We made use of the dual problem to construct the control function, and proved the approximate controllability of a class of parabolic systems with weak or strong degeneracy on a portion of the lateral boundary.

By using the Banach contraction mapping principle and the Schauder’s fixed point theorem, we discussed a fractional differential equation with a class of nonlinear terms depending upon fractional derivative of lower order under fractional integral boundary condition, proved the existence and uniqueness of its solution, and gave some application examples.

Using the renormalization group method, we investigated a class of Hamiltonian systems with two degrees of freedom, and obtained the renormalization group equation to O(ε) order of this kind of Hamiltonian systems. Meanwhile, we proved that the renormalization group equation was also a Hamiltonian system.

By using the Lyapunovtype condition and the truncation technique, we considered the existence of global solutions for stochastic evolution equations with infinite delay, and obtained Khasminskiitype theorems for stochastic evolution equations with infinite delay.

By using the Perov’s fixed point theorem and Schauder fixed point theorem, we considered the existence of solutions for a new class of the sequential fractional qdifferences system. We gave a representation for the solution to this equation by using qexponential, and obtained the existence and uniqueness of solutions for the sequential fractional qdifferences system.

By means of methods and techniques of real analysis, we discussed the necessary and sufficient condition and the best constant factor for a class of Hilberttype integral inequality with a nonhomoeneous kernel K(x,y)=G(x^λ₁y^λ₂), and studied its application in the operator theory.

By  using combinatorial bijective method, the author  studied the compositions of the mutual conjugate partition of positive integers without  2’s, and obtained a  relation between the number of these compositions and the Fibonacci number. Consequently, the author gave several identities about the number of these compositions, the number of compositions into parts equal to 1 or 2, the number of compositions into odd parts and the number of compositions into parts greater than 1.

The concept of deductive system was proposed on formula set F(S) of BL propositional logic system, and the strong congruence relation was introduced. We discussed the connection between deductive systems and strong congruence relations in BL system, gave the method of interconversion between them, and obtained the reducibility of interconversion between them.

The author considered the approximation properties of the BaskakovDurrmeyer operators in Orlicz spaces L^*_Φ［0,∞)generated by the Young function, and obtained the direct, inverse and equivalent theorem of the approximation by the BaskakovDurrmeyer operators by using the equivalence relationship between modified Kfunctional and continuous modulus.

By using the range of the infinite norm of inverse matrix of a strictly diagonally dominant M\|matrix, we obtained a new estimate of the error bounds for the linear complementarity problem of Bmatrix. Both theoretical analysis and numerical examples show that the new estimate improves existing results.

We considered the error bound with a parameter for the linear complementariry problem of BNekrasov matrices. Using the monotonicity of function, we obtained the optimal value for the problem of the parameter error bound under given conditions. Numerical examples were used to verify the corresponding results.

Using the credibility method for interval numbers, the author gave the concepts of the feasible region and the optimal solution for the interval bilevel linear programming problem. By means of the optimal value interval methods of single level and bilevel programming as well as maxmin operator, the author constructed a deterministic equivalent model for the interval bilevel linear programming problem. A numerical example result show that the method is effective.

We presented an improved trustregion derivativefree (TRDF) algorithm. In the proposed method, we established the constraint violation function, chose a better iteration point by using the progressive barrier (PB) strategy modified sub problem of the initial augmented Lagrangian multiplier, and proved the convergence of the improved algorithm. Numerical experiments for different dimensions of the test results show that the improved algorithm effectively reduces the number of iterations and the iteration time for solving polynomial interpolation model.

By using an improved variation constant method: B-mehtod, we studied approximation of the quenching solution and quenching time for a class of parabolic partial differential equation. We proved the existence of the numerical solution and validity of the method in solving quenching equation was proved by numerical simulation.

