A chain condition for groups

A descending chain condition for groups definable in o-minimal structures

We prove that if G is a group definable in a saturated o-minimal structure, then G has no infinite descending chain of type-definable subgroups of bounded index. Equivalently, G has a smallest (necessarily normal) type-definable subgroup G of bounded index and G/G equipped with the “logic topology” is a compact Lie group. These results give partial answers to some conjectures of the fourth auth...

A COMMUTATIVITY CONDITION FOR RINGS

In this paper, we use the structure theory to prove an analog to a well-known theorem of Herstein as follows: Let R be a ring with center C such that for all x,y ? R either [x,y]= 0 or x-x [x,y]? C for some non negative integer n= n(x,y) dependingon x and y. Then R is commutative.

An Equicontinuity Condition for Transformation Groups

1. Definitions. These definitions are essentially those given by Gottschalk and Hedlund (cf. [3]).1 Let X be a topological space, T a topological group with identity e, and ir a mapping of X X T into X with the properties: (1) ir(x, e)=x, (2) 7r(7r(rc, h), t2)=ir(x, tit2), (3) ir is continuous. The triple (X, T, ir) is called a transformation group (or dynamical system). Henceforth we shall wri...

A Necessary Condition for Weyl-Heisenberg Frames

analysis of ruin probability for insurance companies using markov chain

در این پایان نامه نشان داده ایم که چگونه می توان مدل ریسک بیمه ای اسپیرر اندرسون را به کمک زنجیره های مارکوف تعریف کرد. سپس به کمک روش های آنالیز ماتریسی احتمال برشکستگی ، میزان مازاد در هنگام برشکستگی و میزان کسری بودجه در زمان وقوع برشکستگی را محاسبه کرده ایم. هدف ما در این پایان نامه بسیار محاسباتی و کاربردی تر از روش های است که در گذشته برای محاسبه این احتمال ارائه شده است. در ابتدا ما نشا...