低温下铁磁和反铁磁体系的运动学相互作用

我们发展了处理低温下铁磁和反铁磁运动学相互作用的一个新方法。所有运动学相互作用都能用各级关联函数来表示。应用热力学微扰理论,导得低温下s=1/2的铁磁体系的确没有T³项。对反铁磁体系,我们发现运动学相互作用即使在低温下也十分大,它甚至超过动力学相互作用的修正,我们的理论适用于s≥1/2的一切体系。     

双光子系统的波函数和偏振态

求出了双光子系统的所有的波函数,这些波函数所代表的态都有一定的角动量和宇称,并且有系统地分析了这些态中光子的偏振情况。指出了以前杨振宁、锡罗柯夫、夏比罗等的讨论中的缺点。     

在盐的水溶液中非电解质的活度系数的研究Ⅶ.无机盐对甲苯在水中溶度的影响

作者用分光光度计测定25℃下甲苯在十五种盐水溶液中的盐析常数k。所用的盐为:LiCl,NaCl,KCl,CsCl,NH₄Cl,NaF,NaBr,NaClO₃,NH₄Br,(CH₃)₄NBr,(C₂H₅)₄NBr,MgCl₂,CaCl₂,SrCl₂,BaCl₂₀在十五种盐中,只有两个溴化季铵盐对甲苯起盐溶作用,其余均起盐析作用。对于1-1价盐,k值的次序是NaF>NaCl>KCI>NaBr>NaClO₃>LiCl>NH₄Cl>CsCl>NH₄Br>(CH₃)₄NBr>(C₂H₅)₄NBr。这次序和一般非极性非电解质的盐析效应次序相同。定性地符合vanderWaals力理论,Dcbye-McAulay的静电理论以及McDevit和Long的内压力理论。对于2-1价盐,k值的次序是BaCl₂>SrCl₂>CaCl₂>MgCl₂₀即盐析效应随离子晶体半径的增加而上升。这次序和色散力理论的次序恰相反。但是,如果假设二价离子对水的静电作用能伸展到原水化层以外的水分子,并考虑水化离子和水的静电作用,以及它和甲苯的色散作用,以上四种盐的反常次序就得到解释。     

鋼中含氫所引起的内耗峯

钢的内部发裂已经公认为与钢中的氢气有关。现有的理论认为这是由于氢气聚集于钢中的内部缺陷产生破裂压力所引起,然而关于缺陷的性质和引起内部发裂的详细机构迄今还没有明确的了解。本文尝试用内耗测量的方法来研究这个问题。初步实验的结果指出:(1)氢在钢中可以引起内耗峰(将内耗表示为测量温度的函数时);(2)轻微冷加工或保温对于内耗峰的颠值温度有着显著的影响,这表示所得的内耗峰与钢中的缺陷和应力状态有关系;(3)所得的内耗峰表现有反常的振幅效应,即在一定的观测温度时,如将内耗表示为外加应力的函数,则也得到一个内耗峰。这与本文作者之一以前在铝铜合金中所观测到的反常内耗峰的性质和表现相同,因而所得的内耗峰可能是由于氢与钢中的原子脱节的交互作用所引起来的。     

Variations on a Proof of a Borderline Bourgain-Brezis Sobolev Embedding Theorem

This paper offers a variant of a proof of a borderline Bourgain-Brezis Sobolev embedding theorem on R~n. The authors use this idea to extend the result to real hyperbolic spaces H~n.     

Approximation in higher-order Sobolev spaces and Hodge systems

Let $d\ge 2$ be an integer, $1\le l\le d?1$ and φ be a differential l-form on ${\mathbb{R}}^d$ with ${\dot{W}}^{1,d}$ coefficients. It was proved by Bourgain and Brezis ([5, Theorem 5]) that there exists a differential l-form ψ on ${\mathbb{R}}^d$ with coefficients in $L^{\infty }\cap {\dot{W}}^{1,d}$ such that $d\phi =d\psi$. In the same work, Bourgain and Brezis also left as an open problem the extension of this result to the case of differential forms with coefficients in the higher order space ${\dot{W}}^{2,d/2}$ or more generally in the fractional Sobolev spaces ${\dot{W}}^{s,p}$ with $sp=d$. We give a positive answer to this question, provided that $d?\kappa \le l\le d?1$, where κ is the largest positive integer such that $\kappa <\min ?(p,d)$. The proof relies on an approximation result (interesting in its own right) for functions in ${\dot{W}}^{s,p}$ by functions in ${\dot{W}}^{s,p}\cap L^{\infty }$, even though ${\dot{W}}^{s,p}$ does not embed into $L^{\infty }$ in this critical case. The proofs rely on some techniques due to Bourgain and Brezis but the context of higher order and/or fractional Sobolev spaces creates various difficulties and requires new ideas and methods.     

Polynomial Carleson Operators Along Monomial Curves in the Plane

We prove \(L^p\) bounds for partial polynomial Carleson operators along monomial curves \((t,t^m)\) in the plane \(\mathbb {R}^2\) with a phase polynomial consisting of a single monomial. These operators are “partial” in the sense that we consider linearizing stopping-time functions that depend on only one of the two ambient variables. A motivation for studying these partial operators is the curious feature that, despite their apparent limitations, for certain combinations of curve and phase, \(L^2\) bounds for partial operators along curves imply the full strength of the \(L^2\) bound for a one-dimensional Carleson operator, and for a quadratic Carleson operator.     

吸引费米体系多体微扰级数的收敛性

本文用泛函分析的方法,研究了吸引多费子体系中Wigner和Schr?dinger两种微扰级数的收敛性问题。发现这两种微扰级数的“收敛半径”是相同的,但是收敛与发散的速度是不相等的,我们提供了一个较有用的判据。