LIMITING BEHAVIOR OF BLOW-UP SOLUTIONS OF THE NLSE WITH A STARK POTENTIAL

This article is concerned with blow-up solutions of the Cauchy problem of critical nonlinear SchrSdinger equation with a Stark potential. By using the variational characterization of corresponding ground state, the limiting behavior of blow-up solutions with critical and small super-critical mass are obtained in the natural energy space ∑ = {u ∈ H^1; fRN ｜x｜^2｜u｜^2dx 〈 ＋∞）}. Moreover, an interesting concentration property of the blow-up solutions with critical mass is gotten, which reads that ｜u（t, x）｜^2→ ｜｜Q｜｜L^2 2 δx=x1 as t → T.

THE NEAR-CRITICAL AND SUPER-CRITICAL ASYMPTOTIC BEHAVIOR IN THE THERMODYNAMIC LIMIT OF REVERSIBLE RANDOM POLYMERIZATION PROCESSES

In this paper, the near-critical and super-critical asymptotic behavior of a reversible Markov process as a chemical model for polymerization was studied. The results of the present paper, together with an analysis of the sub-critical stage, establish the existence of three distinct stages (sub-critical, near-critical and super-critical stages) of polymerization (in the thermodynamic limit as N --> +infinity,),depending on the value of strength of the fragmentation reaction. These three stages correspond to the size of the largest length of polymers of size N to be itself of order log N, Nm/m+1 (m greater than or equal to 2, m not equal 4n, n greater than or equal to 1) and N, respectively.

LIMIT BEHAVIOR OF GROUND STATES OF 2D BINARY BECS IN STEEP POTENTIAL WELLS

We study the ground states of attractive binary Bose-Einstein condensates with N particles,which are trapped in the steep potential wellsλV(x)inℝ2.We show that there exists a positive number N*such that if N>N*,the system admits no ground state for anyλ>0.Moreover,there exist two positive numbers,M*andλ*(N),such that if N<M*,then for anyλ>λ*(N),the system admits at least one ground state.Asλ→∞,for any fixed N<M*,we give a detailed description for the limit behavior of both positive and semi-trivial ground states.

LIMITING BEHAVIOR OF UNIFORM RECURSIVE TREES

The authors consider the limiting behavior of various branches in a uniform recursive tree with size growing to infinity. The limiting distribution of ξn,m, the number of branches with size m in a uniform recursive tree of order n, converges weakly to a Poisson distribution with parameter 1/m with convergence of all moments. The size of any large branch tends to infinity almost surely.

SUBCRITICAL ASYMPTOTIC BEHAVIOR IN THE MODIFIED LUSHNIKOV PROCESS OF POLYMERIZATION

We consider a modified Lnshnikov process as a model of a chemical polymer ization anf study the asymptotic behavior (in the thermodynamic limit;as N →∞)of a particular probability distribution on the set of N-dimensional vectors,tile kth component of which is the number of k-mers.The study study establisles the existence of three stages (subcritical,near-critical and supercritical stages)of polymerization,dependenting upon the ratio of association and dissociation rates of f polymers.The present paper concentrates on the analysis of tile subcritical stage.In the sibcritical.stages we show that tile size of the largest length of polymers of stize N is of the order.log N as N →+∞.

Long-time limit behavior of the solution to an atom's master equation

We study the long-time limit behavior of the solution to an atom＇s master equation. For the first time we derive that the probability of the atom being in the α-th （α = j ＋ 1 -jz, j is the angular momentum quantum number, jz is the z-component of angular momentum） state is {（1 - K/G）/[1 - （K/G）2j＋1]}（K/G）^α-1 as t → ＋∞, which coincides with the fact that when K/G 〉 1, the larger the a is, the larger the probability of the atom being in the α-th state （the lower excited state） is. We also consider the case for some possible generaizations of the atomic master equation.

Analysis of the Boundary Stability of a Diffusion-Reaction System on a Nanolayer

In this paper, the focus is on the boundary stability of a nanolayer in diffusion-reaction systems, taking into account a nonlinear boundary control condition. The authors focus on demonstrating the boundary stability of a nanolayer using the Lyapunov function approach, while making certain regularity assumptions and imposing appropriate control conditions. In addition, the stability analysis is extended to more complex systems by studying the limit problem with interface conditions using the epi-convergence approach. The results obtained in this article are then tested numerically to validate the theoretical conclusions.

结构化理论视野下的大学生就业行为分析

社会结构性因素塑造大学生的就业行为。社会收益的结构性分割,教育体制中教育理念、专业设置和教育内容等结构性因素造成大学生就业行为的城市、行业和地区指向性。大学生"就业难"问题是劳动力市场需求与大学生就业行为之间的结构性矛盾的结果。解决大学生"就业难"问题,必须从影响大学生就业的结构性因素入手。

企业中政府投资行为方式研究

文章论证了企业中政府投资行为能力的有限性根源于政府与国民签定具有规避风险性质的固定“授权合同”,不过,政府投资的有限性并不妨碍政府为了社会效益最大化在其投资边界内进行公共品投资。政府企业投资应是规避风险投资,以确保政府资本保值增值。文章又分析,随着企业经济效益的变化,企业控制权随机依存于企业不同的利益相关者。只有企业破产时,债权人才控制企业,并且债权合同对企业经营者和股东有激励效应,债权风险小于股权风险。由此得出,在我国,企业中政府投资方式债权化是可行的。

Dynamic analysis on methanation reactor using a double-input–multi-output linearized model

A double-input–multi-output linearized system is developed using the state-space method for dynamic analysis of methanation process of coke oven gas.The stability of reactor alone and reactor with feed-effluent heat exchanger is compared through the dominant poles of the system transfer functions.With single or double disturbance of temperature and CO concentration at the reactor inlet,typical dynamic behavior in the reactor,including fast concentration response,slow temperature response and inverse response,is revealed for further understanding of the counteraction and synergy effects caused by simultaneous variation of concentration and temperature.Analysis results show that the stability of the reactor loop is more sensitive than that of reactor alone due to the positive heat feedback.Remarkably,with the decrease of heat exchange efficiency,the reactor system may display limit cycle behavior for a pair of complex conjugate poles across the imaginary axis.

