Based on the Lagrangian cubic element finite volume method for Poisson equation on triangular meshes constructed by us, we found that the convergence rate of average gradient of the numerical solutions is approximately 4 order at the symmetrical points of triangular element (i.e.midpoints of three edges and three vertices) through the numerical experiments,  which is nearly one order higher than that of the H¹ norm (O(h³)).

The authors presented a class of adaptive diffusion equations which provide a model for multiplicative denoising. This type of diffusion varies according the local gradient information, adaptively aiming at multiplicative noise. The diffusion speed is proportional to noisy level and there is no diffusion in the domains with no noise. The diffusion result from the proposed model is a combination of isotropic diffusion based on heat equation and anisotropic diffusion based on total variation. Theoretical analysis and experimental results illustrate the effectiveness of the model in removing noise and enhancing edges while avoiding the staircasing effect.

Having studied the totally real minimal submanifolds in the quasiconstant holomorphic sectional curvature space by means of the method of moving frames, we got an integral inequality of Simons type and a conlusion.

Firstly, two approximate optimality conditions of the minimum volume axisaligned ellipsoid (MVAE) problem were defined. Secondly, a new approximate solution satisfying the second approximate optimality condition was computed. Furthermore, an approximation algorithm for the MVAE problem was presented, which has the linear convergence. The numerical results show the efficiency of the algorithm.

As for the linear finite volume element schemes for parabolic problems on triangulation, we proved that the superconvergence property held for the semidiscrete scheme and fully discrete scheme. Furthermore, the superconvergence of numerical gradients at optimal stress points was obtained. Finally numerical example was presented to confirm our  theoretical results.

The authors proposed a collocation method for solving a class of Volterra integral equations with weakly singular kernel. Firstly, we showed the existence and uniqueness of the solution by the contraction mapping theorem, and then constructed the collocation scheme for this kind of equations together with the error analysis. Finally, the numerical experiments verified our theoretical results. This numerical method is useful for general nonlinear Volterra integral equations.

A predatorprey model with disease in the prey was established and analysed. The existence of the equilibrium points and the boundedness of solution were studied. The sufficient condition of the local asymptotical stability of the boundary equilibrium was studied with the method of latent root, and furthermore, the global asymptotical stability of two boundary equilibrium points, and the local asymptotical stability of the positive equilibrium point were analyzed, with the sufficient condition of their stability obtained.

The existence of multiple positive periodic solutions for threespecies L-V system with harvesting terms and Holling Ⅱ type functional response was studied via coincidence degree theory and comparison theorem, at least eight positive periodic solutions for L-V system were obtained. Aconcrete example was given to illustrate the effectiveness of our results.

Let OP_n be the orientationpreserving semigroup on ［n］. For an arbitrary integer r such that 2≤r≤n-1, the structures of the maximal regular subsemigroups of the semigroup K(n,r) were studied.  Using MillerClifford theorem, the authors have proved thatK(n,r) has exactly two classes of maximal regular subsemigroups, i.e.:M(α)=K(n,r-1)∪(J_r＼R_α); N(α)=K(n,r-1)∪(J_r＼L_α), α∈J_r, where J_r={α∈OP_n: | Im(α)|=r}, α∈J_r, R_α and L_α are the Rclass and  L class containing α, respectively.

The composition G［H］ of two graphs G and H can be decomposed into two edgedisjoint graphs, one is their cartesian product G□H and the other is a bipartite graph Z, by which χ′_s(G［H］)≤χ′_s(G□H)+χ′(Z),are thus obtained, where χ′_s(G) represents the  vertex distinguishing proper edge chromatic number of G.

We characterized commuting dual Toeplitz operators with pluriharmonic symbols on the orthogonal complement of  Dirichlet space in Sobolev space on the unit ball. We also obtained the sufficient and necessary condition, that is, the product of two dual Toeplitz operators with pluriharmonic symbols for a dual Toeplitz operator.

Based on the properties of α-chain diagonlly dominant matrices, several new sufficient conditions to determine generalized strictly diagonlly dominant matrices were given by means of some techniques for inequalities and a method for finding  positive diagonal matrix factors, and thus the corresponding results are improved and generalized. A numerical example was given to show the advantages of our new criteria.

