dimensional information in the feature map was fused to preserve more spatial context information. Experimental results show that the proposed method can segment the skin lesion on the skin lesion dataset, and the segmentation effect is good.

For the multiplicative updating rule in solving the non-negative matrix factorization, there were some shortcomings of high computational complexity an
d low iterative efficiency. We proposed a stochastic variance parameter adjusted gradient method. Combining the variance reduction strategy with the multiplicative updating rule, a parameter was adopted to adjust the stochastic gradient estimator, and the gradient descent direction was corrected to balance its deviation and variance, so as to reach the optimal solution quickly and accurately. Experiments were carried out on the real data sets, and the results verify the feasibility and effectiveness of the proposed algorithm.

Aiming at the problem that the accuracy of the support vector machines （SVM） in detecting abnormal users of electricity was affected by the imbala
nce of the samples and the selection of kernel function, we proposed a diagnosis model of theft and leakage of electricity based on Smote-SVM. Firstly, based on the distribution of users of electricity, the Smote method was used to expand a few samples, and the TomekLink was used to eliminate noise. Secondly, the SVM kernel function was optimized after dimensionality reduction. Finally, the algorithm was applied to the diagnosis experiment of the theft and leakage of electricity for unbalanced users, and compared with the traditional SVM and Smote-SVM algorithms. The experimental results show that the algorithm can significantly improve the detection accuracy of the users of theft and leakage of electricity.

x(Yb)=18%，x(Er)=2% codoped α-NaYF₄, α-NaLuF₄,β-NaYF₄,β-NaLuF₄4 and LiYF₄ nanocrystals were synthesized by using high temperature thermal decomposition method. X\|ray diffraction (XRD)， transmission electron microscopy (TEM) and photoluminescence spectroscopy were used to characterize the crystal structure， morphology and luminescence properties of the samples. The results show that all as-prepared samples are pure phase. The  size distribution of the as-prepared samples with a nearly spherical shape is about 10—15 nm.    The as-prepared samples exhibit emission at around 1 550 nm under the excitation of 980 nm  laser. Among them， β-NaLuF₄∶Yb,Er has the strongest emission at the around of 1 550 nm.

We studied modulation  of dielectric constant of dielectric column on band gap structure in the two-dimensional functional photonic crystal waveguide and the modulation of the  dielectric constant of point defect dielectric column on the electric field distribution and light propagation direction when  point defect was added into waveguide. The results show that when there is no point defect in two-dimensional functional photonic crystal waveguide，the number and position of band gap, and the number and position of detect modes can be adjusted by changing parameters  b and k  values of dielectric constant of the dielectric column.  When there is point defect in two\|dimensional functional photonic crystal waveguide， the electric field distribution and light propagation direction can be changed by changing parameters b and k values of the dielectric column with point defect.

The geometry of R-threonine (R-Thr) molecules in the implicit solvent methanol was optimized at the B3LYP/6-31G(d) basis set level, based on this structue, the time-dependent density functional theory (TDDFT) method was used to calculate the electronic excitation at the Mo6-2X/6-311G(d),TZVP,def2-TZVP basis set level, and the valence layer electronic excitation type of R-Thr-CH₃OH molecular system was studied  by the method of identifying the type of natural transition orbit (NTO). The results show that the judgement results of TZVP and def2-TZVP basis sets are basically consistent, 6-311G(d) basis set is compared with the other two basis sets, there is a big difference in the judgment results of excitation type. The combination of NTO type analysis and  Δr indes analysis of theoretical data has practical significance for the identification of the electronic excitation type and excitation mode of R-Thr-CH₃OH molecular system.

In order to realize the synchronous control of the chaotic system of brushless DC motor (BLDCM)， firstly, the chaotic characteristics of BLDCM system were analyzed by the mathematical model under load operation. Secondly, the backstepping synchronization controllers were designed based on the Lyapunov stability principle and the stability was studied. Finally， circuit simulator of the BLDCM system based on current converter (CCCⅡ)  was designed. The accuracy and effectiveness  of the method were verified by numerical simulation and circuit implementation.

Hsp-Tat fusion protein was expressed in BL21 (DE3) E.coli cells and purified by using affinity chromatography method. The size and morphology of Hsp-Tat nanoparticles were analyzed by dynamic light scattering and transmission electron microscopy. MTT analysis and live/dead cell staining were used to study the biocompatibility of Hsp-Tat nanoparticles. The siRNA complex properties of Hsp-Tat nanoparticles were detected by gel retardation assay. The siRNA transfection activity was studied by laser confocal fluorescence microscopy imaging. The experimental results show that Hsp-Tat fusion protein with high purity is obtained by affinity chromatography. Hsp-Tat nanoparticles can self-assemble into  spherical nanostructures with a mean diameter of 40.2 nm. The protein nanoparticles show good biocompatibility on HEK\|293T cells. The  complexes formed by Hsp-Tat NP and siRNA can prevent the migration of siRNA in agarose gel. Hsp-Tat nanoparticles can  transport Cy3-siRNA into HEK-293T cells, and can  be used as  a  safe and efficient non-viral nucleic acid delivery vector.

Through laboratory simulation, different amounts of exogenous polycyclic aromatic hydrocarbons (PAHs) monomer standard substances were added to peat soil and farmland soil. After freeze-drying and natural air drying, 16 kinds of exogenous PAHs monomers in the soil were determined by gas chromatography-mass spectrometry (GC-MS),  and the effects of two drying methods on the recovery rate of exogenous PAHs and the  isomer ratio in soil were analyzed to reflect the accuracy of PAHs  determination in the soil and the difference of source determination of PAHs in natural soil under different drying methods. The experimental results show that    with the increase of the amount of exogenous PAHs in peat soil,  the total recovery rate of PAHs  decrease first and then increase. The total recovery rate (56.29%—80.15%) of PAHs after the air-drying treatment is higher than that of freeze-drying treatment (52.82%—78.31%) under the same addition amount, and recover rate of its monomer PAHs low-ring component after air-drying treatment is higher than that of  freeze-drying treatment,  recovery rate of high-ring component after freeze-drying treatment  is higher than that of air-drying treatment. The recovery rate of total PAHs in farmland soil  is significantly different (P<0.05) under different drying methods. The total recovery rate after freeze-drying treatment is  64.40%—73.81%,  and the total recovery rate after air-drying treatment  is  40.88%—57.01%,  and the recovery rate of the monomer PAHs after freeze-drying treatment is higher than that of air-drying treatment. The difference of organic matter mass ratio and water content of the two soils may be the main factors that lead to the difference of  total and monomer recovery rate of PAHs. There is no significant difference in the ratios of PAHs isomers in peat soil,  while the ratios of the PAHs isomers in farmland soil are significantly affected by the drying method.

Arsenic-reducing bacteria (Stenotrophomonas sp.TS28) and root exudates of rape,  wheat and pakchoi were used as experimental objects to study the effects of root exudates on the survival and arsenic reduction ability of arsenic-reducing bacteria TS28 and soil enzyme activities in arsenic contaminated soil. The results show that As(Ⅴ) in soil inhibits the survival of TS28, the addition of root exudates stimulates the survival of TS28,  and increases the survival number and time of TS28. Root exudates can affect the reduction ability of TS28,  which is related to its source. The root exudates of wheat have the best effect on improving the arsenic reduction ability of TS28,  and the reduction amount of As(Ⅴ) is increased by 45.86% within 10 d. TS28 decreases the activities of sucrase and dehydrogenase in arsenic contaminated soil,   the addition of root exudates increases the activities of urease,  acid phosphatase,  sucrase and dehydrogenase,  among which rape root exudates have the best effect.