We numerically solved a class of the KleinGordon equations with a nonlinear timefractional derivative of Caputo by using Jacobi spectral collocation method. First, the fractional KleinGordon equation was transformed into an integral differential equation with a singular kernel in the time by using the relation between the Caputo fractional derivative and the RiemannLiouville fractional integral, and then we used a spectral collocation method in both temporal and spatial discretizations with a spectral expansion of Jacobi interpolation polynomial for this equation. The results show that the numerical solution obtained by this method is a good approximation of the exact solution.

The author gave an optimal perfectly matched layer (PML) method for solving the 3D time harmonic electromagnetic scattering problems. The method was based on the complex coordinate stretching in the frequency domain. The calculation of the optimal PML problem for the scattering problem was not dependent on the thickness of the PML layer by introducing a small parameter ε₀ in the absorbing function. The author proved that the numerical solution converged exponentially to the original 3D time harmonic electromagnetic scattering problems if the parameter ε₀ was sufficiently small.

Taking the complete tripartite graphs K_1,1,p,K_1,2,p as examples, we discussed vertexdistinguishing IEtotal coloring and vertexdistinguishing general total coloring problem of the complete tripartite graphs  K_1,1,p,K_1,2,p by using the methods of the color sets prior distribution, constru
cting the dyeing and proofing by contradiction. We determined the vertexdistinguishing IEtotal coloring chromatic number and vertexdistinguishing general total chromatic number of K_1,1,p,K_1,2,p.

Let {S_k, k≥1} be a random sequence satisfying the almost sure central limit theorem,  and {T_k, k≥1} be a random sequence with T_k→0(or 1) a.s. By using the limit theory, we proved that {S_k+T_k, k≥1} and {S_k/T_k, k≥1} satisfied the almost sure central limit theorem, and gave some examples such as linear processes, selfnormalized sums, error variance estimates in linear models and products of partial sums.

The author considered a k-out-of-n system with covariates. The conditional hazard functions of the residual life of the normally operating variables in the system were assumed to be a proportional hazards model. The author discussed the maximum likelihood estimation of the model parameters, the reliability function and the quantile function of the system, and the asymptotic normality of these estimates. The author gave the confidence intervals of the model and studied the performances of the point and interval estimators by Monte Carlo simulation. The results show that the mean square errors (MSEs) of the estimates decrease with the increases of the sample size.

By using the iterative technique, regularity estimate for semigroup and some a priori estimates, we proved the existence of global attractor for a class of higherorder diffusion equation with Neumann boundary value conditions in fractional order space.

In order to further improve video quality of adaptive sub\|pixel interpolation algorithm and reduce computational complexity, we proposed an adaptive interpolation filter algorithm based on HEVC (high efficiency video coding). Firstly, the algorithm was coded under the video coding framework of new coding standard H.265/HEVC to improve efficiency of video coding. Secondly, the filter coefficients demanded by code stream and the complexity of decoding computation were reduced by the symmetric optimization of filter coefficients. The results of complexity analysis show that compared with other algorithms, the multiplicative complexity of  this algorithm is reduced by 229%, and the addition complexity is reduced by 245%. Simulation results show that, compared with other algorithms, this algorithm has good coding performance and robustness for different resolution video sequences.

In view of the problems of low efficiency and large user recommendation error in the process of semantic search, we proposed a semantic search algorithm based on extraction rules and ontology mapping. Firstly, according to user’s requirements in semantic search, the semantic elements and attributes were extracted to solve the defect of low utilization rate of data. Secondly, we established a semantic model to construct a mapping between elements and attributes between ontology, and eliminated the semantic deviation between user’s need and computer. Finally, the semantic search algorithm was applied to the user’s personalized recommendation system. The experimental results show that the semantic search algorithm effectively improves the search efficiency and reduces the user’s personalized recommendation error.

By abandoning irrelevant tuples and reducing the way of retrieval, we presented an optimization algorithm STRN3, which solved the problem that all the tuples of negative table constraint were traversed in the compatibility algorithm, resulting in redundant retrieval and low efficiency. The experimental results show that the performance of the algorithm STRN3 is better than that of the algorithm STRN when the average number of the valid tuples in the negative table does not decrease substantially in the retrieval process. In the constraint networks, when the number of supported tuples is more than conflict tuples, the performance of the algorithm STRN3 is better than that of  the algorithm STR3, thus the improvement of the negative table constraint algorithm is realized.

