1,324 research outputs found
On finiteness conditions for Rees matrix semigroups
summary:Let be a Rees matrix semigroup where is a semigroup, and are index sets, and is a matrix with entries from , and let be the ideal generated by all the entries of . If has finite index in , then we prove that is periodic (locally finite) if and only if is periodic (locally finite). Moreover, residual finiteness and having solvable word problem are investigated
Automatic structures for semigroup constructions
We survey results concerning automatic structures for semigroup
constructions, providing references and describing the corresponding automatic
structures. The constructions we consider are: free products, direct products,
Rees matrix semigroups, Bruck-Reilly extensions and wreath products.Comment: 22 page
Zeros of some bi-orthogonal polynomials
Ercolani and McLaughlin have recently shown that the zeros of the
bi-orthogonal polynomials with the weight
, relevant to a model of two coupled
hermitian matrices, are real and simple. We show that their argument applies to
the more general case of the weight , a convolution of
several weights of the same form. This general case is relevant to a model of
several hermitian matrices coupled in a chain. Their argument also works for
the weight , , and for a convolution of
several such weights.Comment: tex mehta.tex, 1 file, 9 pages [SPhT-T01/086], submitted to J. Phys.
Constant slope maps and the Vere-Jones classification
We study continuous countably piecewise monotone interval maps, and formulate
conditions under which these are conjugate to maps of constant slope,
particularly when this slope is given by the topological entropy of the map. We
confine our investigation to the Markov case and phrase our conditions in the
terminology of the Vere-Jones classification of infinite matrices.Comment: 33 page
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