Stability and Hopf bifurcation analysis of a predator-prey model with time delayed incomplete trophic transfer

A new nonlinear predator-prey model with incomplete trophic transfer is introduced. In this model,we assume that the rate of the trophic absorption of the predator is less than the rate of the conversion of consumed prey to predator in the Ivlev-type functional responses. The existence and uniqueness of the positive equilibrium of the model and the stability of the equilibrium of the model are studied under various conditions.Hopf bifurcation analysis of the delayed model is provided.     

Boundary Shape Control of the Navier-Stokes Equations and Applications

In this paper, the geometrical design for the blade's surface in an impeller or for the profile of an aircraft, is modeled from the mathematical point of view by a boundary shape control problem for the Navier-Stokes equations. The objective function is the sum of a global dissipative function and the power of the fluid. The control variables are the geometry of the boundary and the state equations are the Navier-Stokes equations. The Euler-Lagrange equations of the optimal control problem are derived, which are an elliptic boundary value system of fourth order, coupled with the Navier-Stokes equations. The authors also prove the existence of the solution of the optimal control problem, the existence of the solution of the Navier-Stokes equations with mixed boundary conditions, the weak continuity of the solution of the Navier-Stokes equations with respect to the geometry shape of the blade's surface and the existence of solutions of the equations for the Gateaux derivative of the solution of the Navier-Stokes equations with respect to the geometry of the boundary.     

On the Growth of Components of Meromorphic Solutions of Systems of Complex Differential Equations

This paper investigates the problem of the growth of the components of meromorphic solutions of a class of a system of complex algebraic differential equations, and generalized some of N. Toda＇s results concerning the growth of differential equations to the case of systems of differential equations. The paper considers the existence of admissible solutions of the system of differential equations.     

拟线性可化约的双曲型方程组的奇性分析

In this paper we investigate the formation of singularities of hyperbolic systems. Employing the method of parametric coordinates and the existence of the solution of the blow-up system, we prove that the blow-up of classic solutions is due to the envelope of characteristics of the same family, analyze the geometric properties of the envelope of characteristics and estimate the blowup rates of the solution precisely.     

An algorithm for decomposing a polynomial system into normal ascending sets

We present an algorithm to decompose a polynomial system into a finite set of normal ascending sets such that the set of the zeros of the polynomial system is the union of the sets of the regular zeros of the normal ascending sets.If the polynomial system is zero dimensional,the set of the zeros of the polynomials is the union of the sets of the zeros of the normal ascending sets.     

基于Legendre多项式的数值微分: 加权$L^2$空间中的收敛性分析

We consider the problem of estimating the derivative of a function f from its noisy version fδby using the derivatives of the partial sums of Fourier-Legendre series of f~δ. Instead of the observation L~2 space, we perform the reconstruction of the derivative in a weighted L~2 space. This takes full advantage of the properties of Legendre polynomials and results in a slight improvement on the convergence order. Finally, we provide several numerical examples to demonstrate the efficiency of the proposed method.     

LOCAL AND GLOBAL HOPF BIFURCATIONS IN A DELAYED HUMAN RESPIRATORY SYSTEM

This paper considers a delayed human respiratory model. Firstly, the stability of the equilibrium of the model is investigated and the occurrence of a sequence of Hopf bifurcations of the model is proved. Secondly, the explicit algorithms which determine the direction of the Hopf bifurcations and the stability of the bifurcating periodic solutions are derived by applying the normal form method and the center manifold theory. Finally, the existence of the global periodic solutions is showed under some assumptions on the model.     

The Formual of Generalized Center－Weak Saddle

In his paper,a problem of center-weak focus of a general system of degree n is transformed into a problem of generalized center-weak saddle.It offers:(1) the calculating formula of the saddle values of the former 4 orders in the general system of degree three;(2) some calculating formulae of the saddle values in the general homogeneous system of degree n. The problem of center-focus(saddle)plays an important role in the qualitative theory of ordinary differential equations.However,since the calculations are difficult,the results have not been satisfactory.On the basis of the author‘s work,Northeast.Math.J.,13(4)(1997),487-494,the paper offers some calculating formulae of the saddle values.     

A local probability exponential inequality for the large deviation of an empirical process indexed by an unbounded class of functions and its application

A local probability exponential inequality for the tail of large deviation of an empirical process over an unbounded class of functions is proposed and studied. A new method of truncating the original probability space and a new symmetrization method are given. Using these methods, the local probability exponential inequalities for the tails of large deviations of empirical processes with non-i.i.d. independent samples over unbounded class of functions are established. Some applications of the inequalities are discussed. As an additional result of this paper, under the conditions of Kolmogorov theorem, the strong convergence results of Kolmogorov on sums of non-i.i.d. independent random variables are extended to the cases of empirical processes indexed by unbounded classes of functions, the local probability exponential inequalities and the laws of the logarithm for the empirical processes are obtained.     

A Regularized Newton Method in Inverse Scattering Problem from Cavities

We consider the inverse problem to determine the shape of a open cavity embedded in the infinite ground plane from knowledge of the far-field pattern of the scattering of TM polarization.For its approximate solution we propose a regularized Newton iteration scheme.For a foundation of Newton type methods we establish the Fréchet differentiability of solution to the scattering problem with respect to the boundary of the cavity.Some numerical examples of the feasibility of the method are presented.     