In order to improve the recognition effect of multipose face, we designed a multipose face recognition algorithm, combining sparse coding and machine learning. Firstly, the multipose face was collected and preprocessed, and feature of face image based on sparse coding was extracted. Secondly, the feature was processed by principal component analysis to reduce the feature dimension of multipose face recognition and improve the efficiency of multipose face recognition. Finally, the support vector machine of machine learning algorithm was used to establish the classifier of multipose face recognition, and the performance of the algorithm was verified by the standard face database and multipose face database. The verification results show that the algorithm can effectively improve the accuracy of multipose face recognition, greatly reduce the average recognition time of the multipose face, and
achieve better recognition results than the contrast algorithm, thus the superiority of the algorithm is verified.

The traditional least squares support vector machine (LSSVM) obtained the low rank of kernel matrix by randomly choosing a part of samples to improve the sparsity of solution. In order to make the approximate decomposition of low rank matrix as small as possible to approximate the original kernel matrix, we proposed QRPLSSVM sparse algorithm based on QR factorization. Using the orthogonal feature of QR factorization to choose some samples with a big diversity, we iteratively selected some columns of the kernel matrix to get Nystrm type low rank approximation of kernel matrix, and used decomposition results to get the sparse solution of LSSVM quickly.  The experimental analyses show  that the proposed algorithm can get more sparse solutions without sacrificing the classification performance, and even get higher accuracy with the sparsity level less than 0.05%, and it can solve largescale training problems effectively.

In view of the shortcomings of high error recognition rate and poor robustness of current face recognition algorithms, we designed a face recognition algorithm based on discriminant analysis and low rank projection to obtain better face recognition results. Firstly, the face images were divided into blocks, the local feature of each sub block was extracted, and the global feature of face was extracted by discriminant analysis. Secondly, we used low rank projection to make up a feature vector that contributed greatly to the face recognition results. Finally, the least squares support vector machine was used to establish multi classifier for light face recognition based on the principle of onetomany, and the simulation experiment was carried out by multiple face database. The experimental results show that the algorithm can find the optimal feature subset of face recognition, reduce the error recognition rate of face, the speed of face recognition is obviously improved, and the effect of face  recognition is better than other face recognition algorithms.

In order to effectively control the energy consumption of wireless sensor network nodes, we proposed an adaptive fuzzy neural control system, and designed an adaptive fuzzy neural topology control algorithm[CD2]AFNTC. In this algorithm, the parameters of fuzzy controller were obtained after training by artificial neural network, and the communication range of the nodes was constantly adjusted through the feedback and circulation to control the transmission power of the node, so that the actual energy consumption of the node was close to the preset expected value, and the network life cycle was prolonged. Experimental results show that AFNTC algorithm can achieve the purpose of controlling energy consumption of nodes. Compared with FCTP and LMA algorithms, the nodes have lower and more stable average energy consumption in AFNTC algorithm.

In view of the shortcomings of the low accuracy and slow speed of current remote sensing image classification algorithm, we proposed a remote sensing image classification algorithm based on quantum particle swarm optimization to improve the classification effect of remote sensing images. Firstly, we analyzed the shortcomings of the current remote sensing image classification algorithm and its reasons. Secondly, we extracted the original features of various types of remote sensing images, and used the quantum particle swarm algorithm to select features and extract important features of remote sensing image classification results. Finally, using least squares support vector machine, we established classifier for remote sensing image, realized remote sensing image classification and recognition, and carried out simulation and contrast experiment of remote sensing image classification. The experimental results show that the proposed algorithm overcomes the limitations of current remote sensing image classification algorithms, and the classification accuracy of remote sensing image has been greatly improved, which effectively reduces the error of image classification and improves the efficiency of image classification.

