CERTAIN SUFFICIENT CONDITIONS FOR STARLIKENESS AND CONVEXITY OF MEROMORPHICALLY MULTIVALENT FUNCTIONS

In this paper we derive certain suffcient conditions for starlikeness and con-vexity of orderαof meromorphically multivalent functions in the punctured unit disk.     

AN INEQUALITY ON THE ZEROS AND POLES OF VECTOR VALUED MEROMORPHIC FUNCTIONS

The author proves that if f : C→Cn is a transcendental vector valued meromorphic function of finite order and assume Σa∈Cn ∪{∞}δ(a) = 2, then,where .This result extends the related results for meromorphic function by Singh and Kulkarni.     

Local Bifurcation of Critical Periods for a Class of Liénard Equations

In this paper,we study the local bifurcation of critical periods near the nondegenerate center(the origin) of a class of Liénard equations with degree 2n,and prove that at most 2n-2 critical periods(taken into account multiplicity) can be produced from a weak center of finite order.We also prove that it can have exactly2n-2 critical periods near the origin.     

Global Stability in a Model for CTL Response to HTLV-I Infection

In this paper, a mathematical model for HTLV-I infection of CD4＋ T cells that incorporates the CD8＋ cytotoxic T-cell（CTL） response is studied. We establish two threshold parameters Ro and R1, the basic reproduction numbers for viral persistence and for CTL response, respectively. We also show that the parameter R1 can be used to distinguish asymptomatic carriers from HAM/TSP patients and as an important control parameter for preventing the development of HAM/TSP.     

AREA INTEGRAL FUNCTIONS AND H∞ FUNCTIONAL CALCULUS FOR SECTORIAL OPERATORS ON HILBERT SPACES

Area integral functions are introduced for sectorial operators on Hilbert spaces. We establish the equivalence relationship between the square and area integral functions. This immediately extends McIntosh/Yagi＇s results on H∞ functional calculus of sectorial operators on Hilbert spaces to the case when the square functions are replaced by the area integral functions.     

GAUSS-MEAN VALUE FORMULA FOR TRIHARMONIC FUNCTIONS AND ITS APPLICATIONS IN CLIFFORD ANALYSIS

In this paper, the integral representation for some polyharmonic functions with values in a universal Clifford algebra Cl(Vn,n) is studied and Gauss-mean value formula for triharmonic functions with va...     

KINETIC FUNCTIONS IN MAGNETOHYDRODYNAMICS WITH RESISTIVITY AND HALL EFFECT

We consider a nonlinear hyperbolic system of two conservation laws which arises in ideal magnetohydrodynamics and includes second-order terms accounting for magnetic resistivity and Hall effect. We show that the initial value problem for this model may lead to solutions exhibiting complex wave structures, including undercompressive nonclassical shock waves. We investigate numerically the subtle competition that takes place between the hyperbolic, diffusive, and dispersive parts of the system. Following Abeyratne, Knowles, LeFloch, and Truskinovsky, who studied similar questions arising in fluid and solid flows, we determine the associated kinetic function which characterizes the dynamics of undereompressive shocks driven by resistivity and Hall effect. To this end, we design a new class of ＂schemes with eontroled dissipation＂, following recent work by LeFloch and Mohammadian. It is now recognized that the equivalent equation associated with a scheme provides a guideline to design schemes that capture physically relevant, nonclassical shocks. We propose a new class of schemes based on high-order entropy conservative, finite differences for the hyperbolic flux, and high-order central differences for the resistivity and Hall terms. These schemes are tested for several regimes of （co-planar or not） initial data and parameter values, and allow us to analyze the properties of nonclassical shocks and establish the existence of monotone kinetic functions in magnetohydrodynamics.     

BOUNDEDNESS OF FRACTIONAL MAXIMAL OPERATOR AND THEIR HIGHER ORDER COMMUTATORS IN GENERALIZED MORREY SPACES ON CARNOT GROUPS

In the article we consider the fractional maximal operator Mα, 0≤α相似文献   

GRADIENT ESTIMATES FOR POSITIVE SMOOTH f-HARMONIC FUNCTIONS

For Riemannian manifolds with a measure,we study the gradient estimates for positive smooth f-harmonic functions when the ∞-Bakry-Emery Ricci tensor and Ricci tensor are bounded from below,generalizing the classical ones of Yau(i.e.,when f is constant).     

