The notion of conformal infinity has a long history within the research in Einstein's theory of gravity. Today, "conformal infinity" is related with almost all other branches of research in general relativity, from quantisation procedures to abstract mathematical issues to numerical applications. This review article attempts to show how this concept gradually and inevitably evolved out of physi...

in this paper, construction rules of the root locus of a positive feedback system whose loop transfer function is not strictly proper have been investigated. the root locus method is being used since 1950. it is demonstrated that some of the steps in this technique are not general and for a positive feedback system whose loop transfer function is not strictly proper are not valid. to overcome t...

This is the expository paper on strong axioms of infinity and elementary embeddings origi;,ally to have been authored by Reinhardt and Solovay. It has been owed for some time and already cited with some frequency in the most recent set theoretical literature. However, for various reasons the paper did not appear in print far several years. The impetus for actual publication came from a series o...

This study describes the behavior of eight statistical programs (BMDP, EGRET, JMP, SAS, SPSS, STATA, STATISTIX and SYSTAT) when performing a logistic regression with a simulated data set that contains a numerical problem created by the presence of a cell value equal to zero. The programs respond in different ways to this problem. Most of them give a warning, although many simultaneously present...

This is the third paper in a series describing a numerical implementation of the conformal Einstein equation. This paper describes a scheme to calculate (three) dimensional data for the conformal field equations from a set of free functions. The actual implementation depends on the topology of the spacetime. We discuss the implementation and exemplary calculations for data leading to spacetimes...

Probability inequalities are. obtained for the supremum of a weighted empirical process indexed. by a Vapnik-Cervonenkis class C of sets. These inequalities are particularly useful under the assumption P(ufC E: C : P(C) < t D -? 0 as t -? o. They are used to obtain almost sure bounds on the rate of growth of the process as the sample size approaches infinity, to find an asymptotic sample modulu...

We study a heavy piston of mass M that separates finitely many ideal, unit mass gas particles moving in two or three dimensions. Neishtadt and Sinai previously determined a method for finding this system’s averaged equation and showed that its solutions oscillate periodically. Using averaging techniques, we prove that the actual motions of the piston converge in probability to the predicted ave...

1. Approximations of arbitrarily large but finite systems are often mistaken for infinite idealizations in statistical and thermal physics. The problem is illustrated by thermodynamically reversible processes. They are approximations of processes requiring arbitrarily long, but finite times to complete, not processes requiring an actual infinity of time. 2. The present debate over whether phase...