In order to improve the effect of abnormal event detection in sensor networks, we proposed a sensor network abnormal event detection model based on compressed sensing algorithm. Firstly, the state information of  sensor network was collected, and the compressed sensing algorithm was used to
sample and reconstruct information, after reducing the abnormal events detection information in the sensor network, we deleted some invalid information. Secondly, we extracted feature from the reconstructed sensor network abnormal events detection information to compose feature vector of sensor n
etwork abnormal events detection. Finally, the sensor network abnormal event detection model was established by using the limit learning machine, the simulation experiment of sensor network abnormal event detection was carried out, and the performance of the model was analyzed. The experimental results show that the compressed sensing algorithm can speed up the detection of abnormal events in sensor networks, and the detection rate of abnormal events in sensor networks is higher than 95%, which is significantly higher than other abnormal event detection models in sensor networks.

In view of the problem that the recognition method of digital signal modulation mode was easy to be affected by noise and the recognition error was large, we designed a recognition method of digital signal modulation mode based on wavelet neural network. Firstly, we collected digital signal and extracted the modulation recognition feature from the signal as the classification basis of the digital signal modulation mode. Secondly, we established classifier of digital signals modulation recognition based on neural network, and selected particle swarm optimization algorithm to determine the parameters of the neural network, so as to realize the digital signal modulation recognition. Finally, the simulation test of digital signals modulation recognition was realized on MATLAB[KG*6]2016 platform. The test results show that, even if the signaltonoise ratio of digital signal is low, the wavelet neural network can still obtain the ideal digital signal modulation recognition results, and the digital signal modulation recognition rate is higher than that of the contrast method, thus improving the performance of digital signal modulation recognition.

By introducing Petri nets, we extended the knowledge reformulation and abstraction model that could represent the static physical world W, in order to enhance its ability to describe the dynamic behavior of physical entities. The improved model was applied to intelligent lab. The results show that the improved moder can meet the formalizing requirements of physical entities in the intelligent lab.

Aiming at the problem that the current feature selection algorithm was applied to the data classification accuracy was not ideal, we proposed a feature selection algorithm based on maximum correlation and minimum redundancy. The algorithm combined feature selection algorithm and clustering analysis algorithm to process the feature, and eliminated redundant features in the classification. We used support vector machine (SVM) to classify the data obtained from a group of patients with heart disease. The experimental results show that this method can effectively screen the features that affect classification, and then improve the classification accuracy.

We proposed a novel matching clustering algorithm by improving the method of clear rational number mean. First, we calculated the clear rational mean of each piece of data, then compared it with the matching item to get the clustering result, and solved the clustering problem of artificial annotation data. This method was tested and verified in the field of antifraudulent Web pages, and compared with the results of Knearest neighbor algorithm using the same name but different types of data sets. Experimental results show that the method is more effective than Knearest neighbor algorithm in the field of antifraudulent Web pages, and it also proves that the novel matching clustering algorithm is reasonable in clustering artificial annotation data.

Using the method of density functional B3LYP, we optimized the ground state stable geometries of  the gas phase alanine (Ala) molecules
 and charged ions at the level of 6-311++G(-d,p-) basis set. The method of time dependent density functional theory (TD-DFT) was used to study the low excited state properties of the gas phase Ala molecules and ions. The results show that the bond length gradually decreases, the excitation energy of the first excited state  decreases, the fluorescence wavelength increase sharply, and the number of electronic transition orbit of S6 increases with the increases of the number of electrons obtained by molecules.

We proposed the spiron wave equation of free and nonfree photons, and gave the spin operator and spin wave functions of photon. By calculating the helicity of photon, we proved that there were lefthanded and righthanded photon. With the spin wave functions of single photon, we obtained the spin wave functions of two photons or multiplephotons, and gave spin entanglement state of multiplephotons.

