This paper aims at a weak coupling evolution p-Laplacian system with the first initial and boundary value conditions. Under appropriate hypotheses, the method of regularization is used to construct a sequence of solutions with the help of monotone iteration technique and the solution to the regularized system can be found. Then the existence of solutions to the evolution p-Laplacian system is obtained by a standard limiting process. Finally, the uniqueness of the solution can be proven by integral method.

We constructed a finite volume scheme of fifth order Hermite type with high accuracy for twopoint boundary value problems, choosing trial and test spaces as the fifthorder finite element space of Hermite type and the piecewise linear function space respectively. We didn’t use higher derivatives as interpolation conditions, which is the same as the thirdorder finite element of Hermite type, but the scheme obtained had higher accuracy. The optimal convergence rates in H-1 and L-2 norms are proved, and the convergence order in L-2 norm is one order higher than that in H-1 norm. The numerical examples confirm the theoretical results.

Since the separable element algorithm of the rational univariate representation (RUR) for solving zerodimensional systems presented by Rouillier makes the size of the coefficients in this representation too long, an improved algorithm for finding separating elements is presented in this paper, which is implemented by confirmingthe separating element of the coordinates step by step. Results show that the size of the coefficientsin the RUR corresponding to the separating element selected by the new algorithm is obviously shorter than that by Rouillier’s. In addition, the average complexity of both the algorithms are close.

Let Mbe a 3-manifold obtained by surgery on then-component framed link LS^{3. We can get the link invariant maintaining isotopy, and K₊ and K_- moves for the framed link (L, f),so as to furthermoreobtain the invariant for 3-manifold. Thus the invariants for 3-manifold are given by finite linear combinations of Kauffman brackets of cabling of L, to be evaluated at primitive 4r-th root of unity. Some difference representations of invariant for 3-manifold are given by using the bracket polynomial, TemperlyLieb algebra, JonesKauffman module and linear skein theory, etc. This paper deals with the relation of these representations of invariants, and shows essentially the consistency of them. A new representation of the invariant of 3-manifolds is also given.}

We developed an optimal perfectly matched layer method for scattering from cavity under both TM and TE polarizations by choosing a particular absorbing function with unbounded integral. The unbounded computational domain is truncated to a bounded one by using a rectangular perfectly matched layer at the open aperture. The thickness of PML is not very large in this method. Especially when the cavity opening is very large, the amount of calculations is saved and the operation sp eed is improved by usingrectangular perfectly matched layer instead of semicircle.Numerical experiments demonstrate that the optimal PML method is efficientand accurate to solve cavity scattering problems.

The existence and uniqueness of the solution of a reactiondiffusion system was studied by means of the method of upper and lower solutions. Existence and nonexistence results about the nonconstant steady states of the system were given. It was also proved that if the diffusion coefficient of the prey with epidemic disease is treated as bifurcation parameter, nonconstant positive steadystate solutions may bifurcate from the constant steadystate solution under some conditions.

We combined the known properties of quasi AP-injective modules with the way of studying quasi P-injective modules to give some new properties on quasi APinjective module. For example: Suppose M_R(S=End(M_R)) is quasi AP-injective, then: (1) Sis a right weakly C₂ ring; (2) if for any nonempty set XM, L_s(X)is generated by an idempotent, and Sis local, left duo, then S_s is continuious.

The explicit formula is presented for computing the reduced sum of two divisors of genus 3 hyperelliptic curves in term of Cantor’ algorithm. The experimental results indicate that our algorithm is superior to Cantor’s algorithm.

On the basis of combining the advandage of spectralgradient method, a spectralconjugate gradient method for the global optimization is presented. This method can avoid the difficult caused by exact line search. The proof of the convergence of the proposed method is given. Numerical experiments show that the method is efficient and feasible.

The ShannonMcMillan theorem was given under the hypothesis of the countable nonhomogeneous Markov information source being supposed to be a ψ-mixing sequence. As a corollary, the ShannonMcMillan theorem of finite nonhomogeneous Markov information source was deduced.

We obtained a wavelet representation of dilation factor a in Besov spaces of generalized smoothness via insention techniques. As a consequence, we showed that compactly supported wavelets of Daubechies type of dilation factor a provide an unconditional Schauder basis in the spaces when the integrability parameters are finite.

The existence of positive periodic solution of food chain system with feedback controls and ratiodependent response was studied by the method of coincidence, a set of sufficent conditions were derived. The continuous and ratio dependent dynamical model was improved.

