We studied the first initial and boundary value problems for a class of pseudoparabolic equations with variable exponent in a smooth domain Ω. Firstly, we constructed the approximate solutions through Galerkin method, then under some conditions limited on the parameter, using energy method, we obtained the uniform estimates for the approximate solutions. At last, using the above estimate, we gave the existence and uniqueness result for the original
 problem.

Using the renormalization group method based on the theory of envelope the authors gave the uniformly valid asymptotic expansion form of the spike solution, on the basis of which the authors also presented the onecycle time of the spike solution.

Nonlinear fractionalorder Volterra integrodifferential equation was transformed into a system of algebraic equations by Legendre wavelet operational matrix of fractional integration. Numerical solution of original equation was obtained through solving algebraic equations and error bound value was estimated. Finally some examples demonstrate the validity and precision of this method.

Employing bifurcation theory and topological theory, we studied the positive solutions for the fourthorder two point semipositone boundary value problemwhere λ is a positive parameter, f: ［0,1］×［0,+∞)→R is continuous, and we obtained a new existence result of positive solutions with the nonlinearity satisfying asymptotically linear growth condition at infinity.

We studied a positive solution of the semipositone boundary value problem of fractional differential equation:
D^α₀₊u(t)=λf(t,u(t)),0<t<1,
        u(0)=u(1)=u′(0)=u′(1)=0
 where 3<α≤4 is a real number, and D^α₀₊ is the standard RiemannLiouville differentiation, and the nonlinear term has no numerical lower bound. We gave an existence theorem of this equation by means of the Krasnosel’skii fixedpoint theorem on a cone.

Using Schauder’s fixed point theorem, we studied the first order antiperiodic boundary value problem involving the distributional HenstockKurzweil integral, obtaining a new existence theorem.

Let E be an equivalence on a finite set X, and OI_E*(X) be the semigroup consisting of all orderpreserving strictly partial oneone transformations of type E, then we  characterized the maximal inverse subsemigroup of OI_E*(X) under certain assumptions.

The conditions of the existence of the solutions of linear complementarity problem and absolute value equation were given. The transformations between linear complementarity problem and absolute value equation were studied, including unconditional and conditional transformations. The idea of solving linear complementarity problem or absolute value equation was presented.

Based on a new class of concept of generalized V-r-type-Ⅰ invexity defined for nonsmooth multiobjective programming problems, FritzJohn and Karush-Kuhn-Tuker sufficiently optimal conditions were obtained for a feasible point to be an efficient solution. Moreover, a mixed type dual was formulated and weak duality and strict converse duality theorems were proved.

The arcsearch interiorpoint algorithm was used to solve the linear programming problem and the iteration complexity O(n^3/4L) was obtained for this algorithm. The proposed algorithm was used to search for the optimizers along the ellipses in a wide neighborhood of the central path. The numerical results show that this algorithm is efficient.

The authors mainly studied the numerical method for valuing American lookback put options under the BlackScholes model. Applying the finite difference method, we obtained the discretization form of the BlackScholes equation, which was used to solve the option value, and we got the optimal exercise boundary by Newton’s method. Solving this problem by the two method in turn, we can get the option price and the optimal exercise boundary simultaneously. Numerical experiments verify the efficiency of the method.

We studied the verifying methods of the multiple roots of nonlinear equations with the help of the interval algorithm and bordered system,  proposing the verifying algorithm, by which an approximate solution and its error bound are output so as to get  an exact solution  within the computed bounds.

The author considered the stability problem of linear singularly perturbed systems with timedelay. Under the norm bounded uncertain matrix constraints, a new sufficient stability criterion was proposed by Lyapunov stability theory and matrix analysis method. This method is expressed in terms of linear matrix inequalities that does not require the system decomposition and reduction technique. Thus, the method is simple and feasible, which can be applied to both standard and nonstandard singularly perturbed systems with timedelay.

We studied the partial functional linear regression model using presmoothing technique. In the model, the response is scalar and explanatory variables consist of finite dimensional vector and functional variables valued in functional space. We proposed a new estimator of the coefficients and showed their consistency.

Under some suitable assumptions, with the help of  the asymptotic distribution of the products of sums of partial sums of ρ-mixing, the author obtained some general results on precise asymptotics of the products of sums of partial sums of ρ-mixing sequences for  more general boundary function and weighted function.