The positive solution of a class of threepoint boundary value problems of fractional differential equation with complex nonlinearity is established on the basis of fixed point theorem on cones. It is noted that the fractional derivative term is involved in the nonlinear term explicitly.

We studied the numerical method for stochastic differential equations with discontinuous coefficients via Heun method. The numerical computational scheme was given to solve such a type of equations. The weak convergence of the method was also discussed. The numerical examples demonstrate that the convergence rate of Heun method was faster than that of Euler method.

With the aid of the setvalued theory, we discussed a particular differential game for the differential game model of twoplayer conflicting with other players indirectly affecting outcome and gave the existencetheorem of the minimax controls.

This paper deals with the existence of random attractors for the stochastic FitzHughNagumo systems with delay on infinite lattice. Under suitable dissipative conditions, it is shown that such a system has a random attractor which is a random compact invariant set.

We mainly applied the conceptions of time scales and exponential dichotomy on time scales to study the roughness for exponential dichotomy on different time scales and discussed the relationship between stable/unstable manifolds for the perturbed equation on different time scales.

This paper deals with the system induced by the nonprimitive and nonconstantlength substitution ζ over the alphabet {0,1}, w
here  ζ(0)=0a₁…a_p-1, ζ(1)=1,…,1. It has been proved  that this system is LiYorke chaotic if and only if there exists i>0  such that a_i=0. In addition, investigating the occurrent frequency of the symbols shows a sufficient condition for the system not to be distributively chaotic.

The existence of global solutions of the modified cellular Potts model(CPM) was investigated via the Moser’s iteration. We can use the modified cellular Potts model to describe the relationship between the cell and the cell secretion the effect of it on chemotaxis. We can also use the new model to consider the impact of  cell nutrients on chemotaxis.

The solution of nonlinear operator equation Tx=μx+p(μ≥1) and Tx=μx(μ≥1) in the Z-P-S space was studied via topological degree method and some theorems and deductions were obtained. Meanwhile some important conclusions were improved and generalized.

The authors discussed almost sure central limit theorem for the sequence of random element and functions of random variables, extended the weight to the classics almost sure central limit theorem, and improved the method of traditional subsection summation for the proof of almost sure center limit theorem.

The curvaturedriven diffusions (CDD) model was applied to the nontexture image inpainting. The numerical discretization scheme was
 developed. The computation is constituted of two steps. For inside the inpainting domain, we employed the time match method; while for outside the inpainting domain,   we employed the addtive operator splitting(AOS) method, which  can gain an accelerated convergence. The experiment results are satisfying.

With the help of the notion of integral map of a partial Doi-Hopf module it is proved that an important result in classical representa
tion theoryMaschke theorem still holds for a partial Doi-Hopf module, that is, if (H,A,C) is a partial DoiHopf structure with a normal integral map and map f: M→N is a partial Doi-Hopf module homology, then f has a section map (retraction map)  of right Amodule if and only if it has a section map (retraction map) of partial Doi-Hopf module.

By constructing Lyapunov function method, the sufficient conditions of the global attractivity in the θth moment and the (θ+1)th moment of positive solutions to the general “food\|limited” species model with random perturbation are given. The results show that the presence of such a noise doesn’t affect the results that we have obtained with the original determinate species model.

An improved method about the camera calibration method based on circular points was proposed, by which one can solve intrinsic parameters lin
early under the conditions of no demand of any physics measurements and matching between model plane and image. Furthermore, we proposed a new nonlinear solution for extrinsic parameters under the condition of no more other known information. Experiment results show that the method proposed is more accurate and robust.

A new algorithm for iris localization was proposed on the basis of contour following, and the new algorithm improved the realtime and accuracy of iris localization. Firstly, the algorithm scans the input binary iris image to find out the start point of the contour. Then after a series of procedures
of contour finding, contour coding and contour filtering, the iris inner contour is located. Finally, the radius of iris outer contour  is got by calculating the average distance between the center of inner contour and gray catastrophe points which are located at outer contour of iris and sclera. This algorithm was testified by JLUIRIS and CASIA iris database, and the results were satisfied. Experimental results show that the proposed algorithm can improve the speed and accuracy, and is further more stable.