The existence of the radially classical solutions with Dirichlet boundary value in unit ball was investigated. Based on perturbation technique, topological method and comparability theorem, the existence of the radially symmetric solutions for the generalized mean curvature equations with proper presupposition wasestablished.

We discussed the numerical computation of the scattering problems for twodimensional Schrodinger equation (-Δ+V(x)-k²)u=0. For a class of specific potentials, i.e., V(r)=b/r^δ outside a circular domain B_r0, where both b>0 and δ>1 are constants, we presented a PML method. We first got the PML equationsby making the radius complex, and then proved that the sesquilinear form in the weak formulation of the PML problem satisfies the Garding inequality under the hypothesis of the absorption factor, and further could prove the existence and uniqueness of the solutions of the PML problem, finally, we gave the numerical experimentswhich show that this method is feasible to a certain extent.

The aim of this paper is to prove that compressible combustion flow in two- and three-spaces dimension converges to the incompres sible flow in the limit as the Mach number tends to zero. The proof relies on energy estimate and Helmholtz decomposition.

This letter covers some results about periodic CahnHilliard type of equations, which include the asymptotic estimates of the solutions to the initial boundary value problems, the attractability of time periodic solutions and the asymptotic behavior of the solutions as the viscosity coefficient tends to zero.

The quasiNewton method was applied to solving the augmented Lagrangian function of nonlinear programming problems. Further, the quasiNewton formula was given.

This note deals with the regularity of the adjoint semigroup of a ring. Acharacterization of adjoint regular rings is presented. For ring R which is a sum of two adjoint regular subrings, sufficient and necessary conditions for the regularity of the adjoint semigroup of R are given, which have extend the results given by Volkov and Tanana, and affirm their conjecture.

Let {ε_t;t∈Z^{+} be a strictly stationary sequence of LPQD random variables with mean zeros, let 02₁<∞,with 0<σ2<∞, {_j;; j∈N } is a sequence of real numbers satisfying. Define a linear process X_t. In this article, by means of the weak convergence theorems and moment inequalities, the precise asymptotics of {M_n} and {S_n}is proved for more general weighted functions and boundary functions.}

We obtained one sufficient condition under which a 2-harmonic submanifold with nonnegative sectioncurvature turns into a maximal submanifold by promoting known theorem. And We also studied the 2-harmonic hypersurfaces by weakening the conditions when the Ricci curvature of the ambient manifold had upper and lower restrict, thus improving the known results.

The existence of positive solutions for the boundary value problems of p-Laplacian difference equations with time delay was p roved. Sufficient conditions that guaranteed the existence of positive solutions for those problems were obtained. Furthermore, the numerical experiment was also carried out to illustrate the main result in this paper.

We discussed complete convergence for ρ^-mixing random sequence, and obtained the general equivelent relationship between the rate of complete convergence and moment condition of random variables by means of the Rosenthal type inequality of ρ^- mixing random sequence and the trun cation method. The results are consistent with those for independent sequence that confirms the similarity in complete convergence between ρ^-mixing sequence and independent one.

For linear illposed problems, the paper presents a fast convergent method of iterated regularization based on the idea of Landweber i terated regularization, and a method of aposteriori choice by the Morozov discrepancy principle, by which the optimum asymptotic convergence order of the regularized solution is obtained. Numerical test shows that the method of iterated regularization can quicken the convergence speed, reduce the calculation burden efficiently.

A twodimensional ninevelocity Lattice Boltzmann model was employed to simulate the flow past a rectangular elongated cylinder numerically. The secondorder interpolation scheme was used for the boundary treatment. The Strouhal number, the drag coefficient and lift coefficient were calculated. The streamlines and the vorticity contours were presented. Under varying the length/width ratio of the rectangular, and keeping the inlet velocity to be parallel to the length side of the rectangular cylinder, numerical results show that the Strouhal number varies linearly with the length/width ratio.

Taking the polynomial system as a semiquasihomogeneous one, and using the so called Kowalevsky exponents, we gave a necessary condition for polynomial systems to have rational first integral. In fact, the result obtained in this paper has provided a simple criterion of nonintegrability for polynomial systems.

Let {X_n,n≥1} be ρ^*mixing sequences with identical distributions belonging to the domain of the normal attraction with non-degenerate stable distribution. By means of the moment inequalities of the ρ^*mixing sequences, it was proved that probability 1 possesses,and some equivaent conditions were obtained.

