The authors investigated the solution matrix of the systems of the linear fractional differential equations with constant coefficients, and obtained some exact solutions of the systems of linear equations using Jordan canonical matrix. We can solve the systems of linear fractional differential equations with constant coefficients using the method of undetermined coefficients, and the results contain the solution of linear firstorder differential equations with constant coefficients.

We first gave two properties of map class K on  abstract convex spaces, and then used the wellknown coincidence point theorem on abstract convex spaces to discuss the existence problem of fixed points for maps on abstract convex spaces and obtained some new fixed point theorems,  from which  several collectively fixed point theorems were established for a family of maps on a product space of a family of abstract convex spaces.

We mainly studied the n-extensions of Koszul algebras with the help of the combination tools in representation theory. We got the conclusion that some n-triangular extensions of Koszul algebras are also Koszul algebras. Finally, an example was given to show that for the integer d≥3, the n-extensions algebras of dKoszul algebras may not be dKoszul algebras.

With the help of d_Ⅰinvexity, a new class of  concept of generalized d_Ⅰ-ⅤtypeⅠ univexity was introduced and a nondifferentiable multiobjective programming problem with inequality constraints was considered and some sufficient optimality conditions were derived under the assumptions of generalized d_Ⅰ-ⅤtypeⅠ univexity. Furthermore, a MondWeir type dual was formulated and weak duality, converse duality and strict duality theorems were proved.

We chose fourth order Lagrange interpolated function associated with the nodes as trial function, piecewise constant function as test function, and derivative superconvergent points as dual partition nodes so that a new kind of Lagrange fourth order finite volume element method was obtained for solving twopoint boundary value problems. It was proved that the method has optimal H¹ and L² error estimates. The superconvergence of numerical derivatives was discussed. Finally, the numerical experiments show the results of theoretical analysis.

With the help of  block operator matrix, the sufficient and necessary conditions for the existence of solutions to the operator equation AXB*+BX*A*=C and the representation of solutions were established. Especially, when 〖WTHX〗B〖WT〗 is an orthogonal projection P, the sufficient
 and necessary conditions for the existence of solutions to the operator equation AXP+PX*A*=C and the representation of solutions were also given.

The authors studied dynamics of the Rayleigh model with two discrete timedelays of the price.First using the linear stability method and the Nyquist criterion, we discussed the local stability of the system equilibrium point and the existence of Hopf bifurcation, then  used normal form
 and the center manifold theorem to determine the formula of the branch direction and branch stability of periodic solutions. In addition, in the model  codimension 2 branch can appear, and we gave the local area map of the parameter a-τ plane stable equilibrium point, finally, via numerical simulation we verified the theoretical analysis.

We  got sufficient conditions of  strong stability of  linear forms in mixing random variables sequence  via  terminating random variables and strong large number law.

Let {Xt,t≥1} be a linear process of the form Xt=∑〖DD(〗∞〖〗j=0〖DD)〗ajξt-j, where {ξt,t∈ Z} is a mixing sequence with zero means, {aj, j≥0} is a sequnce of real numbers with ∑〖DD(〗∞〖〗j=0〖DD)〗j〖JB(|〗aj〖JB)|〗<∞ and {ani,1≤i≤n,n≥1} is a triangular array of real numbers, then under some suitable conditions, by means of the central limit theory and corresponding probability inequalities of mixing sequence, we have obtained the limit theorem for weighted sums of linear processes generated by mixing sequences.

By means of heat kernel and the approach of regularizing generalized functions, HyersUlam stability of Wilson functional equation was
 mainly studied in the spaces of generalized functions such as the Schwartz tempered distributions, Fourier hyperfunctions and Gelfandshilov generalized functions, showing that the result of the stability of Wilson functional equation in generalized functions is similar to that in the usual functional spaces.

Using Schauder’s fixed point theorem, the authors studied Neumann boundary value problems of second order nonautonomous semipositive coupled systems. We established the existence of positive solutions for Neumann boundary value problems of the singular coupled systems under the conditions that the signs of integral disturbance terms are positive, or negative, or different.

Let Jrn,k denote the set of ndimensio
nal cobordism classes containing a representative Mn admitting a (Z2)
kaction with fixed point set of constant codimension r. Jr*,k=
∑〖DD(〗〖〗n≥r〖DD)〗Jrn,k is an idea of the unoriented cobordi
sm ring MO*=∑〖DD(〗〖〗n≥0〖DD)〗MOn. The authors constructed the special genera
tors of MO*  to prove that J2k+7*,k(k≥5)
 consists of all classes of dimension greater than 2k+7 with 0 mod 2 Euler
 characteristic and the decomposables of dimension 2k+7 in which each
 factor of monomials has dimension less than 2k.

