用Coulomb爆炸实测4HeD＋的键长

用1.468 0 MeV ⁴HeD^＋在超薄无衬碳膜中的Coulomb爆炸,获得⁴HeD^＋的键长实测值为(0.097±0.003)nm.讨论了⁴HeD^＋的形成机理.介绍了⁴HeD^＋原始束中D₃＋污染的降低,及产物⁴HeD^＋＋和D^＋高分辨能谱测量中的粒子鉴别方法等.     

范畴 RMRl上的一个函子及范畴A Grn0

本文定义了一个由范畴 _RM_R^l到范畴Ａ G_rn⁰ 的函子Ｇ，并证明了函子Ｇ保持分量正合及全正合，关于范畴ＡＧG_rn⁰ 证明了定理：     

d8(C3v*)EPR理论与CsMgCl3:Ni2+的光、磁性质研究

本文给出了O_h点群表象中的d^2,8(C_3v^*)完全强场矩阵,并借助于这种矩阵的特征值和特征矢量,建立了CsMgX₃:Ni²⁺(X=Cl,B,I)类晶体的全组态混合EPR理论。应用这一理论,对CsMgCl₃晶体中的Ni²⁺杂质离子的光学吸收谱、基态零场分裂参量D、顺磁g因数、基态Zeeman分裂以及EPR条件(B,hv₀)进行了统一的计算。结果与观测非常一致,从而首次对CsMgCl₃:Ni²⁺的光、磁性质作出了统一的理论解释。     

函数空间以及一类奇异积分算子在Hr(Rn)(p＜r≤1)中有界性的准则

在经典H^p(Rⁿ)空间原子分解理论基础上,给出了一种H^p(Rⁿ)空间的新的更为精细的刻划,籍此,给出了一类异奇积分算子在所有H^r(Rⁿ)(p＜r≤1)中有界性的准则     

在e+e-湮灭中粲介子产额的计算

根据文献[1]提出的在e⁺e^-湮灭中夸克产生与组合规律,本文计算了在e⁺e^-湮灭中各种粲介子的产额,计算结果同实验相符,这表明我们对e⁺e^-湮灭为强子所采用的机制是合理的。     

有界对称域上的Dp乘子

设Ω是Cⁿ中包含原点的有界对称域。本文在Ω上得到了关于D^p空间的两个乘子定理。     

关于Pn3的优美性

设G(V,E)是一个简单图,对自然数k,当V(G^k)=V(G,E(G^k)=E(G)∪{uv|d(u,v)=k},则称图G^k为k-次方图,本文证明了图P_n³的优美性。     

SL(2,R)上一类极大算子的(H∞,s1,L1)型

本文我们引入了函数类B_δ(G//K)={φ∈L¹(G//K)||φ(t)|≤Δ^-1(t)(1+t)^1-δ,δ>0),对f∈L^p(G//K),1≤p≤∞,和极大算子(?),证明了这类算子是(H_∞,s¹,L¹)型的.     

相伴于平方根算子的Hp空间

本文利用椭圆算子的平方根所生成的热核给出了H^p空间的极大函数刻画。     

具有常余维数2k+4不动点集的(Z2)k作用

本文通过构造上协边环MO_*的一组生成元决定了J_*,k^2k+4.     

L6 BOUND FOR BOLTZMANN DIFFUSIVE LIMIT

We consider diffusive limit of the Boltzmann equation in a periodic box. We establish L⁶ estimate for the hydrodynamic part Pf of particle distribution function, which leads to uniform bounds global in time.     