BOUNDEDNESS OF STEIN＇S SQUARE FUNCTIONS ASSOCIATED TO OPERATORS ON HARDY SPACES

Let(X, d, μ) be a metric measure space endowed with a metric d and a nonnegative Borel doubling measure μ. Let L be a second order non-negative self-adjoint operator on L2(X). Assume that the semigroup e-tLgenerated by L satisfies the Davies-Gaffney estimates. Also, assume that L satisfies Plancherel type estimate. Under these conditions,we show that Stein's square function Gδ(L) arising from Bochner-Riesz means associated to L is bounded from the Hardy spaces Hp L(X) to Lp(X) for all 0 p ≤ 1.     

THE SCHUR HARMONIC CONVEXITY FOR A CLASS OF SYMMETRIC FUNCTIONS

In this article,we prove that the symmetric function F_n~*(x,r)=i_1+i_ 2_++i_n =r(x_1~(i~1)x_2~(i~2)... x_n~(i~n)1/r is Schur harmonic convex for x∈R~n_+and r∈N={1,2,3,...}.As its applications,some analytic inequalities are established.     

WEIGHTED COMPOSITION OPERATORS ON WEIGHTED DIRICHLET SPACES

We characterize the boundedness and compactness of weighted composition operators on weighted Dirichlet spaces in terms of Nevanlinna counting functions and Caxleson measure.     

NONLINEAR EVOLUTION SYSTEMS AND GREEN’S FUNCTION

In this paper, we will introduce how to apply Green’s function method to get the pointwise estimates for the solutions of Cauchy problem of nonlinear evolution equations with dissipative structure. First of all, we introduce the pointwise estimates of the time-asymptotic shape of the solutions of the isentropic Navier-Stokes equations and show to exhibit the generalized Huygen’s principle. Then, for other nonlinear dissipative evolution equations, we will only introduce the result and give some brief explanations. Our approach is based on the detailed analysis of the Green’s function of the linearized system and micro-local analysis, such as frequency decomposition and so on.     

EXISTENCE OF ENTROPY SOLUTIONS TO TWO-DIMENSIONAL STEADY EXOTHERMICALLY REACTING EULER EQUATIONS

We are concerned with the global existence of entropy solutions of the twodimensional steady Euler equations for an ideal gas, which undergoes a one-step exothermic chemical reaction under the Arrhenius-type kinetics. The reaction rate function φ(T) is assumed to have a positive lower bound. We first consider the Cauchy problem(the initial value problem), that is, seek a supersonic downstream reacting flow when the incoming flow is supersonic, and establish the global existence of entropy solutions when the total variation of the initial data is suffciently small. Then we analyze the problem of steady supersonic, exothermically reacting Euler flow past a Lipschitz wedge, generating an additional detonation wave attached to the wedge vertex, which can be then formulated as an initial-boundary value problem. We establish the global existence of entropy solutions containing the additional detonation wave(weak or strong, determined by the wedge angle at the wedge vertex) when the total variation of both the slope of the wedge boundary and the incoming flow is suitably small. The downstream asymptotic behavior of the global solutions is also obtained.     

