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## Strict measure rigidity for unipotent subgroups of solvable groups

### Inventiones mathematicae (1990-12-01) 101: 449-482 , December 01, 1990

## An application of number theory to ergodic theory and the construction of uniquely ergodic models

### Israel Journal of Mathematics (1979-09-01) 33: 231-240 , September 01, 1979

Using a combinatorial result of N. Hindman one can extend Jewett’s method for proving that a weakly mixing measure preserving transformation has a uniquely ergodic model to the general ergodic case. We sketch a proof of this reviewing the main steps in Jewett’s argument.

## Edge-Colouring Graphs and Embedding Partial Triple Systems of Even Index

### Cycles and Rays (1990-01-01) 301: 101-112 , January 01, 1990

We show that a conjecture about edge-colouring certain graphs implies a conjecture about embedding partial triple systems of even index. We give some evidence to support each of these conjectures.

## Finite-dimensional filters with nonlinear drift, VI: Linear structure of Ω

### Mathematics of Control, Signals and Systems (1996-12-01) 9: 370-385 , December 01, 1996

Ever since the concept of estimation algebra was first introduced by Brockett and Mitter independently, it has been playing a crucial role in the investigation of finite-dimensional nonlinear filters. Researchers have classified all finite-dimensional estimation algebras of maximal rank with state space less than or equal to three. In this paper we study the structure of quadratic forms in a finite-dimensional estimation algebra. In particular, we prove that if the estimation algebra is finite dimensional and of maximal rank, then the Ω=(*∂f*_{j}/∂*x*_{i}−∂*f*_{i}/∂*x*_{j})matrix, where*f* denotes the drift term, is a linear matrix in the sense that all the entries in Ω are degree one polynomials. This theorem plays a fundamental role in the classification of finite-dimensional estimation algebra of maximal rank.

## Groupoids

### Exploring Abstract Algebra With Mathematica® (1999-01-01): 252-320 , January 01, 1999

As we saw in chapter 1, there are several means by which Groupoids can be formed. Here we consider these methods in detail and consider all the available options.

## On the completion of measures

### Archiv der Mathematik (1988-05-01) 50: 259-263 , May 01, 1988

## On PSL(2,q) as a totally irregular collineation group

### Geometriae Dedicata (1994-01-01) 49: 1-24 , January 01, 1994

Non-abelian simple totally irregular collineation groups containing an involutorial perspectivity have been classified by the authors in a recent paper. They are PSL(2,*q*), PSL(3,*q*), PSU(3,*q*), Sz(*q*), the alternating group on 7 letters, and the second Janko sporadic simple group. In this article, we study PSL(2,*q*),*q* congruent to 1 modulo 4, as a collineation group containing an involutory homology.

## Theories of Probability

### Bayes Theory (1983-01-01): 1-13 , January 01, 1983

A theory of probability will be taken to be an axiom system that probabilities must satisfy, together with rules for constructing and interpreting probabilities. A person using the theory will construct some probabilities according to the rules, compute other probabilities according to the axioms, and then interpret these probabilities according to the rules; if the interpretation is unreasonable perhaps the original construction will be adjusted.

## Centralizers satisfying polynomial identities

### Israel Journal of Mathematics (1974-09-01) 18: 207-219 , September 01, 1974

The following results are proved: If*R* is a simple ring with unit, and for some*a*ε*R* with*a*^{n} in the center of*R*, any*n*, such that the centralizer of*a* in*R* satisfies a polynomial identity of degree*m*, then*R* satisfies the standard identity of degree*nm*. When*R* is not simple,*R* will satisfy a power of the same standard identity, provided that*a* and*n* are invertible in*R*. These theorems are then applied to show that if*G* is a finite solvable group of automorphisms of a ring*R*, and the fixed points of*G* in*R* satisfy a polynomial identity, then*R* satisfies a polynomial identity, provided*R* has characteristic 0 or characteristic*p* where*p*✗|*G*|.