Cu₂S quantum dots were prepared and the Raman scattering spectra of Cu₂S quantum dots were simulated by Gaussian software. Based on Maxwell’s electromagnetic wave theory, the surfaceenhanced Raman scattering (SERS) of Cu₂S quantum dots with different particle sizes were simulated by MATLAB. The results show that Cu₂S quantum dots have strong SERS signals. When the size of Cu₂S quantum dots is in the range of 2—10 nm, the SERS signals are enhanced with the increase of particle sizes, and finally reach a stable value.

Using a threedimensional autonomous system as the node, we studied the asymptotic synchronization of globally coupled network with the chaotic system as the node, and used chaos concealment method to apply it to secure communication. By adding Gaussian white noise to interfere with the system, we used wavelet analysis theory to denoise the signal. The results of numerical simulation show that the signal can be recovered without distortion after the wavelet threshold de-noising.

Using the method of density functional theory B3LYP, we investigated the chiral transition process of the phenylalanine molecule in the situation of dualwater at the level of 6-311+G(2-df-). We drew a reaction potential energy surface for chiral transition path by finding the structures of extreme value points including the transition states and intermediates, and analyzed the geometric and electronic structure properties of extreme value points. The results sh
ow that the H atom on the chiral C atom of S-3-Phe&2H₂Ophenylalanine molecule can transfer to the other side of the C atom via the O atoms of carboxyl atoms as a bridge, and achieve the chiral transition of phenylalanine molecule from S-3-Phe&2H₂Otype to R-3-Phe&2H₂Otype. On this path there are four intermediates and five transition states. The maximum reaction energy barrier is 221854 8 kJ/mol, which comes from the fourth transit
ion state TS₂-R-3-Phe&2H₂O.

We studied the chiral transition mechanism of two conformations of lysine (Lys) molecules confined in the helically chiral SWBNNT by using the ONIOM methods of combination of quantum mechanics and molecular mechanics. The results show that the Lys molecular skeleton deformation
 of helically chiral SWBNNT in small tube diameter is obvious. When two conformations of Lys molecules confined in the SWBNNT(6,4), the apparent energy barriers of the optical isomerism reaction are 175.90,230.44 kJ/mol, respectively, the intrinsic energy barriers of the ratedetermining step of the optical isomerism reaction are 211.40,230.44 kJ/mol, which come from the transition states that the proton transfer from the chiral C to amino N and are low
er than the energy barrier of the ratedetermining step of bare reaction (252.60 kJ/mol). The smaller  tube diameter of the helically chiral SWNT, the better  confined catalytic action, and Lys molecules that confined in SWBNNT(6,4) with the single hydrogen bonds between amino group and carboxyl are optical isomerism in the first place.

Maca was extracted by oil removing, water extraction and lyophilized. The water extract was mixed with Escherichia coli OP50 broth and diluted to a final mass concentration of 1,2 mg/mL. The antioxidation effect of water extract of Maca on Caenorhabditis elegans was studied with C.elegans as a model. The experiments of lifespan, spawning, swallowing and motor ability show that the water extract of Maca has no obvious toxic effect on nematodes, and 1,2 mg/mL water extract of Maca can significantly prolong the lifespan of nematodes. The water extract of Maca has protective effect on nematode induced by oxidative stress. The oil red O staining shows that the water extract of Maca has a certain effect on lipidlowering.

