Fuzzy relation equations on a finite set

The family of all the solutions of a fuzzy relation equation on a finite set is considered. It is characterized by the set of all the lower solutions, which can be obtained by a combinatorial algorithm.     

Particle accelerator physics and technology for high energy density physics research

Interaction phenomena of intense ion- and laser radiation with matter have a large range of application in different fields of science, extending from basic research of plasma properties to applications in energy science, especially in inertial fusion. The heavy ion synchrotron at GSI now routinely delivers intense uranium beams that deposit about 1 kJ/g of specific energy in solid matter, e.g. solid lead. Our simulations show that the new accelerator complex FAIR (Facility for Antiproton and Ion Research) at GSI as well as beams from the CERN large hadron collider (LHC) will vastly extend the accessible parameter range for high energy density states. A natural example of hot dense plasma is provided by our neighbouring star the sun, and allows a deep insight into the physics of fusion, the properties of matter at high energy density, and is moreover an excellent laboratory for astroparticle physics. As such the sun's interior plasma can even be used to probe the existence of novel particles and dark matter candidates. We present an overview on recent results and developments of dense plasma physics addressed with heavy ion and laser beams combined with accelerator- and nuclear physics technology.     

Generalized frieze pattern determinants and higher angulations of polygons

Frieze patterns (in the sense of Conway and Coxeter) are in close connection to triangulations of polygons. Broline, Crowe and Isaacs have assigned a symmetric matrix to each polygon triangulation and computed the determinant. In this paper we consider d-angulations of polygons and generalize the combinatorial algorithm for computing the entries in the associated symmetric matrices; we compute their determinants and the Smith normal forms. It turns out that both are independent of the particular d  -angulation, the determinant is a power of d−1$d-1$, and the elementary divisors only take values d−1$d-1$ and 1. We also show that in the generalized frieze patterns obtained in our setting every adjacent 2×2$2\times 2$-determinant is 0 or 1, and we give a combinatorial criterion for when they are 1, which in the case d=3$d=3$ gives back the Conway–Coxeter condition on frieze patterns.     

Elementary and middle grade students’ constructions of typicality

This study addresses the measures chosen by students when selecting or constructing indices to properties of distributions of data. A series of individual teaching experiments were conducted to provide insight into the development of five 4th to 8th grade students’ conceptualizations of distribution over the course of 8 weeks of instruction. During the course of the teaching experiment (emergent) statistical tasks and analogous teacher activities were created and refined in an effort to support the development of understanding. In the process of development, attempts were made by students to coordinate center and variability when constructing measures to index properties of distributions. The results indicate that consideration of representativeness was a major factor that motivated modification of approaches to constructing indices of distributions, and subsequent coordination of indices of variation and center. In particular, the defining features of student's self-constructed “typical” values and notions of spread were examined, resulting in a model of development constituting eight “categories” ranging from the construction of values that did not reflect properties of the data (Category 1) to measures employing conceptual use of the mean in combination with other indices of center and spread (Category 8).     

Comparing material and structural set theories

We study elementary theories of well-pointed toposes and pretoposes, regarded as category-theoretic or “structural” set theories in the spirit of Lawvere's “Elementary Theory of the Category of Sets”. We consider weak intuitionistic and predicative theories of pretoposes, and we also propose category-theoretic versions of stronger axioms such as unbounded separation, replacement, and collection. Finally, we compare all of these theories formally to traditional membership-based or “material” set theories, using a version of the classical construction based on internal well-founded relations.     

AutoCAD与ANSYS接口设计

本文简介了如何运用AutoCAD的点元、线元、面元及文字的基本数据及其扩展数据描述结构计算模型,并利用Auto LISP、C语言、HP—GL绘图语言以及APDL语言建构AutoCAD与ANSYS的接口。运用此接口,用户可在AutoCAD中十分方便的建立ANSYS结构计算模型而无须撑握ANSYS的建模过程;用户也可对工程设计的三维图直接指定单元类型、材料参数、截面数据、施加荷载及约束条件,就可将其转化为ANSYS结构计算模型,这样充分利用了工程设计图的几何信息,提高了输入计算模型的效率;用户还可将ANSYS中图形转成AutoCAD中矢量图形,实现软件间数据共享。     

Catalyst-Oriented Design Based on Elementary Reactions (CODER) for Triarylamine Synthesis

Recently, the application of computational tools to the rational design of catalysts has received considerable attention, but progress has been limited by the reliance on databases and because mechanistic data have been almost neglected. Herein, we report a new strategy for catalyst design, designated c atalyst-o riented d esign based on e lementary r eactions (CODER), which fully utilizes mechanistic data, combines the strengths of computational tools and researcher experience. CODER enabled the development of extremely efficient Pd catalysts for C−N coupling, which markedly improved the efficiency of the synthesis of widely used triarylamine optoelectronic materials by enhancing the turnover numbers (up to 340000) to 1–3 orders of magnitude towards literature values.