基础R0-代数的性质及在L*系统中的应用

研究了王国俊教授建立的模糊命题演算的形式演绎系统L^*和与之在语义上相关的R₀-代数,提出了基础R₀-代数的观点并讨论了其中的一些性质,在将L^*系统中的推演证明转化为相应的R₀-代数中的代数运算方面作了一些尝试,作为它的一个应用,证明了L^*系统中的模糊演绎定理。     

Existence, uniqueness and stability of C m solutions of iterative functional equations

In this paper we discuss a relatively general kind of iterative functional equation G(x,f(x), ...,f ⁿ (x)) = 0 (for allx ∈J), whereJ is a connected closed subset of the real number axis ℝ,G∈C ^m (J ⁿ⁺¹, ℝ) andn ≥ 2. Using the method of approximating fixed points by small shift of maps, choosing suitable metrics on functional spaces and finding a relation between uniqueness and stability of fixed points of maps of general spaces, we prove the existence, uniqueness and stability ofCm solutions of the above equation for any integer m ≥ 0 under relatively weak conditions, and generalize related results in reference in different aspects.     

与高阶抛物型Schrodinger算子相关的Riesz变换的L^p估计——献给陆善镇教授75华诞

令δ/δt＋（-△）^2＋V^2为R^n＋1（n≥5）上的高阶抛物型Schrodinger算子,其中非负位势V与时间t无关且属于逆Holder类Bq1（Rn）（q1〉n/2）.本文得到与高阶抛物型Schrodinger算子相关的Riesz变换▽^2（δ/δt＋（-△）^2＋V^2）^-1/2的L^p（R^n＋1）估计.     

The diophantine equation x3 + 3y3 = 2n

It is proved that the equation of the title has a finite number of integral solutions (x, y, n) and necessary conditions are given for (x, y, n) in order that it can be a solution (Theorem 2). It is also proved that for a given odd x₀ there is at most one integral solution (y, n), n ≥ 3, to x₀³ + 3y³ = 2ⁿ and for a given odd y₀ there is at most one integral solution (x, n), n ≥ 3, to x³ + 3y₀³ = 2ⁿ.     

On x3 + y3 = D

The simplest case of Fermat's last theorem, the impossibility of solving x³ + y³ = z³ in nonzero integers, has been proved. In other words, 1 is not expressible as a sum of two cubes of rational numbers. However, the slightly extended problem, in which integers D are expressible as a sum of two cubes of rational numbers, is unsolved. There is the conjecture (based on work of Birch, Swinnerton-Dyer, and Stephens) that x³ + y³ = D is solvable in the rational numbers for all square-free positive integers D ≡ 4 (mod 9). The condition that D should be square-free is necessary. As an example, it is shown near the end of this paper that x³ + y³ = 4 has no solutions in the rational numbers. The remainder of this paper is concerned with the proof published by the first author (Proc. Nat. Acad. Sci. USA., 1963) entitled “Remarks on a conjecture of C. L. Siegel.” This pointed out an error in a statement of Siegel that the diophantine equation ax³ + bx²y + cxy² + dy³ = n has a bounded number of integer solutions for fixed a, b, c, d, and, further, that the bound is independent of a, b, c, d, and n. However, x³ + y³ = n already has an unbounded number of solutions. The paper of S. Chowla itself contains an error or at least an omission. This can be rectified by quoting a theorem of E. Lutz.     

ltivariate Hausdorff operators on the spaces H1(Rn) and BMO(Rn)

Summary A multivariate Hausdorff operator H = H(, c, A) is defined in terms of a -finite Borel measure on Rⁿ, a Borel measurable function c on Rⁿ, and an n × n matrix A whose entries are Borel measurable functions on rⁿ and such that A is nonsingular -a.e. The operator H*:= H (, c | det A^-1|, A^-1) is the adjoint to H in a well-defined sense. Our goal is to prove sufficient conditions for the boundedness of these operators on the real Hardy space H¹(Rⁿ) and BMO (Rⁿ). Our main tool is proving commuting relations among H, H*, and the Riesz transforms R_j. We also prove commuting relations among H, H*, and the Fourier transform.     

The quadratic form x2−2py2

Using known properties of continued fractions, we give a very simple and elementary proof of the theorem of Epstein and Rédei on the impossibility in a certain case of representing ?1 by the quadratic form x² ? 2py². Two of our theorems, which concern the representation of a² and ?2a², serve to extend our method to an unknown case in which ?1 is not representable.