Based on the definition approach of twoparameter Markov process, singleparameter strong Markov process and the relationship between the various stopping points, the 1-strong Markov process, the 2-strong Markov process and the widefuture strong Markov process with nonrandom parameter tran
sformation were defined. Under the condition of random process being progressive measurability, the *-strong Markov process must be a 1,2-strong Markov process, the 1,2-strong Markov process must be a  singlepoint strong Markov process. Under the condition of (F₄), the 1,2-strong Markov process must be a  singlepoint strong Markov process. Widefuture strong Markov process must be a singlepoint strong Markov process.

The authors studied totally real biharmonic submanifolds in a quaternion projective space by the movingframe method under the guidance of  maximum principle, proved the minimum of pseudoumbilical biharmonic submanifolds and the rigidity theorem on the square of the lenghth of the second fundamental form. And we also gave several sufficient conditions under which complete totally real biharmonic submanifolds are minimal.

This paper deals with the existence of solutions for some fractional elliptic equation (-Δ)su=f(x,u) under Dirichlet boundary condition. When the asymptotic growing of the nonlinearity f at zero and infinity was maintained, a new existence result was obtained by means of used the mountain pass theorem.

Based on the correlation among matrix elements, a new matrix, i.e., symmetric local double αdiagonally dominant matrix was defined by the partition of the row indices. New criteria for the generalized strict diagonal dominant matrix were given on the basis of the properties of the new matrix.

The transition matrix of the downward continuation of boundary conditions about elastic wave equation inversion was established. The solving method and stable conditions of the downward continuation of boundary conditions were obtained. The problem that the boundary conditions at downward continuation depth points cannot be determined has been solved so as to improve the speed and precision of inversion calculation.

We proposed a new method to extract invariant features from human face image. With the help of digital curve fitting, we represented face binary edge map with highorder polynomial and parabola segments. Then, the polar moment of the inertia of pixel block beside the curve segments was used to measure the difference between local texture and shape. From the analysis of the experimental result, it is concluded that compared with line edge map and parabola edge map, this method can give a better way to describe the feature distribution of face images.

Aiming at the problem that affinity propagation algorithm has a difficult to deal with highdimensional data, the authors put forward an selfadaptive affinity propagation algorithm based on singular value decomposition. With the aid of singular value decomposition introdued, the highdimensional data were reconstructed and dimensions were reduced to eliminate the redundant information, based on which, a nonlinear function strategy was adopted to adjust the damping factor adaptively and improve the clustering performance of the algorithm. Experimental results show that the proposed algorithm has obviously better clustering performance than the traditional algorithm on clustering accuracy and the number of iterations.


A mixture IRT model was proposed which is composed of the testlet response model and the partial credit model for representing the subject and object tests. Meanwhile a modified artificial bee colony algorithm was proposed to estimate the parameters in the mixture model. The comparative experiment results based on the simulate data show that the novel method in this work is feasible and effective.

In view of a lot of mixed image pixels contained in remote sensing images classification, fuzzy clustering support vector machine （SVM） was introduced to deal with the remote sensing images unmixing. In the proposed technique, GustafsonKessel is used to select the useful sample points for improving
 the classification performance of support vector machine. The effectiveness of the proposed method was evaluated through the forest cover remote sensing classification. The experiment shows that the accuracy of mixed pixels classification can be increased by applying the learning scheme, compared with that of traditional SVM classification method.

On the basis of traditional tasks scheduling algorithm, we established the optimal sequence of servers and load balance index for tasks in the process of scheduling. Meanwhile, we used a number of connections to realize the constraint of servers, which has improved the performance of load balancing that has ignored in the traditional task scheduling algorithm. The experimental results show that our improved algorithm can achieve the high degree of load balancing and shorten the task completion time. In addition, this algorithm improves the ability of batching task processing for server cluster, thereby achieving the goal of optimization.

In order to improve the performance of digital watermarking system, a watermarking algorithm was proposed for color images based on the combination of discrete wavelet transform, singular value decomposition and Turbo codes. Firstly, digital watermarking was pretreated by chaotic encrypting and Turbo coding; secondly, the blue component of color image was decomposed via discrete wavelet transform; finally, the pretreated watermarking information was embedded into the low frequency band of the blue component which had been DWT of the original image by modifying its singular value. It does not need the original image when the watermarking is extracted, so it can be applied in the practice easily. Simulation results show that the watermarking algorithm has good invisibility and robustness to common attacks and geometric attacks.

Since the useritem matrix is sparse, and there are less users or items satisfying the conditions, the precision of the algorithm can’t be high. By sampling neighbor collaborative filtering algorithms, users take full advantage of score matrix provided information to increase the users or projects participated in the calculation process, so as to solve the shortage of traditional collaborative filtering algorithms in real application. Experiment results show that the new algorithm can effectively improve the precision in recommendation along a small increasing of runtime.