The authors studied the semigroup POn, consisting of all singular partial orderpreserving transformations on a finite chain. Analyzing the idempotent elements, we completely obtained the structures and classification of the maximal subsemibands of the semigroup PO_n.

Using the fixed point theorem and the properties of the distributional HenstockKurzweil integral, we investigated the existence of extremal solutions of the Darboux problem, as well as their dependence on the distributions.

We proposed a new hybrid conjugate gradient method. It does not need to use Wolfe line search to guarantee the global convergence. An initial selfadaptive step size and sufficient descents are obtained to the function at each iteration. Numerical results show that the method is feasible and effective.

A new LQP method for solving variational inequality problems on the polyhedra was presented. Under quite mild assumptions, global conve
rgence of the method was proved. The proposed method is simple and easy to implement.

On the basis of two relations between functions  defined as same positive definite relation and same order relation the properties of the two relations were discussed. Besides a sufficient condition was established to assure that a new quasiconvex function was formed by the quasiconvex functions aggregated, and a sufficient condition was proposed to guarantee that quasiconvex functions were aggregated to form a new pseudoconvex function.

We presented a family of predictor corrector iteration methods for solving nonlinear equations, then proved the iteration methods have at least three orders convergence and avoid the computation of the second derivative, and finally tested the methods on several numerical examples. It is observed that our methods can compete with the other classical thirdorder methods.

This paper deals with a double Cox risk model of variable premium with investment income and reinsuranceU(t)=u+V1(t)=u1+u2+∑〖DD(〗M1(t)〖〗i=1〖DD)〗Xi-∑〖DD(〗M2(t)〖〗j=1〖DD)〗Zj+u2W(t).Using martingale obtained the expression of upper bound of the ultimate ruin probability -ru·C(r) on the assumption that M1(t) and M2(t) were correlated. And under special conditions M1(t)=β(t)M2(t), explicit upper bound of the ultimate ruin probability ψ(u)≤e-Ru was got, where R is Lundberg index.

We investigated a random food limit species modelN[DD(-*3]·[DD)〗(t)=N(t)〖JB((〗〖SX(〗K-N(t)〖〗K+CN(t)〖SX)〗〖JB))〗(r+αB[DD(-*3]·[DD)〗(t))using both stochastic differential equation theory and statistical theory, where B(t) is the 1dimensional standard
 Brownian motion with B(0)=0 and 0<N(0)=N0<K. The consistence and asymptotic distribution of maximum likelihood estimators 〖AKα^〗,〖AKr^〗 of parameters α,r of the equation are studied. The strong consistence and asymptotic normality of estimations 〖AKα^〗,〖AKr^〗 were proved.

With the help of Matlab software, we employed the improved (G′/G) method to obtain exact traveling wave solutions of modified nonlinear DegasperisProcesi equation and nonlinear wave equation. The improved (G′/G) method provided more general forms of solutions. This method is effective.

We used the homotopy method to study the nonlinear complementarity problem, construct a new homotopy equation, and prove the exis
tence, boundedness and convergence of the homotopy path for the new homotopy equation, and we defined a class of new functions, obtained the existence and boundedness of the solution for the complementarity problems corresponded with the new functions.

We studied the structure of 〖KX,1〗Z2graded automorp
hisms of K［x,y,z］, where K is a field of characteristic zero and the
〖KX,1〗Z2grading is defined by deg[KG*4]〖KX,1〗Z2(x)=deg[KG*4]〖KX,1〗
Z2(y)=0〖DD(-*3〗-〖DD)〗, deg[KG*4]〖KX,1〗Z2(z)=1〖DD(-*3〗-〖DD
)〗. We showed that an automorphism of K［x,y,z］ fixing z is tame if and only
 if the induced 〖KX,1〗Z2graded automorphism is graded tame, and we also showed th
at if a 〖KX,1〗Z2graded automorphism is tame, then it is graded tame.

We studied problems about 2n-order delay differential equations with periodic boundary value  using the upper and lower solution method, and established some suffcient conditions for the existence of the solutions of  2n(n≥1)order periodic boundary value problems.

Using the methods of combinatorial analysis and constructing concrete coloring, we discussed the adjacentvertexdistinguishing total coloring of K_15-E(K₃), K₁₇-E(K₃) and obtained  that  the adjacentvertexdistinguishing total chromatic numbers of K_15-E(K₃) and K₁₇-E(K₃) are 16 and 19 respectively.

