DY－刚体转动实验仪的结构及实验原理

本文介绍了ＤＹ－刚体转动实验仪结构，阐述了该实验仪的多功能实验原理。     

Alpha particle scattering in the rigid projectile approximation

We study elastic α-particle scattering offp,α-particle and¹²C targets at 17.9 GeV/c incident momentum in the rigid projectile approximation of the Glauber model. Differential and total cross-sections are computed and compared with the data. Reasonable agreement with the observed differential cross-sections is found for small momentum transfers but short-range dynamical correlations in the target will probably have to be taken into account to get better agreement at larger momentum transfers, particularly in the case of α-¹²C scattering.     

Rigid Particle and its Spin Revisited

The arguments by Pandres that the double valued spherical harmonics provide a basis for the irreducible spinor representation of the three dimensional rotation group are further developed and justified. The usual arguments against the inadmissibility of such functions, concerning hermiticity, orthogonality, behaviour under rotations, etc., are all shown to be related to the unsuitable choice of functions representing the states with opposite projections of angular momentum. By a correct choice of functions and definition of inner product those difficulties do not occur. And yet the orbital angular momentum in the ordinary configuration space can have integer eigenvalues only, for the reason which have roots in the nature of quantum mechanics in such space. The situation is different in the velocity space of the rigid particle, whose action contains a term with the extrinsic curvature.     

On Chaotic Dendrites

Chaotic, rigid and strongly rigid dendrites are studied. Sufficient conditions are shown which imply that a dendrite is chaotic. Constructions of chaotic dendrites are provided that satisfy some conditions related to rigidity.     

Rigid Scaffolds: Synthesis of 2,6-Bridged Piperazines with Functional Groups in all three Bridges

The activity of pharmacologically active compounds can be increased by presenting a drug in a defined conformation, which fits exactly into the binding pocket of its target. Herein, the piperazine scaffold was conformationally restricted by substituted C₂- or C₃-bridges across the 2- and 6-position. At first, a three-step, one-pot procedure was developed to obtain reproducibly piperazine-2,6-diones with various substituents at the N-atoms in high yields. Three strategies for bridging of piperazine-2,6-diones were pursued: 1. The bicyclic mixed ketals 8-benzyl-6-ethoxy-3-(4-methoxybenzyl)-6-(trimethylsilyloxy)-3,8-diazabicyclo[3.2.1]octane-2,4-diones were prepared by Dieckmann analogous cyclization of 2-(3,5-dioxopiperazin-2-yl)acetates. 2. Stepwise allylation, hydroboration and oxidation of piperazine-2,6-diones led to 3-(3,5-dioxopiperazin-2-yl)propionaldehydes. Whereas reaction of such an aldehyde with base provided the bicyclic alcohol 9-benzyl-6-hydroxy-3-(4-methoxybenzyl)-3,9-diazabicyclo[3.3.1]nonane-2,4-dione in only 10 % yield, the corresponding sulfinylimines reacted with base to give N-(2,4-dioxo-3,9-diazabicyclo[3.3.1]nonan-6-yl)-2-methylpropane-2-sulfinamides in >66 % yield. 3. Transformation of a piperazine-2,6-dione with 1,4-dibromobut-2-ene and 3-halo-2-halomethylprop-1-enes provided 3,8-diazabicyclo[3.2.1]octane-2,4-dione and 3,9-diazabicyclo[3.3.1]nonane-2,4-dione with a vinyl group at the C₂- or a methylene group at the C₃-bridge, respectively. Since bridging via sulfinylimines and the one-pot bridging with 3-bromo-2-bromomethylprop-1-ene gave promising yields, these strategies will be exploited for the synthesis of novel receptor ligands bearing various substituents in a defined orientation at the carbon bridge     

2010年全国研究生数模竞赛D题的评阅综述

2010年全国研究生数学建模竞赛D题的素材取自一项科研项目.将本题建为何种模型取决于建模人的数学基础和对本题描述运动过程的认识深度.评述介绍了三种建模思路:刚体平面运动模型,最优控制模型和微分方程模型,其中微分方程模型是在阅卷过程中从考生答卷中发现的,从答卷中发现了不少有共性的毛病,反应出国内大学和研究生数学教育中的弊病,值得有识之士们重视.     

Hilbertian Jamison sequences and rigid dynamical systems

A strictly increasing sequence (nk)_k?0 of positive integers is said to be a Hilbertian Jamison sequence if for any bounded operator T on a separable Hilbert space such that supk?0‖Tnk‖<+∞, the set of eigenvalues of modulus 1 of T is at most countable. We first give a complete characterization of such sequences. We then turn to the study of rigidity sequences (nk)_k?0 for weakly mixing dynamical systems on measure spaces, and give various conditions, some of which are closely related to the Jamison condition, for a sequence to be a rigidity sequence. We obtain on our way a complete characterization of topological rigidity and uniform rigidity sequences for linear dynamical systems, and we construct in this framework examples of dynamical systems which are both weakly mixing in the measure-theoretic sense and uniformly rigid.     

激光空泡在刚性壁面附近空蚀特性

采用脉冲激光聚焦于透明液体中产生单个激光空泡,利用高速相机拍摄空泡在透明液体中整个运动过程,并对刚性壁面造成的空蚀现象进行了观测.实验研究发现,空泡溃灭将产生高速冲击波和高速射流,这是造成刚性壁面损伤的两种主要原因.空泡与刚性壁面的无量纲距离在0.4～1.4之同时,刚性壁面首先受到高速冲击波的破坏,由于空泡的趋壁效应,空泡在第二次收缩过程中将在壁面附近对实验靶材产生高速微射流的空蚀破坏.且这两种作用机制在无量纲距离为1.0时,高速微射流对壁面的空蚀效果更加明显.     

On Support τ-tilting Modules over Endomorphism Algebras of Rigid Ob jects

We consider a Krull–Schmidt, Hom-finite, 2-Calabi–Yau triangulated category with a basic rigid object T, and show a bijection between the set of isomorphism classes of basic rigid objects in the finite presented category pr T of T and the set of isomorphism classes of basic τ-rigid pairs in the module category of the endomorphism algebra End C(T)op. As a consequence, basic maximal objects in pr T are one-to-one correspondence to basic support τ-tilting modules over End C(T)op. This is a generalization of correspondences established by Adachi–Iyama–Reiten.