Based on MVC framework, the authors designed and used meta object facility of the fourtiered management structure model for object modeling tools, with the help of twostage model theory, to divide the traditional modeling work into element construction model and the traditional model in two stages. After analysis of specific areas, domain modeling can be realized by means of the improved XKL domain modeling language from meta object facility metalanguage.

On the basis of H.264/AVC video coding standard, an improved subpixel search algorithm was presented via the analysis of the current UMHexagonS algorithm processes and problems, optimization of the entire pixel search algorithm UMHexagonS with the improved UMHexagonS algorithm process given. Experimental results show the improved algorithm, on the premise of ensuring the quality of the images, significantly reduces the encoding time and improves the coding efficiency.

An asynchronous distributed cache protocol was designed to solve the issue of packets loss during migration downtime so as to guarantee
 the reliability and ordering of communication between virtual machines. Besides, we designed and implemented a hybrid virtual network architecture based on the overlay virtual network model. Our virtual network model enables the live migration to be completed across LANs. Our experiments show that the hybrid virtual network model and data cache protocol can effectively solve the problem of virtual machine live migration across LANs.

One method of dorsal hand vein recognition based on improved FRIT was proposed. Analyzing image line’s singularity, we can obtain the
 characteristics of the dorsal hand vein. That’s just the ability of ridgelet transform. The processing is that hand vein images are decomposed by improved FRIT firstly; then multiscale ridgelet features (MRF) of vein image are obtained in different decomposition scales; finally, pattern matching was done by defining MRF distance. Compared with other vein recognition methods, our approach completely preserves original information of the vein. It not only increases the speed of system but also reduces the complexity of the algorithm.

To elucidate how to optimize combination features and to design a classifier with high classification accuracy, a challenging problem, a method based on error rate of classification as standard to select combined feature was presented so as to raise the classification accuracy. First, four kinds of f
ractal dimensions are extracted as texture features. Then, various combination features are training samples of SVM. With combination feature with the lowest classification error rate as a vector to be applied to the classification, the classification accuracy of the classifier can be improved. A variety of patterns are generated by primitive gene and regenerative gene. The proposed method is simple and easy in operation that can be widely popularized. So it can lay the foundation for the combination of image features.

The authors studied a new polymer network liquid crystal (PNLC) system of  the polymer  dissolved in  N\|(4\|methoxybenzal)-p-butylaniline (MBBA) liquid crystal. The dissolved polymer which did  not require light radiation,  formed spontaneously a   polymer network structure   in the system. Phase grating was engraved on the polymer network via  double\|beams interference method. The differences of the conditions and morphologies of the  Williams domains in the MBBA liquid crystal before and after doping the polymer were  compared. Polymer network structure made the signal frequency of the formation of Williams domains in the MBBA liquid crystal raise from 50.3 Hz to 622 Hz. In the case of without doping the polymer,  Williams domains in the MBBA liquid crystal begin to disappear when the  signal frequency is 65.9 Hz, but Williams domains in the MBBA liquid crystal don’t disappear  when the polymer network structure exists, hence  improving the stability of liquid crystal orientation. Moreover, the phase grating  engraved on the polymer network and the phase grating   formed in the MBBA liquid crystal under the influence of an electric field don’t interfere with each other.

 In the light of the physical circumstances of working of  a TEA CO₂ laser, taking beam divergence angle, mode volume, mode configuration and output power as design parameters, the authors designed  several groups of holophotes with different radii of curvature, output mirrors with different transmissivity and different general air pressure and partial air pressure of working\|laser material.   The  results indicate  that the TEA CO₂ laser could not only obtain a laser output up to several kilowatts, but also  control  beam divergence angle to be  a minimum   via optimizing parameters.

