By using a new technique of treating quasilinear diffusion term and the method of differential inequalities, we discussed the (full) oscillation problems for a class of delay hyperbolic distributed parameter systems with quasilinear diffusion term under homogeneous Neumann boundary value condition. Firstly, the oscillation problems of the systems were transformed into the problems of two order delay differential inequality without eventually position solution, and then some explicit sufficient conditions for the (full) oscillation of each solution of such systems were established by means of some results of the functional differential equations. The obtained results reflected the role of the delay in determining the (full) oscillation of system.

We considered a class of generalized two parameter nonlinear hyperbolic  integraldifferential equation with singular perturbation model. Firstly, the generalized outer solution of the model was obtained by using the generalized Fredholm type integral equation. Secondly, the boundary layer corrective term of the generalized solution was obtained by using the method of multiple scale variables. Thirdly, the initial layer corrective term of the generalized solution was obtained by using the stretched variable method. Finally, the synthetic asymptotic expansion of the generalized singular perturbation solution was constructed, and the uniform validity of the asymptotic expansion of the solution was proved by using the fixed point theory.

We proved the uniqueness of weak solutions of a stationary bipolar quantum energytransport model for semiconductors in onedimensional bounded domain by using some inequality techniques. In other words, when the lattice temperature was large and the Planck constant, the electron current density and the hole current density were all small, the weak solution of the model was unique. This result shows that the solution of the device model is well posed.

The author considered a class of even order nonlinear neutral functional differential equations with distributed delays and damping terms. By using the generalized Riccati transformation, H function method and differential inequality skills, the author established some sufficient conditions for oscillation of all solutions of the equation.

Using the theories of topological systems and Quantale, we first introduced the concept of subsystem of Quantale system to define the embedding between Quantale systems, and then with the help of the structure of Quantale, the embedding theorem of Quantale system was obtained. The embedding theorem was used to study the embedding of spatilization of Quantale system. It was proved that all subsystems of a Quantale system were complete lattices under the defined partial orders.

We considered the optimality conditions for a class of setvalued optimization problems with respect to approximate solutions under two criteria of vector optimization and set optimization. We obtained the necessary and sufficient conditions for optimality of setvalued optimization problems with respect to approximate solutions under two criteria of vector optimization and set optimization by using upper and lower Studniarski derivatives.

Some subdivided line index sets of the matrix were given by using the theory of α-diagonally dominant matrices. A positive diagonal matrix was constructed by constructing iterative coefficients. Some determination conditions of generalized strictly α-diagonally dominant matrices were given, and some subdivided iterative criteria for nonsingular Hmatrices were obtained. Numerical examples show that the given criteria are effective.

Using r-pre-semiopen (r-pre-semiclosed) L-set, we defined presemicountinous mapping, pre-semiopen mapping, pre-semiclosed mapping, pre-semiirresolute mapping, pre-semiirresolute open mapping and presemiirresolute closed mapping in L-fuzzy topological spaces. We proved that every percountinous mapping was presemicountinous mapping, every peropen (preclosed) mapping was persemiopen (presemiclosed) mapping. Moreover, we gave some equivalent characterizations of the above mappings.

By using the method and principle of fuzzy sets, the concept of n-fold fuzzy implicative filter, n-fold fuzzy fantastic filter, n-fold fuzzy positive implicative filter and n-fold fuzzy Boole filter were introduced in residuated lattice. The author obtained the relation among these kinds of n-fold fuzzy filter in residuated lattice, and proved that the equivalence between n-fold fuzzy positive implicative filter and n-fold fuzzy Boole filter in residuated lattice.

We proposed a lattice Runge-Kutta-Boltzmann algorithm for solving the Rossler equations. First,  the classical Runge-Kutta formula was used to construct the lattice Boltzmann model, and we obtained higherorder  truncation error. By using the ChapmanEnskog expansion and multiscale expansion technique, we obtained a series of partial differential equations in different time scales and modified Rssler equations. The numerical results show that the obtained model  can be used to solve  the Rossler equations.

