The authors discussed a class of mathematical model of optimal investment theory. Such mathematical models can be attributed to a mixed initialboundary value problem of a parabolic MongeAmpère equation. We established the existence and uniqueness of classical solutions for the mixed initialboundary value problem of relevant equations using the continuity method combined with a prior estimates.

The authors established the existence and  boundness of the solutions for singular boundary value problems of secondorder p-Laplacian equations by means of Schauder fixed point theorem and LeraySchauder alternative theorem.

We considered the existence of nontrivial solution of Dirichlet problem for a class of  elliptic equation with gradient term by applying mountain pass theorem and iterative method, and we obtain the existence of positive and negative solutions for this problem with  asymptotically linear growth of rigthand side nonlinear term.

y means of  the method of characteristics for firstorder equations, the L^p estimate for elliptic equations, the fixed point theorem and the extension method, we proved a free boundary problem with variable diffusion coefficients has a unique global solution if  the initial data of the concentration of nutrient is continuous bounded function.

Winner process was introduced into the classical linear Volterra integral equations so as to get a class of linear stochastic Volterra  integral equations. Firstly, we researched the existence of solution for this kind of stochastic integral equations in the square integral space, and then proved the uniqueness of solution in the sense of the mean square. We constructed the numerical scheme via collocation method, and numerical experiments confirmed our theoretical results.

For any positive integer n, let (n) be Euler function and Ω(n) denote the total number of prime factors of n, we studied the solutions of three kinds of equations n-(n)=2^Ω(n), n-((n))=2^Ω(n) and (n-(n))=2^Ω(n) using the methods of number theory, obtaining all the positive integer solutions of these kinds of equations.

The complex Ldecomposability and the splitting operation were discussed. It has been proved that if the splitting operation is applied to a quadrant entry, the complex Ldecomposability remains the same.

We used the lattice Boltzmann method to study the coupled Kortewegde Vries equations. We constructed a lattice Boltzmann model for the coupled Kortewegde Vries equations, and performed numerical experiments. Comparing the lattice Boltzmann solution with other numerical solutions, we obtained that the lattice Boltzmann method is an effective method for simulating the coupled Kortewegde Vries equations.

Hermitian antireflexive (antiHermitian antireflexive) least squares solutions of matrix equations (AX=B, XC=D) were considered. With special properties of partitioned matrices and Hermitian antireflexive (antiHermitian antireflexive) matrices, the general expression of the solution was obtained. Moreover, the related optimal approximation problem to a given matrix over the solution set was considered.

A new inexact smoothing algorithm for solving largescale secondorder cone programming problems(SOCP) was proposed. This algorithm allows the search direction to have the certain error, and the nonmonotone linear strategy is used to select the step length. The algorithm can get its local quadratic convergence from any point.

A new method to  absolute value equations was presented. Firstly, absolute value equations were transformed into linear complementarity problems. Combining Newton direction and centering direction, we obtained search direction by solving a linear system, then established a feasible interior point algorithm for absolute value equations. We proved that by this method an optimal solution can be obtained after a finite number of iterations. At last, we gave some numerical examples to indicate that the method is feasible and effective.

For the programming problems with inequalities constraints, we constructed a new homotopy equation by selecting a suitable new moving function, and proved the existence, boundedness, convergence, obtained the K-K-T point of the programming problems, when the feasible region is nonempty and the boundary of the feasible set satisfies positively linearly independent conditions.

The metric properties of special logical algebra were discussed. Firstly, we gave the definition of  special logical algebra named metric residual lattice, and then established a metric structure in  this algebra system. Secondly, the problem about closed set, cluster point were discussed in the logical metric space induced by the given metric structure. Finally, the continuity of the basic operators of the algebras were proved in the logical metric space.

By means of geometries of Banach spaces and Orlicz spaces method, the characterizations over rotundity of the Orlicz sequence spaces were discussed. For the Orlicz sequence spaces generated by an Orlicz function and equipped with p-Amemiya norm, the criteria of extreme points were presented. Based on the criteria, sufficient and necessary conditions were derived to make them  rotund.

The matrixtype network DEA model was established for evaluating the relative performance of the matrixtype structure. The existence of the solution for the new model was proved and the relationship between weak DEA efficiency and weak pareto was discussed. The result shows that it is feasible for one to use the new model to evaluate the relative performance of the matrixtype structure.