The authors used the  cuttingofftail method and some other methods to study the complete convergence property for the sum of partial
sums of  i.i.d.random variables sequences and obtained the same equivalent conditions as those of complete convergence property of the partial sums of i.i.d. random variable sequences. The results supplement the limit theorems of the sum of partial sums.

Based on security risks for RC4 algorithm,  we presented some improvements. The improved algorithm can resist the fault induction attack via adding the selferror detection phase, and resist Knudsen’s attack via adding the byte conversion phase. After analyzing the security of the improved algorithm, we proved that the improved algorithm can resist the fault induction attack and Knudsen’s attack validly, the security of the RC4 algorithm is hence enhanced.

The codeword space was reduced according to calculating the longest interval so that codeword is never recurred by other variable in tuple, and the interval is not stored in codeword, thus 6tuple based codeword is replaced by 5tuple. The experimental result shows that the new codebook model is as fast and accurate as the original model. Moreover, the memory space demanded is reduced.

At first, the authors gave counting theorem on the basis of  analyzing the properties of ergodic matrices. In addition, the related definitions and
theorems of ergodic matrices and irreducible polynomials, and the relationship between the linear feedback shift register and ergodic matrix over finite field were also given.

A multifeature fusion flame detection algorithm using videotype judgment algorithm was proposed. In this algorithm, the videotype of each frame was first judged. Then candidate flame region was extracted by the algorithm that corresponds image types, at last the flame frequency feature based on DCT and image correlation feature between frames in the candidate region were detected to determine the existence of flame. The traditional visualization fire detection technology is basically based on analyzing the images from infrared cameras or visible camera to detect flame. The method can not meet the requirements of roundtheclock monitoring flame in engineering application. Experiments show that the proposed detection algorithm can resolve this problem, detect flame fast and reduce the error rate.

We analyzed the vehicle characteristics in low altitude platform, and proposed a fast object tracking method via particle filter based on Meanshift optimization. In our method, we used color distribution histogram to represent an object. Then Meanshift algorithm was applied to iterative optimization in particle selecting stage. This innovation is able to reduce the particle number in tracking. The experiments show that our method has strong robustness and stability, and it can be applied in fast tracking in low altitude platform.

The authors presented the experimental observations and theoretical calculations of double electromagnetically induced transparency (EIT) windows in a four-level inverted\|Y atomic system. The results show that the locations of two EIT windows can be controlled by manipulating the parameters of the two coupled fields.  The physical mechanism of double EIT is double dark resonances induced by the two coupled fields simultaneously interacting with the atomic system. The sub\|Doppler spectral resolution in the center of the absorption spectrum is induced due to the interaction between double dark resonances. A narrow absorption peak with a width of 30 MHz is obtained in the experiment.

OZI rule violations were investigated in the decay of  J/Ψ mesons, and an estimate of the contributions from intermediate states to the decay branching ratios was given.  OZI rule violations in the  J/Ψ  meson decay processes were discussed. The calculation results for  J/Ψ→f0 decay are in agreement  with the experimental results, which shows there are large OZI rule violations in those decay processes.

The Casimir effect between contaminants of the Bose\|Einstein condensed system in the one\|dimensional squeezed vacuum states was studied by means of  Riemann Zeta function. The Casimir energy of the system in the squeezed vacuum state and the Casimir force between the contaminants were calculated, the relationship of the Casimir force with squeezing parameter and distance was  discussed.

According to the characteristics of finger vein image, a new denoising model based on partial differential equations was presented. This model uses the new diffusion function based on the traditional PM model, and combines with fourthorder partial differential equations model to transform the original model structure. The performance of the new model is verified by both synthetic and real finger vein images. It shows that the new model could increase the signaltonoise ratio up 5 dB and maintain the features of finger vein image better compared with the original model.

The authors proposed a Markov chain model and a continuous idle slots model for the transmission mechanism of IEEE 802.11p/1609. Using these two models, we got the conflict probability of WAVE system, on the basis of which, a channel chose policy was presented to get the best access channel. This policy can balance the throughput of all the channels and solve the channel congestion problem in the basal protocol. The simulation results show that the average throughput rate was improved obviously.