N,O-carboxymethyl chitosan （N,O-CMC）/nano-β-tricalcium （n-β-TCP） composite materials were prepared by means of mechanical mixing coupled with  hot press molding.   In order to compare the physical properties and morphologies  of the composites with different mass ratios,  the water absorption,  apparent porosity and compressive strength of the composite materials were investigated.   The results show that  with n-β-TCP content increasing the water absorption and apparent porosity increase ,  but  the compressive strength decreases first and then increases.   The confocal laser scanning microscopy shows that with the increase of the addition amount of n-β-TCP,  the pores existed in the composites are well distributed,  what’s more,  the pore size tends to be uniform.   When m(N,O-CMC)∶m(n-β-TCP)=1,  the pores are well distributed in the obtained composites and the pore sizes are about 1— 6 μm.   Moreover,  the n-β-TCP powder is  well distributed in the N,O-CMC.

h-BN nanopowder was prepared from hexagonal boron nitride powder by means of ball mill method, and   it was sintered in a tubular furnace under  air or  vacuum condition.   The composition and structure of the samples were investigated  by means of  X-ray  diffraction (XRD) and transmission electron microscope (TEM). The results indicate that  the samples were well crystal composite BN-B₂O₃ nanorods.

A novel mesoporous aluminosilicate material was synthesized with citric acid as pore forming agent, tetraethoxysilane (TEOS) and

Al₂(SO₄)₃·18H₂O as silica source and aluminum source, respectively. The sample was characterized by XRD and TEM. The results of N₂ adsorptiondesorption showed that the mesoporous structure of novel material was maintained under the condition of both calcinations at 1 173 K in air for 5 h and treatment in the boiling water for 48,96,192 and 288 h.

Five elements of Cu,Zn,Mn,Fe and Ca in Trollius chinensis were decocted in boiling water. The decocted solution was separated into watersoluble fraction and suspension fraction by microporous filtering film. Watersoluble fraction was divided into organic fraction and inorganic fraction by macro porous adsorption resin. The content of the trace elements was detected via microwave digestion method. Furthermore, the total content of Cu,Zn,Mn,Fe and Ca and the amounts in different fractions were determined with flame atomic absorption spectrophotometry (FAAS). The  results show the content of Cu,Zn,Mn,Fe or Ca was correspondence in the water solution with the content in Trollius chinensis. Therefore, the trace elements existed in various species in Trollius chinensis.

DFT B3LYP/LanL2DZ+6\|31G* method was adopted to investigate the secondorder NLO properties of pyridinetriazine Pt(Ⅱ) complexes with different dithiolates. The calculation results show that the bond distance between coordinating atoms is related to the length of S〖CDS1〗C conjugate chain. In the four complexes, the pyridine and triazine parts play the electrondonating role. Rather, the dithiolate part shows the ability to pull electrons. Metal Pt serves as a conjugate bridge of electron donor. The dipole moment μ of the complexes vary directly with the polarizability α. The four complexes have big β_tot values and would act as the potential NLO materials.

Rana chensinensis Changbaishanensis oviduct glycoprotein was separated and identified in the test. Saturated ammonium sulfate was uesd to pre
cipitate Rana c Changbaishanensis oviduct glycoprotein(the optimization saturated degree of saturated ammonium sulfate is 70%), followed by DEAE Cellulose52 ion exchange chromatography initial purification, then Sephadex G100 further purification.To collect the overlap peak of protein and sugar. It’s the Rana  c. Changbaishanensis oviduct glycoprotein sterling(OGP-Ⅰ) after lyophillization. The result of SDSPAG electrophoresis indicates OGP-Ⅰ is only a colored zone. The molecular weight of glycoprotein was 116 000. The result of SDSPAG electrophoresis combined with coomassie brilliant blue staining and shiff staining provs it is glycoprotein, OGP-Ⅰ is only a colored zone at the same local. The ultraviolet scanning of OGP-Ⅰ indicates that it exhibits polysaccharide characteristic absorption band and protein absorption band. Therefore
, these can further indicate that OGP-Ⅰ is glycoprotein.