We considered a variant of the Weyl’s theorem: the generalized Weyl’s theorem. By defining a new spectral set, we gave sufficient and necessary conditions for the operator T and its functional calculus to satisfy the generalized Weyl’s theorem by using the spectral set. We obtained a new discriminant for T and its functional calculus to satisfy the generalized Weyl’s theorem.

Aiming at the problem that the original initialization strategy of the activeset algorithm took more time to compute minimum volume enclosing ellipsoid (MVEE). Firstly, we gave a new initialization strategy based on sample covariance matrix. Secondly, we applied the initialization strategy to the ranktwo update algorithm, and gave a modified activeset algorithm to compute MVEE. The results of numerical experiments show that activeset algorithm based on the new initialization strategy can effectively improve the computational efficiency of solving the MVEE problem of largescale date sets.

We derived the equation of motion and corresponding boundary conditions for a simply supported microbeam with vonKarman nonlinearity by using the modified couple stress theory and the variational principle, and analyzed the influences of the width, height, length of the beam and the initial gap between the microbeam and the stationary electrode on the pullin voltage and the change rule of corresponding scale effects.

Using the Lyapunov stability theory and linear matrix inequality approach, we considered the reducedorder H_∞ filtering problem for singular neutral systems. Firstly, some sufficient conditions for the reducedorder H_∞ filter of singular neutral systems were given such that the resulting filtering error system was asymptotically stable and H_∞ norm was less than a given performance index γ. Secondly, the expression of the reducedorder H_∞ filters were given in the form of parametric display. Numerical results show that the conclusions are feasible and effective.

We obtained a complete convergence theorem for maximum of weighted sums  of rowwise (α,β) mixing arrays  by using the Rosenthal type maximum inequality for (α,β) mixing sequence, and made use of this theorem to prove  a MarcinkiewiczZygmund type strong law of large numbers for maximum of weighted sums of (α,β) mixing sequence. The obtained results  weakened the required moment conditions.

By using a Trefftz class algorithm, we gave a numerical method for solving the scattering problem of a class of timeharmonic wave by penetrable obstacle. The method was based on the leastsquares algorithm, FourierBessel functions were used to approximate the local state of the field, and a model was established by using multipole expansion to approximate the behavior of scattered field at infinity. The results show that the method is appropriate for the scatters  whose domain may be multiple or even multi-connected. Moreover, it does not need to truncate the space, and high accuracy can be achieved by adding the number of the basis functions in the coarse mesh. Numerical examples are carried out to illustrate the effectiveness of the proposed algorithm.

A new class of generalized convex functions were defined by using differential Exhausters, including upper Exhauster convex function and lower Exhauster convex function. By using the generalized convexity of functions, we proved the sufficiency of the necessary conditions of optimality under the condition of upper Exhauster convexity and lower Exhauster convexity for unconstrained nonsmooth minimum and maximum problems.

We considered the existence of solutions for a class of  fractional Schrdinger equations. Under the condition that nonlinear term satisfied nonquadratic growth,  the existence of nontrivial solution was obtained by applying the variational methods.

Let the service time {X_n, n≥1} be a nonnegative nonstationary negatively associated (NA) random variable sequence and N(t) be the renewal process generated by {X_n, n≥1}. By the results of  the precise asymptotics for the partial sums of NA sequence and the relations between S_n and N(t), that is {N(t)<n}={S_n>t}, we proved the precise asymptotics for renewal processes of nonstationary NA sequences.

We used the theory of topological degree to study a sufficient condition for solvability of absolute value equation. The results show that the absolute value equation has a solution or has a exceptional family of elements. Furthermore, by this conclusion, we obtain the noexistence of the exceptional family of elements, when matrix A is a generalized cubic matrix, so the absolute value equation has a solution.

We studied  stochastic Volterra-Levin equations driven by fractional Brownian motion. Aiming at the problem that  the stability in probability and the exponential stability were sometimes too strong in some cases, we discussed a kind of weaker stability: the stability in distribution, and obtained  the stability conditions in distribution of the segment process of the solutions.