Let {Xn,n≥1} be a sequence of i.i.d., positive sq
uare integrable random variables with continuous medium tailed distribution func
tion. For a fixed constant a>0, let Sn=∑〖DD(〗n〖〗i=1〖DD)〗Xi, M
n=max〖DD(〗〖〗1≤i≤n〖DD)〗 Xi, Sn(a)=∑〖DD(〗n〖〗i=1〖DD)〗X
iI{Mn-a<Xi≤Mn}, the trimmed sum Tn(a)=Sn-Sn(a). Using
 the weak convergence theorem and continuous mapping theorem, we proved the
 invariance principle for the product of trimmed sums.

We considered a perturbed renewal risk model with two classes of claims, for which both the two claim number processes are renewal processes with Phase interclaim time. We derived the integrodifferential equations of the GerberShiu functions and obtained the analytical solutions, and when the densities of the two classes of claims belong to rational family, we got some explicit expressions. Finally, we gave a numerical example to illustrate theses results.

In consideration of  the probability density estimation problem with surrogate  and validation data, a recursive kernel estimation of probability density function is so defined to comprise both surrogate  and validation variates that the proposed estimators are proved to be asymptotically normal. The  simulation results indicate at a given constant of N, the total number of data, the method performs better as the validation variate n increases. Also, for a given n, simulation result becomes better in terms of top as N increases, but becomes bad in terms of tail. We also noted that the simulation result, as N and n together increases, more approaches the f(x) and is smoothing.

A class of stochastic neutral technical progress and investment system was discussed. By successive approximations of solutions in a general functional setting, the existence and uniqueness of solution for stochastic agedependent population dynamic system were proved by means of the Bihari inequality,
the Burkholder-Davis-Gundy’s inequality and the Gronwall inequality under nonLipschitz condition, which depends on time.

Using the contingent claim model and the hedging method, we solved the investment and financial problems of a company so as to get the value of the company and the price critical value for its stopping production. The results show that  if the prices of the investment products are falling, the lever company shall stop the operating activities prior to the nonliability company when the other conditions are the same, otherwise, they will do business at a sacrifice.

We used  the polynomial theorem to analyze the distribution of the roots of the associated characteristic equation for a Gausetype predatorprey model. A group of conditions of stability and the existence of Hopf bifurcation were obtained at the co\|existing equilibrium. The result indicates that in the model, there exists a Hopf bifurcation point τ=τ₀. The co\|existing equilibrium is local asymptotically stable when 0<τ<τ₀ and a stable periodic solution appears near the equilibrium point when τ>τ₀.

We proved the  uniqueness result of magnetic resonance electrical impedance tomography (MREIT) problem with orthotropic conductivity under the hypothesis that  there are  at least two couples of imposed electric current density  which are not parallel to each other based on some eletromagnetism theorems and the result of the index theory.

We investigated the existence of nontrivial solutions of some quasilinear elliptic equations, obtaining a new existence result solution of the equations by applying the mountain pass theorem under asymptotic behavior of the nonlinearity at zero and at infinity.

The authors studied the stochastic Logistic model in a polluted environment. Some conditions for stochastic weak average persistence and local extinction of the population were obtained by using the theory of stochastic differential equations. The threshold can be established in some cases.

The authors constructed and analyzed an example of a secondorder threepoint boundary value problem. The authors considered the equation and the methods of solving the equation  directed at t with the singularity. First, the authors  used the analysis of upper and lower solution method to prove this kind of problems in two resonance and nonresonance  cases, respectively, to have infinitely many different solutions, and finally on the basis of the shooting method,  the authors showed the numerical solution of this kind of problems.

HardyLittlewoodSobolev (HLS) inequality and the Wolff inequality were used to obtain the L^p estimate of the Wolff potentials. At the same time,  EulerLagrange equations of the extremal functions for the more general weighted HLS inequalities were also established by means of the method of calculus of variations.

With the help of PoincareBendixson theorem, the existence for the limit cycles about a kind of predatorprey systems with functional response x^·=xg(x)-yφ(x), y^·=y(-d+eφ(x)) was discussed, obtaining the sufficient conditions for nonexistence, existence and uniqueness of the limit cycles around an equilibrium point in the case of g(x)=a-bx^m, φ(x)=cx^θ, m=θ=k/n, n>2, 1≤k<n, k,n∈Z⁺.

Using the formula of the first twist coefficient for Newtonian equations and the thirdorder approximation method, we studied the Lyapunov stability of periodic solutions for a nonlinear damped singular differential equations. Moreover, we presented a sufficient condition for the nonlinear damped singular differential equation.

The nonexistence of finite energy solutions to quasilinear elliptic equations with singular and gradient terms was proved via the first eigenvalue of p-Laplacian equations involving weight functions and the inequality for ODE.

