Incoherent scattering of 59.5 keV gamma-rays by light,medium and heavy elements

Summary Total atomic incoherent-scattering differential cross-sections were determined experimentally for 59.5 keV gamma-rays in Ti, Ni, Zn, Se, Mo, Ru, Cd, Sn, Te, Yt, W and Pb at 120° scattering angle using Ge(Li) detector. The background correction and detection efficiency are also included in the study. The experimental values have been compared with those estimated on the basis of the non-relativistic Hartree-Fock wave functions. Good agreement is observed between theory and experiment.     

常曲率空间中具平行平均曲率向量的子流形

本文利用第二基本形式的长度平方和平均曲率的关系研究常曲率空间中具平行平均曲率向量的子流形为全脐的ｐｉｎｃｈｉｎｇ问题，获得了一定条件下的最佳ｐｉｎｃｈｉｎｇ区间，并确定了ｐｈｉｎｃｎｉｎｇ区间端点处对应非全脐子流形的分类．     

U(1)-invariant current forms

Let λ : U(1) → GL (V) be a linear representation. Lagrangians defined on J¹(T*M × V)whose universal current form is gauge invariant, are described in terms of gauge invariant Lagrangians and invariant functions on V. A characterization of gauge invariant Lagrangians depending on matter fields only, that is, L : J¹V → ?, is also obtained.     

非完整系统Hamilton正则方程的形式不变性

研究非完整系统Hamilton正则方程的形式不变性，给出形式不变性的定义和判据，建立形式不变性和系统守恒量之间的关系，并举例说明结果的应用. 关键词： 非完整系统 Hamilton正则方程 形式不变性 守恒量     

从对称矩阵代数到全矩阵代数的线性群逆保持

设F是一个特征不为2的域,Mn(F)和Sn(F)分别记F上的n×n全矩阵代数和对称矩阵代数.所有的从Sn(F)到Mn(F)的保群逆的线性映射被刻划,作为一个中间步骤,三个矩阵的同时相似标准形也被证明.这个标准形简化了从Sn(F)到Mn(F)的保群逆的线性映射的刻划.     

条件正定型与扩张

讨论条件正定型与扩张问题．得到了Pontrjagin空间上对称算子的扩张定理．     

单面完整约束力学系统的形式不变性

研究单面完整约束力学系统的形式不变性.根据运动微分方程的形式在无限小变换下的不变性，给出了单面完整约束力学系统形式不变性的定义和判据，建立了系统的形式不变性与Noether对称性、Lie对称性之间的关系，并举例说明结果的应用. 关键词： 分析力学 单面约束 形式不变性 Lie对称性 Noether对称性 守恒量     

Riesz Potentials and Liouville Operators on Fractals

An analogue to the theory of Riesz potentials and Liouville operators in R ⁿ for arbitrary fractal d-sets is developed. Corresponding function spaces agree with traces of Euclidean Besov spaces on fractals. By means of associated quadratic forms we construct strongly continuous semigroups with Liouville operators as infinitesimal generator. The case of Dirichlet forms is discussed separately. As an example of related pseudodifferential equations the fractional heat-type equation is solved.     

Derivatives of Dedekind sums and their reciprocity law

In this paper derivatives of Dedekind sums are defined, and their reciprocity laws are proved. They are obtained from values at non-positive integers of the first derivatives of Barnes’ double zeta functions. As special cases, they give finite product expressions of the Stirling modular form and the double gamma function at positive rational numbers.     

The Hilbert–Carathéodory Form for Parametric Multiple Integral Problems in the Calculus of Variations

We define, and discuss some properties of, a form which bears a relation to the Carathéodory form for multiple integral problems in the calculus of variations similar to the relation that the Hilbert 1-form of Finsler geometry bears to the Poincaré–Cartan form for one-dimensional variational problems.