Sobolev-Type Classes of Functions with Values in a Metric Space. II

We prove equivalence of the definitions by the author and by Korevaar and Schoen of the Sobolev classes of mappings of a domain of an arithmetic n-dimensional space to a metric space.     

Pearson-χ~2距离的若干性质

本文对数理统计中常用的 Pearson- χ2距离的分析特性进行了讨论 ,得到了这一距离的一些解析性质 ,最后我们还给出了几个常用距离的关系 .     

Fermi, Majorana and the Statistical Model of Atoms

We give an account of the appearance and first developments of the statistical model of atoms proposed by Thomas and Fermi, focusing on the main results achieved by Fermi and his group in Rome. Particular attention is addressed to the unknown contribution to this subject by Majorana, anticipating some important results reached later by leading physicists.     

Dimethylamino-substituted 7H-Benzo[de]pyrazolo[5,1-a]isoquinolin-7-ones and Their Behavior under Vilsmeier-Haack Conditions

The behavior of dimethylamino-substituted 7H-benzo[de]pyrazolo[5,1-a]isoquinoline-7-ones, synthesized for the first time, under conditions of the Vilsmeier-Haack reaction. It has been shown that, on heating with POCl₃ and DMF, they are converted by electrophilic substitution at the position ortho to the dimethylamino group, followed by cyclization of the iminium adduct to a quinazolinium salt. When an acetyl group is present, the Arnold reaction, leading to the formation of a chloroaryl, accompanies the heterocyclization. The rates and proportion of the reaction products depend on the position of the dimethyl groups relative to the pyrazole ring.     

Partially Classical States of a Boson Field

Employing positive-definiteness arguments we analyse Boson field states, which combine classical and quantum mechanical features (signal and noise), in a constructive manner. Mathematically, they constitute Bauer simplexes within the convex, weak-*-compact state space of the C*-Weyl algebra, defined by a presymplectic test function space (smooth one-Boson wave functions) and are affinely homeomorphic to a state space of a classical field. The regular elements are expressed in terms of weak distributions (probability premeasures) on the dual test function space. The Bauer simplex arising from the bare vacuum is shown to generalize the quantum optical photon field states with positive P-functions.     

双光束相干控制产生多次谐波的实验验证

利用两束相干度可改变的飞秒脉冲光对产生的五次谐波的强度特性进行了研究，发现谐波信号的强度随相干程度的增大而增加，谐波信号的最大值相对于相干零点(双光束相干度最大处)是非对称的，从而证明了合成的激光脉冲波形变化对谐波信号的影响.同时对谐波的受激放大理论进行了初步的实验探索和展望. 关键词： 五次谐波 波形变化 相干 受激放大     

标度系统一致性矩阵容量的计算方法

本文研究正互反矩阵的变换性质 ,提出一种保持正互反矩阵一致性程度的等价分类 ,为计算各种标度系统下的一致矩阵容量提供了计算方法     

Letter: Note on Invariants of the Weyl Tensor

Algebraically special gravitational fields are described using algebraic and differential invariants of the Weyl tensor. A type III invariant is also given and calculated for Robinson-Trautman spaces.     

水力机械内鲤鱼草鱼的压力损伤模拟试验

通过试验人工模拟水力机械内压力变化过程,测量压力时间变化,观察并解剖分析不同压力变化过程对鲤鱼和草鱼造成损伤的情况。试验发现,负压状态下的压力变化过程会对鱼的生存构成直接威胁,并得到了新型环保水力机械设计中应采用的压力时变导数极限值。