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.

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.

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.

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.

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.

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.

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.

LIMITING WEAK-TYPE BEHAVIORS FOR CERTAIN LITTLEWOOD-PALEY FUNCTIONS

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.

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.

On limit behavior of quasi-local mass for ellipsoids at spatial infinity

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.

My Limiting Behavior of MHD Flow with Hall Current, Due to a Porous Stretching Sheet

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.

企业数据的知识产权保护

企业数据和知识产权的客体之间存有共性。二者的保护基础理论相互融通,并且企业数据权利与知识产权权利结构相近似,这为企业数据的知识产权保护奠定了基础。检视现有知识产权制度框架下保护模式的有限性以识别现有制度与企业数据保护问题之间真正无法重合的地带。构建和完善企业数据保护规则须对企业数据进行类型化结构,基于类型化区分和场景化差异探寻不同保护路径。从解释论角度而言,对于无法纳入既有法定权利范畴的企业数据权益,适用《反不正当竞争法》一般条款规制未被类型化权益,关键在于客观审查数据使用行为是否违反商业道德。从立法论角度而言,可参照知识产权的行为规制赋权化路径,将规制焦点建立在对企业数据的利用行为上,对利用行为进行类型化提炼,建构一种以禁止权和报酬权为核心的不完满的控制权和有限度的排他权。

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.

政府参与下考虑有限注意力的CCUS项目股权投资决策分析

碳捕获、利用与封存(carbon capture, utilization and storage, CCUS)项目的规模化需要风险资本支撑,然而气候政策与项目研发的不确定性造成注意力有限的风险投资机构投资意愿较低。为打破“能源企业不改造,风险投资机构不投资”的“囚徒困境”,本文基于投资方的注意力驱动交易行为构建了能源企业-风险投资机构-政府的演化博弈模型,从政策的“显著性”事件特征入手探讨政府在CCUS项目推广中的激励作用。结果表明:(1)向风险投资机构传递“显眼”信息的政府政策有助于打破当前融资困境;(2)三方参与概率高于30%即可实现CCUS项目股权投资的帕累托最优,且概率越高,演化速度越快;(3)政府实施的补贴和风险分担机制对融资的促进作用均显著,但初期风险分担机制因无法呈现“显著性”特征而难以吸引投资方注意力,效果弱于补贴机制。鉴于此,本文从引导多主体参与,建立信息披露机制,完善政府激励机制和提高碳资产管理效率等方面提出建议,以期为加快CCUS项目商业化提供理论借鉴。

消极情绪对学前儿童问题行为的影响:父母严厉管教的中介作用

本研究以358名学步儿为被试,探讨儿童早期不同消极情绪表现是否会通过父母严厉管教影响学前期的问题行为。结果显示:(1)母亲严厉管教在受限后沮丧和学前儿童外化问题行为之间起部分中介作用,即受限后沮丧不仅直接正向预测外化问题行为,还会通过母亲严厉管教影响外化问题行为。(2)恐惧对学前儿童内化问题行为的直接作用显著,但父母严厉管教在其中的中介作用不显著。研究结果揭示了早期受限后沮丧和恐惧对学前期问题行为的作用机制存在差异。

TA2/Q235B复合板不同作用面成形极限及界面损伤行为

采用Nakazima实验法对不同尺寸的退火态TA2/Q235B复合板样品进行胀形实验,研究不同作用面对TA2/Q235B复合板的成形极限和界面损伤行为的影响。结果表明,当凹模与碳钢侧接触时,由于接触材料、界面变形协调能力和应变状态的不同,复合板的胀形高度和成形极限增加,其中R140试样的极限拱高达到最大值(46.17 mm),R60和R180试样在3个方向上的厚度减薄量和界面裂纹更大。此外,由于硬度和拉应力不同,两组样品中所有的水平和斜向孔都向纯钛侧延伸。

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 →+∞.

公共场所犯罪向元宇宙空间的拓展研究

公共场所犯罪系刑法中极少数以“犯罪空间”决定“罪与非罪”“罪轻罪重”的犯罪类别,当元宇宙划时代地为人类打造出一个虚实共生的“桃花源”时,新型犯罪空间也随之生成。有别于传统网络空间的扁平化与局限性,元宇宙以立体式和沉浸式的样态予以展现,通过公共场所犯罪中危害行为的异化,元宇宙复刻了在现实空间中实施同等犯罪行为所侵害的法益之效果,由此为公共场所犯罪向其拓展的留白。这种拓展不仅存在于个罪中,在整个公共场所犯罪体系中均有体现。但允许拓展的同时,还需保持刑事法网扩张的克制,明确拓展之限度,从而维护好社会秩序与公众自由的价值平衡。

选区激光熔化成形钛合金薄壁件热行为及打印极限高度研究

为了研究钛合金薄壁件在选区激光熔化工艺下的热行为及工艺参数对打印极限高度的影响,采用理论建模、模拟仿真和正交试验法等手段开展了钛合金薄壁件在复杂热循环作用下的热行为及打印极限高度研究。分别从单层单道、单层多道和多层单道展开研究。模拟结果表明,对于单层单道成形,当激光束从节点N1移动到节点N3时,熔池峰值温度和最大冷却速率逐渐增加;对于单层多道成形,当激光束从第1道扫描至第3道时,熔池尺寸和熔池峰值温度呈递增趋势;对于多层单道成形,当激光束从第1层扫描至第5层时,熔池尺寸呈递增趋势。试验结果表明,打印极限高度与激光功率成正相关,与扫描速度呈负相关,随着扫描间距的增加先增加后减小,且与激光能量密度呈线性增长趋势。

基于资源有限的反捕食生态模型的分支分析

农业害虫的爆发往往都伴随着控制资源的有限,借助Hill函数来刻画有限的农业资源,在此基础上发展了一类具有反捕食行为的害虫-天敌治理模型。首先研究了系统害虫灭绝周期解的存在性和全局稳定性。同时从数值上研究了系统的分支现象,研究发现:有限的资源可导致系统的动力学行为变得极为复杂,这给害虫治理带来了极大的挑战。