In view of the active energy of motor feedback system, the current waveform and the energy conversion process of a motor in brake state were analyzed, and the mathematical model of the threephase voltagetype inverter grid was established in the synchronous rotating dq coordinate system, the
 independent control of the feedback current active component and reactive component grid was achieved with SVPWM direct current control algorithm, building experimental platform of motor energy feedback system in order to complete the resistive load experiments and feedback experiments of threephase gridconnected inverters. The experimental results show that bidirectional flowing of the energy is implemented with energy feedback, and the harmonics are suppressed effectively.

A novel stability analyisis method was proposed for addressing the problem of stability analysis of continuoustime nonlinear systems based on the Takagi-Sugeno fuzzy model. In the process of stability analysis, aslack matrix method was applied to further considering the useful underlying fuzzy membership functions’ time derivative. Owing to more freedom can be introduced in virtue of the slack matrix method, the obtained stability criteria are less conservative than those existing ones. Furthermore, the stability criteria proposed are given in terms of linear matrix inequality, which is easily solved via MATLAB numerical software. Finally, a numerical example was given to illustrate the effectiveness of the proposed result.

The equation of fixed point was established for LLT image denoising model based on a theory in convex analysis. Numerical solutions of the equation were obtained through the fixed point iteration. A numerical experiment was conducted to compare our method with the one provided in the original LLT paper in terms of both the speed of convergence and the denoising effect. The numerical experiment results show that our method is faster in convergence and
more effective in denoising.

To obtain the weak signal light from the high background light, a narrow bandwidth Faraday anomalous dispersion optical filter (FADOF) was studied. The theoretical model for the filter was reported. The Faraday anomalous dispersion optical filters have two working modes: two side peak transmission and center peak transmission. The former work mode can get single peak transmission of 25% with a bandwidth of about 600 MHz. The other work mode can get a spectra with a transmission rate of almost 100% and a bandwith of about 700 MHz. The experimental measurements are consistent with theoretical results.

An easy carbonization and activation approach was employed to synthesize porous carbon material with coffee grounds as carbon source. X-ray diffraction (XRD), Raman spectroscopy, and scanning electron microscopy (SEM) show that the prepared material possesses a disordered structure with a relatively high graphitization degree. The existence of mesopores was confirmed by the nitrogen adsorption/desorption isotherms as well as the pore size distribution curve. At a mass current density of 0.1 A/g, the initial discharge and charge capacities of the prepared material can reach as high as 1 029 and 461 mA·h/g, respectively, much higher than the theoretical capacity of graphite (372 mA·h/g).

We studied the absorption property and electric field distribution of onedimensional photonic crystals, the effects of absorbing medium and active medium defect layer on photonic crystals absorption property, and the electric field distribution of photonic crystals with and without defect layer, respectively.

The light propagation characteristic in onedimensional function photonic crystal with metal defect was studied by transfer matrix, and compared with that of the function photonic crystal without defect layer, showing electric field intensity enhance obviously. We researched the effects of the position and the number of defect layers on electric field distribution. Then we studied the electric field distribution via changing the half period numbers.

The crystal structure, mechanical, thermodynamic, and electronic properties of the B19 phase of superconducting alloy LiBe were investigated by means of firstprinciple method based on the density functional theory. The results show that the elastic constants of LiBe alloy meet the BonnHuang kun criterion up to 120 GPa, and thus its lattice is dynamics stable. With increasing pressure, LiBe alloy exhibits anisotropy to some degree, and axis c is more compressible than axis a. The Debye temperature of LiBe alloy increases with increasing pressure. The populations analysis shows that the electron mainly transfers from s electron of Li atom to p electron of Be atom in LiBe alloy under pressure.

Meso-tetra(4-hydroxyphenyl)porphyrin (THPP) interacting with lysozyme was investigated by the fluorescence spectroscopy under simulate
d physiological conditions. The results indicate that THPP quenched the intrinsic fluorescence of lysozyme via a static quenching procedure. The binding constant KA between THPP and lysozyme was 5.97×104 L/mol at 291 K. According to the thermodynamic parameters, it was obtained that hydrophobic was a main acting force between THPP and lysozyme. The presence of Fe²⁺,Fe³⁺,Cu²⁺,Mg²⁺,Ca²⁺and Zn²⁺ did not affect the binding constant of THPP and lysozyme. According to Frster’s nonradiative energy transfer theory, the distance between THPP and lysozyme was 3.35nm. The synchronous fluorescence spectra reveal that the vicinity of tryptophan becomes more hydrophobicity with the increase of THPP.