Aiming at the problem that there was a lot of noise in the measurement of the direction of the gyroscope, resulting in a large error to the dead-reckoning navigation, we proposed a method of dead\|reckoning navigation based on neural network. The method used neural network to investigate  the time-varying relationship between acceleration measurement and orientation measurement. Thus, we used acceleration value to calculate direction value through this timevarying relationship without using the gyroscope, and then completed the autonomous underwater vehicle (AUV) dead\|reckoning navigation. The results show that the algorithm can  only use the accelerometer to complete dead\|reckoning navigation. So we can avoid dead-reckoningerrors caused by gyroscope noise at the sea surface. Simulation results show that the algorithm has higher accuracy.

In order to improve the spatial resolution of adaptive optics (AO) images, we proposed multi\|frame joint deconvolution algorithm for AO images based on frameselection and maximum likelihood estimation. The algorithm took maximum likelihood estimation as the basic principle. According to the Gaussian noise model of the image, the joint log likelihood function of multi\|frame AO images was established. Firstly, we selected frames of the observed multi\|AO
 images and selected the high quality degraded images. Secondly, combined with the observed conditions and characteristics of AO system, the estimation model of point spread function was derived. Finally, we established iterative solution formulas, and obtained multi\|frame AO images joint deconvolution
 method. The experimental results show that, compared with the RichardsonLucy EM or CPFAdaptive algorithm, the PSNR values of the proposed algorithm are increased by 9% and 5% respectively, and the Laplacian gradient moduli are increased by 11% and 8% respectively, and clearer target images are obtained.

Aiming at the problem that the current target tracking algorithm was subject to large environmental interference and poor anti\|occlusion ability, the author
designed an anti\|occlusion tracking algorithm for moving objects. Firstly, the limitations of the classical tracking algorithm for moving objects—mean
 shift algorithm were analyzed, and then salient features that contributed most to the tracking were selected from the target candidate features, and the adaptive template updating strategy was adopted to improve the accuracy of the moving objects. The simulation results show that the algorithm can track moving object accurately and realtime, accelerate the tracking speed of moving object,  have good robustness to occlusion object, and obtain better tracking results for moving object.

Due to the algorithm for motion object segmentation had poor adaptation of complicated scene, and the time complexity was too high, we proposed a new motion object segmentation algorithm, which used adaptive manifold denoising to achieve motion segmentation between rigid and nonrigid objects. We first introduced an adaptive kernel space in which two feature trajectories were mapped to the same point if they belonged to the same rigid object. Then, we adopted an embedded manifold denoising algorithm based on the adaptive kernel to segment the motions of rigid and nonrigid objects. Finally, we did contrast experiments with several traditional algorithms on several datasets. Experimental results show that the algorithm can achieve better segmentation and tracking effects in different scenes.

Aiming at the problem that there were many block obstacles to communication between blocking nodes in the actual application environment, so that the communication between nodes became non lineofsight (NLOS) type, we proposed a kind of NLOS mobile node localization algorithm based on
 error prior knowledge. The algorithm first calculated the number of NLOS measurements with errors in the total number of percentage K according to the error prior knowledge. And then according to the K to select the larger measured value of error. Finally, the NLOS measured value with larger error was corrected. The simulation results show that, compared with the traditional mobile node localization algorithm, the proposed algorithm can effectively reduce the NLOS error and improve the node localization accuracy.

In order to obtain higher accuracy of face recognition, it could meet the realtime requirement of face recognition, we proposed a face recognition algorithm based on optimal discriminant feature and relevance vector machine. Firstly, wavelet transform was used to denoise face image, and multi direction and multiscale Gabor features of face were extracted. Secondly, kernel principal component analysis was used to screen Gabor features of faces to find the optimal discriminant feature which had a great influence on face recognition results, the number of features was effectively reduced, and redundant information among features was removed. Finally, relevance vector machine was used to learn the optimal discriminant feature vectors and establish multiclassifier for face recognition, and standard face database was used to carried out experiments to test performance compared with the classical face recognition algorithms. The experimental results show that the average face recognition rate of the proposed algorithm is greatly improved, and the average face recognition time is less than that of the classical face recognition algorithms.