The authos analyzed the method existed and got an improved implementation method on Koblitz curve cryptograph on computing . The analysis shows that the efficiency was increased by a factor of over 55% and this method can be used to improve the efficiency of elliptic curve cryptography (ECC).

Using the Floquet’s theory firstly, we gave the necessary condition of formal first integrals in a neighborhood of a constant solution for the periodic systems. Furthermore, we also gave a criterion for the partial existence of formal first integrals for these systems near some neighborhood of a constant solution.

This paper presents a new method of similarity measurement, on the basis of which an global K-means algorithm is presented that is selfadaptive to the determination of the number of cluster, so as to solve the problem that the existing methods of co-regulated gene clustering can take into account all the four co-regulating relationships, that is, reverse, asynchronous, parttime, and differences in the expression. The present algorithm has been applied to the microarray data, and the compare experimental results with CLUSTER 3.0 prove that the algorithm is efficient.

This paper presents an algorithm based on the improved suffix tree and interactclustering idea. Hierarchical clustering for document title and summary is implemented by improved traditional suffix tree structure. Meanwhile, the interactive clustering is employed instead of traditional recursive algorithm. The algorithm is not related with language. Not only is it applicable to wordbased English, but also it can deal effectively with characterbased Chinese without dictionarybased Chinese word segmentation. Furthermore, the interactive clustering engine was realized on the basis of the algorithm, the system was tested in different network environments, and the performance of the system was compared with other metasearch engines. The experimemnt demonstrates that it is feasible effectively to conduct realtime interactive cluste ring by using the improved suffix tree algorithm.

The commodity market model was compared with the auction model from the aspects of resource allocation and task scheduling based on eco nomic models in computational grids. To evaluate these two models, we simulated them respectively in underdemand and excessdemand circumstances. We have examined the overall price stability, market equilibrium, producer efficiency, and consumer efficiency by simulation and drawn a conclusion that the commodity market model is more suitable to computational grids, and makes the whole resource market more fair, stable and efficient.

The methods were presented for measuring and analysising laser energy density distribution. First, the spot images were detected and lo cated. Then wavefront was fitted based on Zernike polynomial. Finally, 3D-pseudocolor visualization algorithm was used for 2D-laser spot images. Experimental results indicate that the Zernike polynomial fitting realized wavefront detection and reconstruction. The method of fitting sample points selection was studied based on the least average error of laser energy intensity testing precision. The visualizationmethod reflected the relative sizes and positions of laser spot energy distribution in different areas. The testing system fully satisfied the demand of laser energy intensity measurement.

As a generalization of the conventional possibilistic and kernel based possibilistic clustering model, a new kernel based possibilistic clustering model was proposed. The new approach performs the clustering by optimizing the proposed kernel possibilistic Xie-Beni index using the RJMCMC (Reversible Jump Markov Chain Monte Carlo) based simulated annealing algorithm (SA), which makes the number of clusters change in a given range and the optimal number of clusters and partitioning obtained automatically. In contrast to the conventional SA based possibilistic or kernel based possibilistic clustering, it has a higher efficiency and avoids the problem of generating coincident clusters. The contrast experiments on real and artificial data show the effectiveness of the proposed algorithm.

Using frequency weighting mining algorithm with realtime data processing capability to calculate each system call’s frequency value for existed audit records, we got a vector set of progresses. The vector set was linearly scanned and its progresses were labeled as “normal” or “attack” according to their distance relations. Then, we got a SVM training set without manmade supervision. Finally, the normal behavior profiles for monitoring the target system were generated by SVM classifier so as to construct a practicalon line intrusion detection system without human intervention.

Based on ontology theory, this paper addresses a novel workflow model that can accommodate the change of personnel and operation. To achieve the object of adapting to change more powerfully, the model adopts the method of extending the definition of conceptions and relationships inside the submodel as well as betweenthe submodels. To address the result of reducing the negative impact on the model relationships and structure, the model makes the organization, the roles and the personnel separately at different levels in the organization model. And the authority assignation model adopts the authority assignation based on task. Consequently, it also addresses the result that the change of task will not affect the organization model and will avoid the change of the complicated relationships. Especially, it makes the conception represented by ontology. Therefore, this paper produces the conclusion that the model has covered the defect of unshared feature in traditional models, at the same time, it is more secure and flexible.