On the Initial Layer and the Limit Behavior for Chemotaxis System with the Effect of Fluid in Fourier Space

The paper deals with a Cauchy problem for the chemotaxis system with the effect of fluid■where d≥2.It is known that for each∈>0 and all sufficiently small initial data(u_(0),n_(0),c_(0))belongs to certain Fourier space,the problem possesses a unique global solution(u^(∈),n^(∈),c^(∈))in Fourier space.The present work asserts that these solutions stabilize to(u^(∞),n^(∞),c^(∞))as∈^(-1)→0.Moreover,we show that c^(∈)(t)has the initial layer as∈^(-1)→0.As one expects its limit behavior maybe give a new viewlook to understand the system.

On the limit behavior of the magnetic Zakharov system

In this paper,we prove that the solutions of magnetic Zakharov system converge to those of generalized Zakharov system in Sobolev space H s,s > 3/2,when parameter β→∞.Further,when parameter (α,β) →∞ together,we prove that the solutions of magnetic Zakharov system converge to those of Schro¨dinger equation with magnetic effect in Sobolev space H s,s > 3/2.Moreover,the convergence rate is also obtained.

Limit behaviors of extended Kalman filter as a parameter estimator for a sinusoidal signal

In this note, the basic limit behaviors of the solution to Riccati equation in the extended Kalman filter as a parameter estimator for a sinusoidal signal are analytically investigated by using lira sup and lim inf in advanced calculus. We show that if the covariance matrix has a limit, then it must be a zero matrix.

Existence and multiplicity of normalized solutions for a class of fractional Choquard equations

In this paper, we study the existence and multiplicity of solutions with a prescribed L2-norm for a class of nonlinear fractional Choquard equations in RN:(-△)su-λu =(κα*|u|p)|u|p-2u,where N≥3,s∈(0,1),α∈(0,N),p∈(max{1 +(α+2s)/N,2},(N+α)/(N-2s)) and κα(x)=|x|α-N. To get such solutions,we look for critical points of the energy functional I(u) =1/2∫RN|(-△)s/2u|2-1/(2p)∫RN(κα*|u|p)|u|p on the constraints S(c)={u∈Hs(RN):‖u‖L2(RN)2=c},c >0.For the value p∈(max{1+(α+2s)/N,2},(N+α)/(N-2s)) considered, the functional I is unbounded from below on S(c). By using the constrained minimization method on a suitable submanifold of S(c), we prove that for any c>0, I has a critical point on S(c) with the least energy among all critical points of I restricted on S(c). After that,we describe a limiting behavior of the constrained critical point as c vanishes and tends to infinity. Moreover,by using a minimax procedure, we prove that for any c>0, there are infinitely many radial critical points of I restricted on S(c).

The Cauchy Problem for the Generalized Korteweg-de Vries-Benjamin-Ono Equation with Low Regularity Data

The Cauchy problem of the generalized Korteweg-de Vries-Benjamin-Ono equation is considered, and low regularity and limit behavior of the solutions are obtained. For k = 1, local well- posedness is obtained for data in H^s（R）（s 〉 -3/4）. For k = 2, local result for data in H^S（R）（s 〉1/4） is obtained. For k = 3, local result for data in H^S（R）（s 〉 -1/6） is obtained. Moreover, the solutions of generalized Korteweg-de Vries-Benjamin-Ono equation converge to the solutions of KdV equation if the term of Benjamin-Ono equation tends to zero.

A NONLOCAL NONLINEAR BOUNDARYVALUE PROBLEM FOR THE HEAT EQUATIONS

The existence and limit behaviour of the solution for a kind of nonlocal nonlinear boundaryvalue condition on a part of the boundary is studied for the heat equation, which physicallymeans that the potential is the function of the total flux. When this part of boundary shrinksto a point in a certain wayt this condition either results in a Dirac measure or simply disappearsin the corresponding problem.

Uniform local well-posedness and inviscid limit for the Benjamin-Ono-Burgers equation

In this paper,we study the Cauchy problem for the Benjamin-Ono-Burgers equation ∂_(t)u−ϵ∂^(2)/_(x)u+H∂^(2)_(x)u+uu_(x)=0,where H denotes the Hilbert transform operator.We obtain that it is uniformly locally well-posed for small data in the refined Sobolev space H~σ(R)(σ■0),which is a subspace of L2(ℝ).It is worth noting that the low-frequency part of H~σ(R)is scaling critical,and thus the small data is necessary.The high-frequency part of H~σ(R)is equal to the Sobolev space Hσ(ℝ)(σ■0)and reduces to L2(ℝ).Furthermore,we also obtain its inviscid limit behavior in H~σ(R)(σ■0).