The reinforcement learning mechanism was applied to the processbased Web service composition and the Web service composition algorithm with continual selfadaptability was proposed herein so as to enable continuous adaptation to the dynamic Web environment. The algorithm integrates the exploitation of past data about the Web service performance with the continual explor
ation of new options according to QoS actual performance and approaches the optimal Web service composition policy corresponding to the process model gradually. Compared with other similar methods, the algorithm can adjust the Web service composition solution so as to adapt to the dynamic Web continually by means of perceiving the change of Web service and its performance on the Web, and  exploiting the acquired data about the past performance of individual services at any runtime. The relation between exploitation and exploration is accounted for by discussing the range in which the entropy takes its values. Two kinds of experiments were performed to verify the algorithm’s adaptability to the static and dynamic environment.

In order to overcome the shortcomings of conventional detectors and improve the detection rate of the current smoke detection algorithms, a new smoke detection approach based on motion block was proposed. Firstly, motion blocks were extracted by frame difference method. Then, candidate smoke regions were determined according to the area and the result of the motion estimation of every connected region. Lastly, the high/low frequency energy eigenvalues were obtained via discrete wavelet transformation and the movement maintenance eigenvalue was obtained according to the result of the estimated direction of movement. These eigenvalues were used to determine whether there is smoke. The experimental results prove that the proposed algorithm is robust, anti\|disturb. It could detect the appearance of smoke timely and prevent fire effectively.

An improved algorithm based on dark channel prior was proposed which compenstaes the transmission estimated via dark channel prior, redefines atmospheric light via analyzing the fog images fail to recover by original method based on physical model. Experiments prove our algorithm works better than original method, especially on sunlight lacking or sky including images. Meanwhile, mean square error(MSE) was used in our method to verify the images we recovered are close to true images based on fog database.

By means of the introduction of  intuitionistic fuzzy set theory  into the least squares support vector machine, the mathematical  model of the intuitionistic fuzzy least squares support vector machine was established, and the solution to the model was  derived. The simulation experiments were performed on both artificial data sets and benchmark data sets to verify the effectiveness of the proposed algorithm. The results show that the intuitionistic fuzzy least squares support vector machine  algorithm can reduce the serious impact of sample noise and outliers on classification effect.

Based on the continuation method, active power and reactive power inputted by wind power and the admittance of wind power generation system were taken as bifurcation parameters, Hopf bifurcation points and twoparameter Hopf bifurcation boundary were calculated to analyze theinfluences of the system parameters on the voltage stability of wind power generation system. Meanwhile, the control action of static var compensation on Hopf bifurcation was researched. Research result shows that reactive power is a main Hopf bifurcation parameter, and Hopf bifurcation can be effectively delayed by static var compensation.

On the basis of chargecoupled device and microcomputer technology, we designed a data acquisition system of linear CCD array with 2 160 pixels. According to the driver of linear CCD array, we completed the highvelocity data acquisition module, RS232 communication and the display software. It has two operation modes (trigger mode and continual mode), the frame per second reaches to 5 f/s. The tests show that this low cost data acquisition system is reliable and easy to use, and can be used in the untouch size measurement of product.

The authors introduced a new delegation model based on the permissionbased delegation model (PBDM). The roles are divided into three sets, which include regular roles, private roles and delegation roles. The permissions are divides into two sets, which include delegatable permissions and undelegatable permissions. This new model supports usertouser and roletorole delegation, effectively avoids some problems such as name space explosion and void roles, ensures the safety of access to the system, and makes the delegation more flexible.

After analysis and research on the traditional fingerprint image segmentation algorithm, an improved Mean Shift algorithm for fingerprint image segmentation was introduced. The algorithm makes fully use of the inherent directional characteristics of fingerprint image to abstract each area of fingerprint image after segmenting  into a sample point and to consider  the grayscale mean value of the pixels within the fingerprint region as  the mean vector, thus achieving the fingerprint image segmentation effectively. Experimental results show that the background area and fuzzy algorithm can accurately be separated from fingerprint image with the algorithm. The algorithm improves the accuracy of segmentation and  has good accuracy for most of fingerprint images.

Crystal structure, tetragonal distortion, magnetism, electronic structure and pressure response of Mn2NiAl were calculated by means of first\|principles method based on the density functional theory. The calculation results show the equilibrium structure of Mn₂NiAl in the cubic austenitic phase is the MnMnNiAl structure with Mn atoms occupying  A and B   non-equivalent positions. In the process of transform from a cubic to a tetragonal structure, Mn2NiAl alloys exhibit a stable martensitic phase in c/a≈1.24. In both the austenite and martensite phases, the contribution of Mn atoms  to the total moments for  Mn2NiAl is the largest, the magnetic moments of Mn(A) and Mn(B) atoms are inequality and antiparallel couple. The direct d-d exchange interactions between Mn(A) and Mn(B) atoms are weak because of the small overlap of d-projected DOS of Mn(A) and Mn(B) atoms nearby the Fermi level, but the intra-atomic interactions in Mn atoms are strong, this is the reason why the Mn2NiAl alloys show ferrimagnetism.