In order to improve the utilization ratio of cloud computing resources, combined with the characteristics of cloud computing resource optimization problem, we designed a glowworm algorithm for solving the optimization problem of cloud computing resources. Firstly, the constraint condition of cloud resource load scheduling was established, and the minimum user task execution time was used as the objective function of cloud computing resource load scheduling optimization. Secondly, glowworm algorithm was used to find the value of the objective function of the optimal resource scheduling strategy. The simulation experiment of cloud computing resource load scheduling was implemented on CloudSim platform. The experimental results show that the proposed algorithm reduces the computation time of cloud computing tasks, balances the load of cloud computing resources, makes the cloud computing resources allocate reasonably, and has obvious advantages over other algorithms.

Aiming at the problem that current device to device (D2D) communication resource sharing algorithm could not solve the contradiction between resource utilization and channel interference, in order to improve the performance of D2D communication, we designed a D2D communication resource
 sharing algorithm based on game theory. The algorithm took the communication system throughput as the goal. By introducing game theory, the communication resource sharing among various users could be realized, so that resources could be reasonably allocated among communication links, interference between channels could be reduced, and communication quality of cellular link could be improved. Compared with the classical D2D communication resource sharing algorithm. The result shows the proposed algorithm obviously improves the quality of D2D communication, improves the channel utilization, and improves the total system throughput greatly.

Aiming at the problems that traditional collaborative filtering algorithm existed data sparseness, data redundancy and low efficiency, we proposed a collaborative filtering recommendation algorithm based on social relation and condition completion. The algorithm applied the data of social relationship into the process of matrix completion to reduce the sparse degree of the original matrix and improve the accuracy of the data completion. The vector data involved in computation was conditionally chosen to reduce the redundancy of the data and the time complexity of the algorithm in the computation of the project similarity. The experimental results show that the accuracy of recommendation of the proposed algorithm is obviously improved.

Aiming at the problem that the traditional model could not accurately identify and detect network traffic anomalies, we proposed a network traffic anomaly detection model based on time series analysis. Firstly, the original data of network traffic was extracted, and the original data was denoised by wavelet threshold to eliminate the influence of interference factors. Secondly, time series analysis method was used to mine the relationship among network traffic data, and network traffic anomaly detection model was established. Finally, simulation experiments were used to verify the effectiveness and superiority of the detection model. The result shows that time series analysis can accurately and timely detect abnormal behavior of network traffic, and the detection results are better than other current network traffic anomaly detection models.

Aiming at the characteristics in vehicular ad hoc networks (VANET) such as randomness and uncertainty of sending and receiving information, high speed movement of VAENT node and fast topology change, we proposed a quantitative verification method based on model detection. In order to improve the reliability of VANET broadcast protocol information transmission, the IPTA model of interval probabilistic real\|time automata was used to represent the nodes in the VANET, and using the interval probability to represent the probability of automatic state transition. We verified the successful probability of sending and receiving broadcast information in VANET, and proved the feasibility of the method.

Using the modeling method in model checking, the audit method, its calculation process and the expected calculation results were built to a model, and the audit method of voucher number checking which had strong logic was verified using model checker, we proposed a framework of using model checking method to verify the logic correctness of the audit method. The verification of the audit method was modified by using the counterexample of the model checker. The experimental results show that model checking method can verify the logical correctness of audit methods.

Aiming at the problem of low detection accuracy for abnormal behavior of network states, we proposed an anomaly detection model  of network state based on data mining. Firstly, the network state signal was extracted, and the signal was pretreated by wavelet transform, and the features of the network
 anomaly detection were extracted. Secondly, the network state anomaly detection model was built by echo state network, and genetic algorithm was used to optimize the parameters of the echo state network. Finally, the network state anomaly data sets were used to test the effectiveness of the model. The test results show that data mining technology can accurately detect abnormal behavior of various network states.