THE NAVIER-STOKES EQUATIONS WITH THE KINEMATIC AND VORTICITY BOUNDARY CONDITIONS ON NON-FLAT BOUNDARIES

We study the initial-boundary value problem of the Navier-Stokes equations for incompressible fluids in a general domain in R^n with compact and smooth boundary, subject to the kinematic and vorticity boundary conditions on the non-flat boundary. We observe that, under the nonhomogeneous boundary conditions, the pressure p can be still recovered by solving the Neumann problem for the Poisson equation. Then we establish the well-posedness of the unsteady Stokes equations and employ the solution to reduce our initial-boundary value problem into an initial-boundary value problem with absolute boundary conditions. Based on this, we first establish the well-posedness for an appropriate local linearized problem with the absolute boundary conditions and the initial condition （without the incompressibility condition）, which establishes a velocity mapping. Then we develop apriori estimates for the velocity mapping, especially involving the Sobolev norm for the time-derivative of the mapping to deal with the complicated boundary conditions, which leads to the existence of the fixed point of the mapping and the existence of solutions to our initial-boundary value problem. Finally, we establish that, when the viscosity coefficient tends zero, the strong solutions of the initial-boundary value problem in R^n（n ≥ 3） with nonhomogeneous vorticity boundary condition converge in L^2 to the corresponding Euler equations satisfying the kinematic condition.     

WELL-POSEDNESS OF A COMPRESSIBLE GAS-LIQUID MODEL FOR DEEPWATER OIL WELL OPERATIONS

The main purpose of this paper is two-fold:(i) to generalize an existence result for a compressible gas-liquid model with a friction term recently published by Friis and Evje [SIAM J. Appl. Math., 71(2011), pp. 2014–2047];(ii) to derive a uniqueness result for the same model. A main ingredient in the existence part is the observation that we can consider weaker assumptions on the initial liquid and gas mass, and still obtain an existence result. Compared to the above mentioned work, we rely on a more refined application of the estimates provided by the basic energy estimate. Concerning the uniqueness result, we borrow ideas from Fang and Zhang [Nonlinear Anal. TMA, 58(2004), pp. 719–731] and derive a stability result under appropriate constraints on parameters that determine rate of decay toward zero at the boundary for gas and liquid masses, and growth rate of masses associated with the friction term and viscous coefficient.     

ON THE BASIC REPRODUCTION NUMBER OF GENERAL BRANCHING PROCESSES

Under a very general condition （TNC condition） we show that the spectral radius of the kernel of a general branching process is a threshold parameter and hence plays a role as the basic reproduction number in usual CMJ processes. We discuss also some properties of the extinction probability and the generating operator of general branching processes. As an application in epidemics, in the final section we suggest a generalization of SIR model which can describe infectious diseases transmission in an inhomogeneous population.     

STABILIZATION OF MARKOVIAN JUMP LINEAR SYSTEMS VIA RANDOM COMMUNICATION TIME DELAYED AND IMPULSIVE CONTROLLERS

This paper deals with the stabilization problems for a networked control system via time-delayed and impulsive controllers. The random communication delays in the model signal are modeled as a Markov chain. First, we introduce a hybrid controller with delay and impulses for the networked control systems. Then, some sufficient conditions are proposed for the design of a hybrid controller such that the closed-loop system is stochastically stable.     

A CLASS OF MULTIWAVELETS AND PROJECTED FRAMES FROM TWO-DIRECTION WAVELETS

This article aims at studying two-direction refinable functions and two-direction wavelets in the setting Rs, s 1. We give a sufficient condition for a two-direction refinable function belonging to L2(Rs). Then, two theorems are given for constructing biorthogonal(orthogonal) two-direction refinable functions in L2(Rs) and their biorthogonal(orthogonal) two-direction wavelets, respectively. From the constructed biorthogonal(orthogonal)two-direction wavelets, symmetric biorthogonal(orthogonal) multiwaveles in L2(Rs) can be obtained easily. Applying the projection method to biorthogonal(orthogonal) two-direction wavelets in L2(Rs), we can get dual(tight) two-direction wavelet frames in L2(Rm), where m ≤ s. From the projected dual(tight) two-direction wavelet frames in L2(Rm), symmetric dual(tight) frames in L2(Rm) can be obtained easily. In the end, an example is given to illustrate theoretical results.     

A MATHEMATICAL MODEL OF ENTERPRISE COMPETITIVE ABILITY AND PERFORMANCE THROUGH EMDEN-FOWLER EQUATION （Ⅱ）

In this paper we work with the ordinary equation u＇＇ - u2 （u ＋ ） = 0 and ob- tain some interesting phenomena concerning, blow-up, blow-up rate, life-span of solutions to those equations.