Using density functional theory at the level of B3LYP/6-31+g(d,p), we investigated the chiral transition process of the isolated α-alanine molecule. Further more, a complete chiral transition path reaction potential energy surface was drawn by looking for the extreme value point structures including the transition state and intermediate, and the geometry and electronic structure properties of extreme value points were also analyzed. The results show that the hydrogen atom on the chiral carbon atom of Sα-alanine molecule can transfer to the other side of the carbon atom via the oxygen atoms of carboxyl atoms as a bridge, to achieve the chiral transition of α-alanine molecule from Stype to Rtype. On this path there is one intermediate and two transition states. The biggest reaction energy barrier is 326.6 kJ/mol derived from the first transition state TS1.

Triisopropanolamine borate was synthesized through the esterification of triisopropanolamine and boric acid, and purified by recrystallization. The structure of triisopropanolamine borate was characterized by MS, ¹H NMR and FTIR. Effects of raw material ratio, reaction temperature, reaction time, and reaction solvent on the synthesis, and those of recrystallization solvent and solvent ratio on the purification were investigated. The product was obtained with a purity of 99.8% and a yield of 87.1%, respectively.

Apoptosis of pancreatic β cell RINm-5F was induced by glucose coupled with sodium palmitate. Effects of DhHP-6 or/and Exenatide on the apoptosis of RINm-5F cell were detected by methyl thiazolyl tetrazolium (MTT) assay. DhHP6 and Exenatide decreased the apoptosis induced by Glu-Pal significantly without no synergistic effect between them. In addition, we also found that DhHP6 and Exenatide both stimulated the proliferation of RINm-5F cells, and there was a synergistic effect between them.

The molecular structure of glycinin was investigated by FTIR and Raman spectroscopy. The frequency and signal intensity of IR and Raman bands were assigned. The data suggest that FTIR and Raman spectra reflect a large amount of structural information. The secondary structure of glycinin was ass
essed by the deconvolution amide Ⅰ band and curvefitting. Quantitative analysis of secondary structure reveals that the results of the folded glycinin β
sheet had no significant difference, while the glycinin αhelix, turning angle, random coil had significant difference (\%p\%<0.05). The IR bands at 
1 618 cm^-1 and 1 682 cm^-1 were considered to reflect the formation of intermolecular aggregates (11.1%) and intramolecular aggregates (
9.5%). The \%I\%850/830 intensity ratio of Raman tyrosine doublet suggests that the contents of the buried tyrosine residue and exposed tyrosine residue were 14% and 86% in glycinin.

Fmoc solidphase peptide synthesis was used to synthesize cyclic peptide in light of the known isocitrate lyase linear peptide sequence according to the end to end way. Mass spectrometry demonstrates that the measured value of relative molecular mass is consistent with the theoretical value. Inhibition test confirms that the cyclic peptide shows significant inhibition to the ICL activity (the inhibition rate was more than 50%). At the same time, halflife of linear peptide and that of cyclic peptide in plasma were measured by HPLC. Results indicate that halflife of cyclic peptide in plasma amounts to 11 min, which is increased by 175% compared with that of linear peptide.

The peptides, which show enhanced memory effect, from Panax ginseng were separated on a Sephadex LH20 column, the mobile phase was volume fraction 10% of methanol, and purified by HPLC. Then the amino acid sequence was analysed by protein sequencer. The results of amino acid sequential analysis showed that a novel tripeptide whose amino acid sequence is GlnThrSer was obtained.

Biomass charcoals were made from 3 kinds of biomass wastes, maize straw, branches and leaves trees at 350,550,750 ℃, respectively. The
 structure and composition characteristics of biomass charcoals were characterised by thermogravimetric analysis, FTIR analysis, Boehm titration and X-ray diffraction analysis. The results show that maize straw has the lowest thermal stability and the highest mass loss, followed by those of the branches and leaves. Compared with branches and leaves, maize straw has the greatest dispersion degree in Xray diffraction with a less layer number of microcrystalline. The total quantity of surface functional groups in biomass charcoals made from different feedstocks at the same temperature is similar, the pH value has larger differences and biochars derived from maize straw have the highest pH value. Results of characterization of biochars derived from the same feedstock show that with the increase of pyrolysis temperature, the aromatization degree of biochars increases; the content of surface functional groups decreases; pH value increases; the characteristic peaks of cellulose and hemicellulose disappear; the structure of biomass charcoals tends to graphite crystallite structure.