Aiming at the problem that the algorithm for traditional C45 decision tree classification algorithm needed to be scanned several times, resulting in defects of running low efficiency, the author proposed a new improved C45 decision tree classification algorithm by optimizing the logarithmic operation related information gain derivation algorithm in order to reduce the running time of the decision tree classification algorithm. And the simple split attribute of the continuous attributes in the traditional algorithm was improved to the optimal partition point splitting processing in order to improve the efficiency of
the algorithm. Experimental results show that compared with the traditional C45 decision tree classification algorithm, the improved C45 decision tree classification algorithm greatly improves the execution efficiency and reduces the demand space.

We considered the theory of Noether’s symmetry and conserved quantity for elastic continuous system. Firstly, basic formulas for the Hamilton action variation of elastic continuous system were derived based on the equivalent and nonequivalent parameters variations. Secondly, we gave the definition of Noether’s symmetry for elastic continuous system and obtained the determinant  condition of Noether’s symmetry： Noether’s identity. Then we obtained the Noether’s conserved quantity resulting from the Noether’s symmetry of the system, and put forward the Noether’s theorem for elastic continuous system. Finally, the example of plane wave propagating in the elastic medium was used to illustrate the application of the results.

We gave the quantum transmissivity of onedimensional photonic crystals with nonvertical incidence, and studied the effects of the defect layer, incident angle, thickness of medium layer and refractive index of medium layer on the transmission characteristics of onedimensional photonic crystals, respectively, and compared their results with the classical method results. The results show that when the light enters onedimensional photonic crystals at a certain angle, the quantum method results has quantum effect.

We used the planewave expansion method to derive the master equation of twodimensional photonic crystal for transverse magnetic mode and transverse electric mode, and obtained the complete photonicbandgap of twodimensional photonic crystal for two modes. We studied the change rule
of filling ratio and dielectric constant of background medium with the complete photonicbandgap width and center frequency location of twodimensional photonic crystal. Thus, the optimal design of the complete photonicbandgap was realized.

Using density functional B3P86 method, we optimized the ground state stable geometries of the gasphase acetone molecules and charged ions at the level of 6311++G(d,p). At the same time, using the method of timedependent density functional theory (TDDFT), we studied the low excited state properties of the gasphase acetone molecules and ions. The results show that the energy of the system increases gradually, the difference between S1 excited state energy and ground state energy decreases, molecular fluorescence wavelength increases sharply, and the number of electron transition orbitals decreases with the increase of the number of electrons obtained by molecules.

Using the method of density functional theory B3LYP,  we investigated the third reaction channel of the chiral transition process of the nonrest
ricted area monomer methionine molecule at the level of B3LYP/6-311+G(2-df-). We drawed a complete reaction potentialenergy surface for chiral transition path of methionine molecule by finding the structures of the extreme value points in the reaction process, and analyzed the geometric and electronic structure properties of extreme value points too. The results show that the hydrogen atom on the chiral carbon atom of Smethionine molecule can transfer to the other side of the carbon atom via the 6C--10O atoms as a bridge, and achieve the third reaction channel of the chiral transition of methionine molecule from Stype to Rtype. On this path there are four intermediates and five transition states. The maximum reaction energy barrier is 321.361 2 kJ/mol, which comes from the second transition state TS₂-S3-Met.

We studied reaction mechanism and water solvation effect of chiral transition of tryptophan molecules of two most stable configurations by
 using the B3LYP method of density functional theory, the MP2 method of perturbation theory, and SMD model method of selfconsistent reaction field (SCRF) theory. The results show that there are three chiral transition channels a,b and c of tryptophan molecules of two configurations. The dominant reaction channel of configuration one is channel a, and the stepdetermining free energy barrier is 2567 kJ/mol.  The dominant reaction channels of configuration two are channel b and c,  and the stepdetermining free energy barriers are 258.8, 256.7 kJ/mol, respectively. The stepdetermining free energy barriers come from the transition state of proton transfer from the chiral C to the amino N. The water solvation effect reduces the stepdetermining energy barrier to 113.4 kJ/mol for the dominant reaction channel of the configuration one. Monomer tryptophan molecule is stable. The chiral transition of tryptophan can molecules can proceed slowly in water solvent environment.

