In this paper,we study the following pseudo-relativistic Hartree equation i∂_(t)Ψ-(|x|^(-1)*|Ψ|^(2))Ψwith(t,x)∈R×R^(3)We mainly focus on the normalized ground state solitary waves of the formΨ(t,x)=e^(itμ)...In this paper,we study the following pseudo-relativistic Hartree equation i∂_(t)Ψ-(|x|^(-1)*|Ψ|^(2))Ψwith(t,x)∈R×R^(3)We mainly focus on the normalized ground state solitary waves of the formΨ(t,x)=e^(itμ)φm(x)with||φm||_(2)^(2)=N.We investigate limit behaviors of energy and minimizer of the corresponding frinetional of this equationas m→+∞.We prove that m_(k)^(-3/2)φm_(k)→φ∞(x)in H^(-1/2(R^(3)))by energy method and lim_(m→+∞)+m^(-1)e(N)=e(N),whereφ_(m)(β∞)is a minimizer of e(N)(e(N).展开更多
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...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.展开更多
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 quantu...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.展开更多
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*,th...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.展开更多
We discuss the spatial limit of the quasi-local mass for certain ellipsoids in an asymptotically flat static spherically symmetric spacetime.These ellipsoids are not nearly round but they are of interest as an admissi...We discuss the spatial limit of the quasi-local mass for certain ellipsoids in an asymptotically flat static spherically symmetric spacetime.These ellipsoids are not nearly round but they are of interest as an admissible parametrized foliation defining the Arnowitt–Deser–Misner mass.The Hawking mass of this family of ellipsoids tends to-∞.In contrast,we show that the Hayward mass converges to a finite value.Moreover,a positive mass type theorem is established.The limit of the mass has a uniform positive lower bound no matter how oblate these ellipsoids are.This result could be extended for asymptotically Schwarzschild manifolds.And numerical simulation in the Schwarzschild spacetime illustrates that the Hayward mass is monotonically increasing near infinity.展开更多
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...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.展开更多
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...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.展开更多
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 Fourie...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.展开更多
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 li...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.展开更多
In this paper, we establish the following limiting weak-type behaviors of Littlewood-Paley g-function g_φ: for nonnegative function f∈ L^1(R^n),■and ■where f_t(x) =t^(-n)f(t^(-1) x) for t > 0. Meanwhile, the co...In this paper, we establish the following limiting weak-type behaviors of Littlewood-Paley g-function g_φ: for nonnegative function f∈ L^1(R^n),■and ■where f_t(x) =t^(-n)f(t^(-1) x) for t > 0. Meanwhile, the corresponding results for Marcinkiewicz integral and its fractional version with kernels satisfying L_α~q-Dini condition are also given.展开更多
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 t...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.展开更多
An electrically conducting fluid is driven by a stretching sheet, in the presence of a magnetic field that is strong enough to produce significant Hall current. The sheet is porous, allowing mass transfer through suct...An electrically conducting fluid is driven by a stretching sheet, in the presence of a magnetic field that is strong enough to produce significant Hall current. The sheet is porous, allowing mass transfer through suction or injection. The limiting behavior of the flow is studied, as the magnetic field strength grows indefinitely. The flow variables are properly scaled, and uniformly valid asymptotic expansions of the velocity components are obtained through parameter straining. The leading order approximations show sinusoidal behavior that is decaying exponentially, as we move away from the surface. The two-term expansions of the surface shear stress components, as well as the far field inflow speed, compare well with the corresponding finite difference solutions;even at moderate magnetic fields.展开更多
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-dimens...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 →+∞.展开更多
We consider the limiting property of the distribution function of L^p function at endpoints 0 and ∞ and prove that for λ 〉 0 the following two equations limλ→＋∞λ^p（{x ： ｜f（x）｜ 〉 λ}） = 0, limλ→0＋λ^...We consider the limiting property of the distribution function of L^p function at endpoints 0 and ∞ and prove that for λ 〉 0 the following two equations limλ→＋∞λ^p（{x ： ｜f（x）｜ 〉 λ}） = 0, limλ→0＋λ^p（{x ： ｜f（x）｜ 〉 λ}） = 0hold for f ∈ L^p（Rn） with 1 ≤ p 〈 ∞. This result is naturally applied to many operators of type（p, q） as well.展开更多
This paper presents the results of four partially prestressed ultra-high strength concrete beams in flexure. The test results are used to evaluate the effects of prestressing tendon depth and area on flexure behavior ...This paper presents the results of four partially prestressed ultra-high strength concrete beams in flexure. The test results are used to evaluate the effects of prestressing tendon depth and area on flexure behavior of specimen beams. The test results indicate that: the cracking load,yielding load,peak load and stiffness postcracking of specimen beams are enhanced by reducing prestressing tendon depth or increasing prestressing tendon area, and the flexural ductility is improved by increasing prestressing tendon depth or reducing prestressing tendon area. The effect of complex reinforcement index considering the strength of the equivalence principle and the reinforcement position on loading levels under serviceability limit state,flexural strength and displacement ductility factor are studied. The influence coefficient of prestressing tendon kpis introduced in the complex reinforcement index. As the complex reinforcement index increases, the loading levels under serviceability limit state and flexural strength increases linearly,and the displacement ductility factor decreases linearly. The test results also verify the conventional beam flexural theory based on the plane cross-section assumption for predicting ultimate flexural strength of partially prestressed ultra-high strength concrete beams is valid. After the introduction of the coefficient kp,the calculation method of cracks in code for design of concrete structure in china are appropriated for the specimen beams.展开更多
文摘In this paper,we study the following pseudo-relativistic Hartree equation i∂_(t)Ψ-(|x|^(-1)*|Ψ|^(2))Ψwith(t,x)∈R×R^(3)We mainly focus on the normalized ground state solitary waves of the formΨ(t,x)=e^(itμ)φm(x)with||φm||_(2)^(2)=N.We investigate limit behaviors of energy and minimizer of the corresponding frinetional of this equationas m→+∞.We prove that m_(k)^(-3/2)φm_(k)→φ∞(x)in H^(-1/2(R^(3)))by energy method and lim_(m→+∞)+m^(-1)e(N)=e(N),whereφ_(m)(β∞)is a minimizer of e(N)(e(N).