Zinc oxide (ZnO) nanorods were grown on three kinds of substrates by means of the chemical solution deposition (CBD) method. The crystal structure, morphologies and photoluminescence properties of the  nanorods were studied by means of X\|ray diffraction (XRD), scanning electron microscopy (SEM), atomic force microscopy (AFM) and photoluminescence spectroscopy (PL). The results show that the products, ZnO nanorods were uniformly distribationed on the substrate, the crystallization quality of the ZnO on the ITO conducting glass and bare glass substrates are better than that of  the sample on the Si substrate. And the nanorods grown on the bare glass have the most  coverage density and their tropisms are unity. The ZnO nanorods grown   on the Si substrate have the best photoluminescence. The small shift in the UV emission was caused by the stress due to the different sizes of the nanorods.

This work focused on the synthesis of norbornene macromonomers with poly(ethylene glycol)(PEG) and the preparation of graft copolymer by ringopening metathesis polymerization (ROMP) of these macromonomers. The molecular weight and  polydispersity of graft copolymer were studied by gel permeation chromatography (GPC). It was found that the molecular weight of graft copolymer was between 10 000 and 44 000  with polydispersity between 1.11 and 1.22. Moreover, the polydispersity of the polymer became narrowed with the increase of ［M］/［I］.

A new 5-［4-(3,5-dicetyloxybenzoylamino)phenyl］-10,15,20-triphenylporphyrin (DDTPP) and its relative zinc compound (DDTPPZn) were
 synthesized and characterized by means of elemental analyses, UVVis, IR and ¹H NMR spectroscopies. Furthermore, and the oxidation and reduction properties of the compounds were studied by the cyclic voltammetry, and the oxidationreduction potentials were obtained.

 Pea starch was used as raw material to produce film forming agent in this study. The starch was processed by isoamylase firstly, and then the obtained product was subjected to hydroxypropylation. We studied the effects of enzyme reaction time, the dosage of propylene oxide, etherification time, reaction temperature and the dosage of sodium hydroxide on the performance of film forming agent. The reaction conditions were optimized via orthogonal test as follows: enzyme reaction time was 12 h, propylene oxide 4 g, reaction time 16 h, reaction temperature 45 ℃, sodium hydroxide 0.4 g. The results show that the modified product as the filmforming agent in glass fibre sizing could ensure the successful drawing process.

Using the computer simulation technology of docking and the phage peptide library for optimum screening of the isocitrate lyase peptide inhibitor. First the binding peptides were screened by phage peptide library, which has a high affinity for isocitrate lyase(ICL). And then via the Discovery Studio 21, the docking of peptides to ICL protein crystal (1F8I) was simulated.  Finally, the solidphase synthesis of Fmoc was used to synthesize peptide, and their biological activities were detected. We got 29 heptadpeptide sequences by phage peptide library screening, 12 of which can successfully dock to ICL protein crystal. The biological activity detecting shows that they all have conspicuous inhibition on the ICL activity (rate of inhibition 50%).

Scanning electronmicroscopy was used for the qualitative analysis of the sources of PM₁₀. The routine monitoring points in Longyan City, Fujian Province were chosen for the instantaneous sampling from September 16(th) to 23(rd) in 2009. Micromorphological features and elemental composition of PM₁₀ in the samples were analyzed and compared to those of the particulates that composed the typical local pollution sources, by which the primary pollution sources could be identified. The results indicate that there are striking differences in micromorphology and eigenelement among pollution sources. And the micromorphology and elemental composition of PM10 vary with the sampling points. The obtained results of source apportionment of PM₁₀ are in accordance with the analysis by chemical mass balance receptor model (CMB8.2).

We used Pb²⁺ and Cd²⁺ as target pollutants to  study the effect of freezethawing cycles on the adsorption of heavy metals by soil, decuced the effect mechanisms, and analyzed the effect of  temperature on heavy metal adsorption on freezethaw soils. The results show that the freezethawing cycles reduced the Pb²⁺ and Cd²⁺ adsorption  on soil, and changed the slope of Pb²⁺ and Cd²⁺ adsorption isotherms. Freezthawing cycles changed the adsorption mechanism of soil from specific adsorption to nonspecific adsorption, and it promotes soil to desorbe and release Pb²⁺ and Cd²⁺ to the environment. Freezethaw did not change the therm odynamic property of Pb²⁺, Cd²⁺ adsorption on soil, with the rise of temperature, Pb²⁺ adsorptions on freezethaw soil and untreated soil were increased, which belong to endothermic reaction; but the adsorption of Cd²⁺ reduced with temperature rise, which belongs to the exothermic reaction. Under the same pH conditions,  the adsorption quantities of Pb²⁺ and  Cd²⁺ on freezethaw soil were lower than those on untreated soil.