The authors  proposed a concept of new function photon crystals, the  refractive index of which is a function of space position.  The light motion equation in one-dimensional function photon crystals was obtained by means of Fermat principle,  and  the transmission matrix was obtained via calculation, with  the dispersion relation, band gap structure and transmissivity given. The more wide and more narrow band gap structure than conventional photon crystals were obtained by choosing different distribution function n(z) of refractive index.

A Yb³⁺-doped ring fiber laser based on the principle of nonlinear polarization rotation was constructed. Two kinds of dual-wavelength output (DWO) including the equal\|amplitude and unequal-amplitude DWOs were obtained and their output powers were measured. The results show that   the laser conversion efficiencies of different wavelengths were rather different due to gain difference. The DWO tunability was also analyzed, and  the influence of pump power on DWO at 1 029 nm and 1 048 nm was investigated. The laser outputs from dual-to seven-wavelengths were observed, and the corresponding pump power ranges and the maximum output power were measured.

The effect of microarc oxidation ceramic membrane on NiCr alloy on the release of Ni ions by means of microarc oxidation was studied with NaAlO₂ and Na₅P₃O₁₀  as electrolytes. The membrane was characterized by means of scanning electron microscopy (SEM) and X-ray diffraction (XRD). The corrosion resistance and the release of Ni ions from NiCr alloy were analyzed by electrochemical test and ICP-OES. The results indicate that the major crystalline phase on NiCr alloy is γ-Al₂O₃, which can prevent   Ni ions from release and improve the corrosion resistance of NiCr alloy.

ZnB₂O₄ ∶Eu³⁺,Yb³⁺ nearinfrared(NIR) lightemitting materials were prepared with a hightemperature solidstate method. The condition of preparation and the effects of Eu³⁺ and Yb³⁺ on lightemitting properties were studied by X-ray diffraction (XRD) and fluorescence spectroscopy, and the influences of reaction time and the doping concentration of Eu³⁺ and Yb^3+ on the emission intensities were also  investigated. The results show that the NIR lightemitting of ZnB₂O₄ ∶Eu³⁺,Yb^3+ was achieved by the energy transfer from Eu³⁺ to Yb³⁺.

The experiment was designed to use D-galactosamine as ligand, and FFSepharose 4B as immobilization phase to synthesize D-galactosamine-FF-Sepharose chromatography stuffing. Soybean agglutinin was isolated and purified with its purity measured; immunogenicity and agglutination activity were determined and then compared with those of American Sigma company standard sample. The result shows the GalN-FF-Sepharose-4B could adsorb 10 mg of SBA per milliliter. After purification, soybean agglutinin molecular weight was
30 000; SDSPAGE determined purity of it was over 98%; the western blot test was positive; 1 mg/mL SBA hemagglutination titer was 1/2¹⁰; its purity, immunogenicity and agglutination activity were the same as those of soybean agglutinin standard sample and consistent with the theoretical values.

The purpose of the present work is to investigate the potential role of DhHP-6 with the help of DAF-16 in the lifespan regulation of Caenorhabditis elegans. Our results indicate that DhHP-6 can effectively increase the average lifespan of C.elegans by a factor of over 20%. Nevertheless the lifespan extending effect of DhHP-6 is inhibited by daf16 mutant strains, which implies the effect of DhHP-6 uponlongevity is associated with DAF-16. Our data demonstrate that DhHP6 activated the nucleic translocation of DAF-16 and enhanced the transcription of daf-16 downstream gene sod-3. Our results also show that the  ROS levels of nematodes in vivo is specifically reduced under DhHP-6 treatment. These results suggest that DhHP-6 may extend the lifespan of C.elegans by reducing the ROS levels through DAF-16.

By modifying the model and adding several constraints,  the revised model was applied to optimizing the emissions reduction scheme of r
egional total amount control, showing that the major pollutants controllable indexes of COD, NH₃-N, SO₂ and NO_x (not including the emissions trading  amount) are 3.01,0.47,5.00,125 (104 tons), with the increasing cuts proportions of 6.85%,8.63%,17.34%,6.51%. And the total cost is decreased to 494.02 billion yuan, with 28.00 billion yuan reduced compared with that of the regional total amount control planning for the “12th Five Year Plan” and a reduced ratio of 5.36%. This optimized scheme can economize the total cost, meanwhile giving out the reduced detail of all kinds of industries.