The leaves of Astilboides tabularis (Hemsl.) Engler were extracted with 85% ethanol, the extract was separated by column chrom
atography on a silica gel column to obtain the chemical constituents, whose structures were elucidated by spectral analysis and chemical evidence. Six compounds were isolated and were identified as quercitrin(1),  kaempferol-3-O-α-L-rhamnoside(2), quercetin-3-O-β-D-galactoside(3), gallic acid([STHZ]4[ST]), bergenin(5) and quercetin(6).

To establish headspaceGC method for the determination of residua of macroporous resin in the saponins extracted from the roots of Panax ginseng C A Meyer, the chromatographic separation was performed. The column temperature was programed, with an initial temperature of 60 ℃ (hold 22 min), at an increasing rate of 50 ℃/min to 200 ℃ (hold 6 min); the injector temperature was set at 220 ℃ and FID detector temperature was set at 260 ℃; solvent was 40% N,NDimethyl acetamide (DMF)； the carrier gas was nitrogen.  All the residua including nhexane, benzene, toluene, 1,4xylene, styrene and 1,4diethylbenzene gave good linearities and the recoveries.

A BP artificial neural network (ANN) model was developed via MATLAB to estimate Cu/Zn adsorption in the surficial sediments (SSs)
and natural surface coating samples (NSCSs), by which the mean square error of training set, the deviation of training set, the mean square error of verification set, and the deviation of test set are 0.002 2(0.001 5), 1.542 9×10^-6(2.648 4×10^-6), 0.087 1(0.069 2), and 0018 7(0.035 7), respectively. The predicted results of the BP ANN model established not only reveal the law of the adsorption of Cu/Zn by the active constituents of SSs (NSCSs) changed in grade, but also highlight the significant interaction among the activeconstituents in the SSs (NSCSs) on the adsorption of Cu/Zn preliminary. The adsorption capacity of Cu/Zn increases with the decrease in content of active constituents, and the maximum ratios between the adsorption variation value of the changed SSs (NSCSs) and their original adsorption value are 1 420.30%/54.30% (SSs) and 79.27%/703.31% (NSCSs) respectively; the interaction among the active constituents in SSs (NSCSs) promote Cu/Zn adsorption, and the maximum ratios between the adsorption variation value of the changed SSs (NSCSs) and their original adsorption value are 386.14%/30.08% (SSs) and 66.17%/47.92% (NSCSs) respectively.

Infrared spectrum technique was applied to analyzing the changes of surface —OH structures and characteristic adsorption peaks of the
goethite and δ-MnO₂ which had adsorbed Cu²⁺ under different ionic strengths (c(NaNO₃)=0.01—1.0 mol/L). The results show that the surface free —OH participated in the adsorption of Cu²⁺ on goethite and δ-MnO₂, the hydrogen ions of Fe—O—(H) and Mn—O—(H) were replaced by copper ions, resulting in the formation of Fe—O—(Cu) and Mn—O—(Cu). With the ionic strength increasing, —NO₂ from NO^-₃ of NaNO₃ can be attached to the surfaces of goethite and δ-MnO₂. After the adsorption of Cu²⁺, the infrared spectrum of δ-MnO₂ was not changed significantly, but that of goethite was inverse.

The photochemical degradation of dimethyl phthalate(DMP) in aqueous solution was investigated via a comparative assessment in vario
us advanced oxidation systems (UV, H₂O₂, UV/H₂O₂, UV/Fe²⁺, Fenton and UV/Fenton). The degradation trends followed the following order: UV/Fenton>UV/H₂O₂>dark/Fenton>UV/Fe²⁺>UV>H₂O₂. It could be inferred from the studies that UV radiation enhanced the removal rate of DMP in the Fenton process and UV/Fenton was the most effective for the decomposition of DMP. According to the experimental result, the concentrations of Fe²⁺ and H₂O₂ and pH value were the three main factors that could greatly influence the degradation rate of DMP, and the effect of the factors followed the order: pH value>H₂O₂ concentration>Fe²⁺ concentration. The optimum conditions were obtained by orthogonal experiment at initial pH=3—4 for the UVFenton system, with original Fe²⁺ and H₂O₂ concentrations of 3.6×10^-4—7.2×10^-4 mol/L and 1.9×10^-2 mol/L, respectively.