基金This work was supported by the National Natural Science Foundation of China （No. 61374084）.
文摘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.
基金Project supported by the National Natural Science Foundation of China (Grant No. 11105133)
文摘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.
基金supported by NSFC(12075102 and 11971212)the Fundamental Research Funds for the Central Universities(lzujbky-2020-pd01)。
文摘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.
基金partially supported by the Natural Science Foundation of Hunan Province(Grant 2018JJ2073)partially supported by the National Natural Science Foundation of China(Grant 11671089).
文摘We discuss the spatial limit of the quasi-local mass for certain ellipsoids in an asymptotically flat static spherically symmetric spacetime.These ellipsoids are not nearly round but they are of interest as an admissible parametrized foliation defining the Arnowitt–Deser–Misner mass.The Hawking mass of this family of ellipsoids tends to-∞.In contrast,we show that the Hayward mass converges to a finite value.Moreover,a positive mass type theorem is established.The limit of the mass has a uniform positive lower bound no matter how oblate these ellipsoids are.This result could be extended for asymptotically Schwarzschild manifolds.And numerical simulation in the Schwarzschild spacetime illustrates that the Hayward mass is monotonically increasing near infinity.
基金supported in part by National Natural Science Foundation of China (GrantNos. 11001022 and 11071240)supported in part by National Natural Science Foundation of China(Grant Nos. 10801102,11171241 and 11071177)
文摘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.
基金supported in part by National NaturalScience Foundation of China!196610O3
文摘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.
基金partial supported by the National Natural Science Foundation of China(Grant Nos.71774073,71988101)Social Scienceof Jiangxi Provincial(Grant No.20YJ02)+1 种基金Natural Science Foundation of Jiangxi Provincial(Grant No.20171BAA208019)partial supported by Jiangxi Provincial Department of Education Science and Technology Research Project(GJJ213110)。
文摘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.
基金Supported by National Science Foundation of China (11071177)Excellent Youth Foundation of Sichuan Province (2012JQ0011)
文摘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.
文摘In this paper, we establish the following limiting weak-type behaviors of Littlewood-Paley g-function g_φ: for nonnegative function f∈ L^1(R^n),■and ■where f_t(x) =t^(-n)f(t^(-1) x) for t > 0. Meanwhile, the corresponding results for Marcinkiewicz integral and its fractional version with kernels satisfying L_α~q-Dini condition are also given.
基金This work was supported by the National Natural Science Foundation of China(10671188)and Special Foundation of USTC.
文摘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.
文摘An electrically conducting fluid is driven by a stretching sheet, in the presence of a magnetic field that is strong enough to produce significant Hall current. The sheet is porous, allowing mass transfer through suction or injection. The limiting behavior of the flow is studied, as the magnetic field strength grows indefinitely. The flow variables are properly scaled, and uniformly valid asymptotic expansions of the velocity components are obtained through parameter straining. The leading order approximations show sinusoidal behavior that is decaying exponentially, as we move away from the surface. The two-term expansions of the surface shear stress components, as well as the far field inflow speed, compare well with the corresponding finite difference solutions;even at moderate magnetic fields.
文摘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 →+∞.
基金Supported by the National Natural Science Foundation of China(Grant Nos.114713091127116211561062)
文摘We consider the limiting property of the distribution function of L^p function at endpoints 0 and ∞ and prove that for λ 〉 0 the following two equations limλ→＋∞λ^p（{x ： ｜f（x）｜ 〉 λ}） = 0, limλ→0＋λ^p（{x ： ｜f（x）｜ 〉 λ}） = 0hold for f ∈ L^p（Rn） with 1 ≤ p 〈 ∞. This result is naturally applied to many operators of type（p, q） as well.
基金Sponsored by the National Natural Science Foundation of China(Grant No.50878037,51078059,51178078)
文摘This paper presents the results of four partially prestressed ultra-high strength concrete beams in flexure. The test results are used to evaluate the effects of prestressing tendon depth and area on flexure behavior of specimen beams. The test results indicate that: the cracking load,yielding load,peak load and stiffness postcracking of specimen beams are enhanced by reducing prestressing tendon depth or increasing prestressing tendon area, and the flexural ductility is improved by increasing prestressing tendon depth or reducing prestressing tendon area. The effect of complex reinforcement index considering the strength of the equivalence principle and the reinforcement position on loading levels under serviceability limit state,flexural strength and displacement ductility factor are studied. The influence coefficient of prestressing tendon kpis introduced in the complex reinforcement index. As the complex reinforcement index increases, the loading levels under serviceability limit state and flexural strength increases linearly,and the displacement ductility factor decreases linearly. The test results also verify the conventional beam flexural theory based on the plane cross-section assumption for predicting ultimate flexural strength of partially prestressed ultra-high strength concrete beams is valid. After the introduction of the coefficient kp,the calculation method of cracks in code for design of concrete structure in china are appropriated for the specimen beams.