We simulated the dynamical mechanism of excited states of water complexes 7-hydroxyflavone-(H₂O)₄ (7HF-(H₂O)₄) at the basis set level of TZVP, by means of B3LYP methods of density functional theory and timedependent density functional theory. The results show that intramolecular charge transfer process of the 7HF appears in the frontier molecular orbits of the first electron excited state. The molecular structure of the 7HF is reversed in the ground state and the first electron excited state. Five intermolecular hydrogen bonds in the complex appears to be a strengthening mechanism in the first electron excited state, which can drive the multiple proton transfer reaction of the excited state.

The mesoporous materials SBA15 and phosphotungstic acid were evaporated and concentrated under 80 ℃ water bath to prepare supported phosphorus acid catalyst HPWSBA15, which was used as the catalyst for the synthesis of dioctyl sebacate. The effects of acid catalysis, different HPW loadings, reaction temperature, reaction time, molar ratio of acid to alcohol on the synthesis of dioctyl sebacate were studied. The results show that when the loaded amount of phosphotungstic acid of 50%, the reaction time of 2.5 h, n(sebacic acid)∶n(isooctyl alcohol)=1∶3, the highest esterification rate is 95.47%.

Three monoFe(Ⅲ)substituted Keggintype phosphotungstates with different organic ammonium cations were systhesized: [JP2]［CTA］₄PW₁₁Fe(H₂O)O₃₉ (CTAFe), ［TEA］₄PW₁₁Fe(H₂O)O₃₉ (TEAFe) and ［TMA］₄PW₁₁Fe(H₂O)O₃₉ (TMAFe) (CTA=cetyl trimethyl ammonium bromide, TEA=tetraethyl ammonium bromide, TMA=tetramethyl ammonium bromide). The structure and morphology of three phosphotungstates were characterized by infrared spectroscopy (IR), UV\|visible spectroscopy (UV\|Vis)， Xray diffraction (XRD) and scanning electron microscopy (SEM). The inhibitory effect of three phosphotungstates on the growth of human colorectal carcinoma HCT116, HT29 cells and rat colorectal carcinoma CT26 cells was studied by MTT assay. The results show that the phosphotungstates with different organic ammonium cations still keep Keggintype structure. But the cations affect the morphology. Longer carbon chain of organic ammonium cations makes crystallinity decrease, no clear crystal morphology of CTAFe. TEAFe and TMAFe have no inhibition on HCT116, HT29 and CT26 cell proliferation, but CTAFe can inhibit these three tumor cells proliferation, showing dosedependent. The IC₅₀ value for CT26 and HCT116 cell was 0.038,0.08 mg/mL, respectively. So longer carbon chain of organic ammonium cation makes Keggintype phosphotungstates inhibit tumor cell growth stronger.

By homologous sequence and protein structure analysis, we found that A380 was an absolutely conserved site of aspartate kinase, and performed the sitedirected mutagenesis, isolation, purification and characterization of the site. The results show that compared with the wild type (WT), the V_max of the mutant A380H is increased by 4.28 folds. The optimum temperature of the mutant A380H is increased from 28 ℃ to 35 ℃, the optimum pH  is still 7.5, and the halflife is shortened from 4.5 h to 3.5 h. The substrate inhibitors have inhibitory effects on WT and mutants, threonine and lysine show synergistic inhibition effects. However, threonine alone has an activation or inhibitory effect on A380H, Mg²⁺ and Ni²⁺have an activation effect on WT,  1,5 mmol/L of Cu²⁺ has an activation effect on A380H. Compared with WT, the inhibitory effect of methanol and isopropanol on A380H is enhanced. The inhibitory effect of nbutanol and acetonitrile on A380H is reduced and show activation.