UNCONDITIONAL STABLE DIFFERENCE METHODS WITH INTRINSIC PARALLELISM FOR SEMILINEAR PARABOLIC SYSTEMS OF DIVERGENCE TYPE

The general finite difference schemes with intrinsic parallelism for the boundary value problem of the semilinear parabolic system of divergence type with bounded measurable coefficients is studied. By the approach of the discrete functional analysis, the existence and uniqueness of the discrete vector solutions of the nonlinear difference system with intrinsic parallelism are proved. Moreover the unconditional stability of the general difference schemes with intrinsic parallelism justified in the sense of the continuous dependence of the discrete vector solution of the difference schemes on the discrete initial data of the original problems in the discrete W_2~(2,1) (Q△) norms. Finally the convergence of the discrete vector solutions of the certain difference schemes with intrinsic parallelism to the unique generalized solution of the original semilinear parabolic problem is proved.     

On singular Lüroth quartics

Plane quartics containing the ten vertices of a complete pentalateral and limits of them are called Lüroth quartics.The locus of singular Lüroth quartics has two irreducible components,both of codimension two in P14.We compute the degree of them and discuss the consequences of this computation on the explicit form of the Lüroth invariant.One important tool is the Cremona hexahedral equations of the cubic surface.We also compute the class in M 3 of the closure of the locus of nonsingular Lüroth quartics.     

The asymptotic distributions of the statistics of the skew elliptical variables

In this paper, the asymptotic properties of the quadratic forms and the T statistic of the skew elliptical variables are studied. Consistent estimators of some parameters are obtained. The robustness of the significance level of the one-sided t test within the family of the skew normal family is investigated.     

Time to most recent common ancestor for stationary continuous state branching processes with immigration

Motivated by sample path decomposition of the stationary continuous state branching process with immigration, a general population model is considered using the idea of immortal individual. We compute the joint distribution of the random variables： the time to the most recent common ancestor （MRCA）, the size of the current population, and the size of the population just before MRCA. We obtain the bottleneck effect as well. The distribution of the number of the oldest families is also established. These generalize the results obtained by Y. T. Chen and J. F. Delmas.     

Gamma-Dirichlet algebra and applications

The Gamma-Dirichlet algebra corresponds to the decomposition of the gamma process into the independent product of a gamma random variable and a Dirichlet process. This structure allows us to study the properties of the Dirichlet process through the gamma process and vice versa. In this article, we begin with a brief survey of several existing results concerning this structure. New results are then obtained for the large deviations of the jump sizes of the gamma process and the quasi-invariance of the two-parameter Poisson-Dirichlet distribution. We finish the paper with the derivation of the transition function of the Fleming-Viot process with parent independent mutation from the transition function of the measure-valued branching diffusion with immigration by exploring the Gamma-Dirichlet algebra embedded in these processes. This last result is motivated by an open R. C. Gritfiths. problem proposed by S. N. Ethier and     

Motivic Milnor Fibre of Cyclic L_∞-algebras

We define the motivic Milnor fiber of cyclic L_∞-algebras of dimension three using the method of Denef and Loeser of motivic integration. It is proved by Nicaise and Sebag that the topological Euler characteristic of the motivic Milnor fiber is equal to the Euler characteristic of the étale cohomology of the analytic Milnor fiber. We prove that the value of Behrend function on the germ moduli space determined by a cyclic L_∞-algebra L is equal to the Euler characteristic of the analytic Milnor fiber. Thus we prove that the Behrend function depends only on the formal neighborhood of the moduli space.     

THE EXISTENCE OF GLOBAL SOLUTIONS FOR THE FULL NAVIER-STOKES-KORTEWEG SYSTEM OF VAN DER WAALS GAS

The aim of this work is to prove the existence for the global solution of a nonisothermal or non-isentropic model of capillary compressible fluids derived by J. E. Dunn and J. Serrin(1985), in the case of van der Waals gas. Under the small initial perturbation, the proof of the global existence is based on an elementary energy method using the continuation argument of local solution. Moreover, the uniqueness of global solutions and large time behavior of the density are given. It is one of the m...     

WEIGHTED NONLINEAR REGRESSION

Minimization of the weighted nonlinear sum of squares of differences may be converted to the minimization of sum of squares. The Gauss-Newton method is recalled and the length of the step of the steepest descent method is determined by substituting the steepest descent direction in the Gauss-Newton formula. The existence of minimum is shown.     

Convergence of the Cesàro mean for rational orthonormal bases

This paper deals with the convergence of the Cesaro mean for the rational orthonormal bases. Provided the set of zeroes of rational orthonormal bases is formed by a periodic repetition of the same finite sequence, the explicit expression of so-called block-Fejer kernel is available, and some properties of the block-Fejer kernel are discussed. Based on the convergence of the block-Cesaro mean, the convergence of Cesaro mean is also provided.     

ON THE STABILITY OF DIFFERENTIAL SYSTEMS WITH TIME LAG

In this paer the inequality of Lemma 1 of [1] is extended.By means of our inequality and the method of Lyapunov function we study the stability of two kinds of large seate differential systems with time lag and the stability of a higher -order differential equation with time lag.The sufficient conditions for the stability(S.),the asymptotic stability(A.S.),the uniformly asymptotic stability(U.A.S) and the exponential asymptotic stability(E.A.S.) of the zero solutions of the systerms are obtained respectively.