A closed four-level system in atomic vapor was proposed, which was made to possess left handedness by means of the technique of quantum coherence. The density matrix method was utilized in view of the rotating-wave approximation and the local-field effect in high dense gas. The conclusion of the numerical simulation shows that the medium can simultaneously exhibits left handedness in two visible frequency bands, and one can manipulate the width of the frequence bands by changing the intensity of the control field. 

Nanocrystalline γ′-Fe_{4^{Nthin films were synthesized on single crystal Si (100) substrate by facing target magnetron sputtering. The structure and magnetic properties at room temperature and low temperatures were characterized by means of X-ray diffraction (XRD) and vibrating sample magnetometer (VSM). The results indicate that the film had a single easy magnetized direction along (111). In a temperature range of 80~350 K, the saturation magnetization σs and coercive force Hc increased, whereas the ratio σr/σsdecreased with decreasing measured temperature. The relation between the coercive force Hc and temperature T obeyed the T1/2 law, the relation between σs and T did not obey the Bloch T3/2 law, which means that the interaction among spin waves should be considered. }}

When propagating light\|ray passes through two fixed points in the gradient index (GRIN) mediums and a cuspidal variable\|point （at this point the trace equation of propagating light\|ray is non\|differentiable） at the borderline of two different GRIN mediums, the mathematical relationship, which the trace equation of propagating light\|ray and borderline equation of two different GRIN mediums should satisfy, is derived by the Fermat’s principle and calculus of variation. Some applied examples show that the differential relationship not only contains fundamental content in geometrical optics, such as the three laws of geometrical optics, imaging formula of single spheric face, but is another form of differential equation of the light ray.

A new single-core and double-winding magnetic field sensor prepared from Co-based amorphous ribbon was studied. Using frequency measurement approach to measuring magnetic fields increases the measurement sensitivity of the sensor. Using the closed\|loop system increases the stability of the sensor.

The optical properties of an erbium\|doped polymer material Er(DBM)3Phen/PMMA\|GMA were researched and its absorption spectrum, refractive index and other parameters were also tested. An erbium\|doped organic polymer waveguide amplifier was fabricated by means of photolithography combined with reactive ions etching. Then the characteristics of the optical waveguide amplifier were tested by coupling the signal light and pump light into the waveguide directly. When the pump power was 150 mW and the signal power was 0.2 mW, the maximum relative gain of approximate 0.9 dB was observed on the device with a length of 1.24 cm.

Detection of weak signals in heavy noise background based on stochastic resonance was studied via numerical calculation. The relations of the amplitude and the signaltonoise ratio of the output signals of a nonlinear bistable stochastic resonance system to the noise intensity were researched under the high frequency condition. The results of numerical simulation show that the noise is restrained intensively by the nonlinear bistable system. High frequency weak signals in heavy noise background can be detected clearly based on stochastic resonance. The time domain and the characteristic spectrum of the frequency domain of output signals is obtained by extracting the high frequency weak signals with filtering wave technique. By means of the linear filter, the time domain of output signals can be obtained clearly.

Nearinfrared spectroscopy combined with partial least squares (PLS) method was applied to establishingan optimal mathematic calibration model, by which the concentrations of amino nitrogen, total acid and salt content in the soy sauce were predicted, and the color ratio of the soy sauce was determined. Furthermore, the influences of spectral preprocessing methods and the numbers of principal components on the prediction ability of the PLS model were discussed. The results show that the calibration model established with firstderivative preprocessing spectra was the best, 18 samples of tested set were predicted with this model, the relative standard errors for the prediction of ami no nitrogen, total acid, salt content and color ratio were 1.516%, 1.811%, 1.798% and 1.893%, respectively. Experimental results demonstrate that this method is fast and convenient, and it has a high ability of prediction, thus it is promising for the nondestructive quality control of soy sauce.

Nanometer TiO₂ thin films were prepared by means of a sol-gel process with ［Ti(OBu)₄］ as the precursor and characterized by XRD, TG-DTA, TEM and PL spectra. XRD results show that the referentially oriented (101) anatase films were formed. TEM results show the TiO₂ grainsize distribution of the sample was even and its size was about 15 nm. At room temperature, the PL intensity was found to have a well matching relation to the doping concentration of Tb³⁺ ions. Luminescence intensity was improved obviously after co-dopingof Gd³⁺ ions because of the sensitization effect of Gd³⁺ ions to Tb³⁺ ions in TiO₂ system. The energy transfer mechanism from Gd³⁺ ions to Tb³⁺ ions was proposed.