We studied the effect of Fenton advanced oxidation on the removal of levofloxacin hydrochloride in water, and investigated the effects of n(H₂O₂)∶n(Fe²⁺), H₂O₂ dosage, initial pH value, reaction time and initial mass concentration on the removal efficiency. The results show that the removal rates of levofloxacin hydrochloride, chemical oxygen demand (by K₂Cr₂O₇, COD_Cr) and total organic carbon (TOC) increase first and then decrease with the increase of n(H₂O₂)∶n(Fe²⁺) in the range of 5—25. When the dosage of H₂O₂ was 15 mL/L, the removal rates of levofloxacin hydrochloride, COD_Cr and TOC are 88.40%, 59.52% and 33.80%, respectively. When pH=3, the removal rates of levofloxacin hydrochloride, COD_Cr and TOC are 9240%,5952% and 3451%, respectively. The removal rate of levofloxacin hydrochloride, COD_Cr and TOC gradually increase with the time, and the removal rate decrease with the initial mass concentration. When the reaction time is 3 h, the removal process is basically comp
leted. The effect of Fenton advanced oxidation on the removal of levofloxacin hydrochloride in water is the best at the conditions of pH=3, temperature is 20 ℃, H₂O₂ dosage is 15 mL/L, n(H₂O₂)∶n(Fe²⁺)=10, the removal efficiency is 96.40%.

Escherichia coli phage  vB_EcoMep3 detected in contaminated water was selected as a model virus, and the indoor dynamic migration simulation experiment  was carried out. We analyzed the migration process of nanoscale pathogenic microorganism—virum in groundwater by using DLVO theory and colloid filtration theory, and investigated the migration regularity of enterovirus colloid under different groundwater acidbase environments. The results show that: When the groundwater environment changs from acidic condition （pH=5.0） to alkaline condition （pH=9.0）, the particle sizes of virus colloid decrease and the mass recovery rates increase, which are 125%,291% and 618%, respectively; the coefficients of deposition rate decrease, which are 41×10^-4,28×10^-4 and 1×10^-4, respectively; Zeta potential decreases, while DLVO barrier and the stability of the virus increase; the ability of the virus colloid to deposit on the surface of the lithology medium weakens.

By the indoor culture method, the albic soils amended with lignin as the tested object, we studied the effects of kaolinite or montmorillonite on the humic composition of albic soils by setting six microbial culture sequences of Bacillus subtilis, Aspergillus niger and Streptomyces griseus. The results show that the promotion effect of C(HA)C(FA) of albic soils caused by kaolinite is greater than montmorillonite when A.niger is served as the Ⅰ period cultured strain or B.megaterium is served as the Ⅰ period cultured strain and A.niger is served as the Ⅱ period cultured strain. The montmorillonite is more beneficial to making the HA molecular structure complicated, and the montmorillonite is more beneficial to the increase of the 
C(HA)C(FA) when S.griseus is served as the Ⅰ period cultured strain; under the influence of B.megaterium→S.griseus→A.niger, compared with SiO₂, two kinds of minerals are beneficial to the increase of the C(HA)C(FA); in addition to S.griseus→B.megaterium→A.niger, the kaolinite is more beneficial to the formation of C(Hu) in the other five microbial culture sequences; the montmorillonite is more beneficial to the mineralization of total organic carbon (TOC) of albic soils than kaolinite when the A.niger is served as the Ⅱ period cultured strain; the degree of mineralization of TOC is the weakest in the microbial culture sequence of S.griseus→A.niger→B.megaterium, and the kaolinite is more likely to promote the microbial consumption of C(WSS); the two kinds of minerals do not affect the wC(WSS) in the ulture sequence of \%A.niger→B.megaterium→S.griseus\%, and montmorillonite is more likely to promote the microbial consumption of C(WSS) in other four kinds of culture sequence; compared with SiO₂, the two kinds of minerals can promote the consumption of C(HE) of albic soils.

Taking scoria as an adsorbent material, we studied its adsorption effect on SO^2-₄ in low temperature water and its influence factors. The experimental results show that the scoria has a good adsorption effect onSO^2-₄. When the initial mass concentration of SO^2-₄ is 100—1 000 mg/L, the adsorption amount increases with the increase of the initial mass concentration. When ρ（SO^2-₄）=1 000 mg/L, the maximum adsorption amount is 6.42 mg/g, and the shortest equilibrium time is 4 h. The optimum pH for adsorption of SO^2-₄ is 7. Ca^2+ and Mg²⁺ have a slight promoting effect on SO^2-₄ adsorption by scoria, while Cl^- and NO^-₃ have inhibitory effect.