The dihydrogen bonds B—H…H—X and traditional Hbonds N—H…X and X—H…X (X=F,Cl,O) between B₃N₃H₆ and each of HF, HCl or H₂O were theoretically studied by use of the ab initio quantum mechanics method (MP2). We found that the action of the dihydrogen bond made the BH and HX bonds redshifted, and that the formation of the traditional Hbonds made the NH and HX bonds redshifted. The topological properties of the complexes show that these intermolecular interactions were indeed Hbonds. The natural bond orbital analysis shows that these Hbonds can be interpreted by the theory of hypercon jugation and rehybridization.

Under microwave heating, the degradation conditions (catalyst concentration, reaction temperature and time) were optimized, and the optimal conditions were φcatalyst= 5%, reaction temperature 100 ℃ and reaction time 2 h, with a yield of reducing sugars concentration 2.15 g/L. Under the optimized conditions, a comparative study was performed to evaluate the effects of micowave heating and conventional heating on the yield of reducing sugars, and the results show that the yield of reducing sugars obtained by the degr adation via microwave heating is increased by a factor of 33.5%, and the degradation rate is increased by a factor of 487%. The morphologies of degradation product via microwave heating and conventional heating were tested with SEM and the results show that decrease in degree of polymerisation is caused by microwave irradiation. The degradation products obtained by microwave heating and co nventional heating respectively were similar with FTIR spectra.

A supermolecular compound, ［Cd₂(Dppz)₄(1,2-BDC)₂］·4H₂O was obtained from the hydrothermal reaction of cadium(Ⅱ) nitrate with mixed ligands ［phthalic acid (1,2-H₂BDC) and dipyrido［3,2-a: 2′,3′-c］phenazine(Dppz)］, and structurally characterized by singlecrystal Xray diffraction. Result reveals that the compound belongs to the monoclinic system wit h space group C2/c. The cell parameters are: a=2.496 17(10) nm, b=1.7 15 96(10) nm, c=1.822 32(8) nm, β=96.293(1)°, V =7.758 6(6) nm3,  Z=4, R₁=0.045 6, wR₂=0.093 9. The result of fluorescence spectrum shows that the title compound exhibits blue emission in the solid state at room temperature.

Effects of malic acid and succinic acid on the sorption and distribution of fluoride in tea garden soil was studied by the sampling of tea garden soil and the simulated testing. The sorption capacity of fluoride by tea garden soil was depressed to some extent in the presence of malic acid and succinic acid when the initial concentration of fluoride was lower than 0.42 mmol/L for the low concentration of the organic acids and 2.1 mmol/L for the high concentration of the organic acids. The depressed function of the two organic aicds for the sorption of fluoride in tea garden soil, however, was weakened when the initial concentration of fluoride was higher than 0.42 mmol/L for the low concentration of the organic acids and 2.1 mmol/L for the high concentrationof the organic acids. On the contrary, there was a distinct enhancing function for the sorption capacity of fluoride in tea garden soil in the presence of the two organic acids with increasing the initial concentration of fluoride, and the enhancing function of malic acid was larger than that of succinic acid. The residual species was the major form and water soluble species was secondary form for sorbed fluoride under the control treatmentand in the presence of malic acid and succinic acid. There were also differences in the distributionand transformation of sorbed fluoride in tea garden soil in the presence of the different organic aicds and their concentrations, but the general distribution law of sorbed fluoride was in the order: residual>water soluble>organic≈Fe-Mn oxide>exchangeable.

Effects of initial TOC of butyric acid, catalyst dosage, reaction temperature, and initial oxygen pressure on the degradation reaction process of butyric acid under catalytic wet air oxidation were investigated, and a BP artificial neural network model for the degradation process of butyric acid under catalytic wet air oxidation was established. The simulated efficiency factor of the model was calculated to be 0.973 2 (more than 0.80), indicating the model established could well and truly forecast the residual butyric acid in the degradation reaction process of catalyticwet air oxidation. Meanwhile, the reaction condition optimization of butyric acid under catalytic wet air oxidation based on the BP artificial neural network model was carried out, and the results show that the degradation efficiency of butyric acid under catalytic wet air oxidation was nearly enhanced by 20%.