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Physical Sciences and Mathematics Commons

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Applied Mathematics

University of Nebraska - Lincoln

Department of Mathematics: Faculty Publications

2000

Articles 1 - 5 of 5

Full-Text Articles in Physical Sciences and Mathematics

The Structure Of Free Semigroup Algebras, Kenneth R. Davidson, Elias Katsoulis, David R. Pitts Jun 2000

The Structure Of Free Semigroup Algebras, Kenneth R. Davidson, Elias Katsoulis, David R. Pitts

Department of Mathematics: Faculty Publications

A free semigroup algebra is WOT-closed algebra generated by an n-tuple of isometries with pairwise orthogonal ranges. The interest in these algebras arises primarily from two of their interesting features. The first is that they provide useful information about unitary invariants of representations of the Cuntz-Toeplitz algebras. The second is that they form a class of nonself-adjoint operator algebras which are of interest in their own right. This class contains a distinguished representative, the "non-commutative Toeplitz algebra", which is generated by the left regular representation of the free semigroup on n letters and denoted . This paper provides a general …


Euclidean Weights Of Codes From Elliptic Curves Over Rings, José Felipe Voloch, Judy L. Walker Jun 2000

Euclidean Weights Of Codes From Elliptic Curves Over Rings, José Felipe Voloch, Judy L. Walker

Department of Mathematics: Faculty Publications

We construct certain error-correcting codes over finite rings and estimate their parameters. For this purpose, we need to develop some tools, notably an estimate for certain exponential sums and some results on canonical lifts of elliptic curves. These results may be of independent interest.

A code is a subset of An, where A is a finite set (called the alphabet). Usually A is just the field of two elements and, in this case, one speaks of binary codes. Such codes are used in applications where one transmits information through noisy channels. By building redundancy into the code, transmitted …


Codes And Curves, Judy L. Walker Jan 2000

Codes And Curves, Judy L. Walker

Department of Mathematics: Faculty Publications

When information is transmitted, errors are likely to occur. Coding theory examines effi cient ways of packaging data so that these errors can be detected, or even corrected. The traditional tools of coding theory have come from combinatorics and group theory. Lately, however, coding theorists have added techniques from algebraic geometry to their toolboxes. In particular, by re-interpreting the Reed- Solomon codes, one can see how to defi ne new codes based on divisors on algebraic curves. For instance, using modular curves over fi nite fi elds, Tsfasman, Vladut, and Zink showed that one can defi ne a sequence of …


Two-Groups With Few Conjugacy Classes, Nigel Boston, Judy L. Walker Jan 2000

Two-Groups With Few Conjugacy Classes, Nigel Boston, Judy L. Walker

Department of Mathematics: Faculty Publications

An old question of Brauer asking how fast numbers of conjugacy classes grow is investigated by considering the least number cn of conjugacy classes in a group of order 2n. The numbers cn are computed for n ≤ 14 and a lower bound is given for c15. It is observed that cn grows very slowly except for occasional large jumps corresponding to an increase in coclass of the minimal groups Gn. Restricting to groups that are 2-generated or have coclass at most 3 allows us to extend these computations.


Translation Theorems For Fourier-Feynman Transforms And Conditional Fourier-Feynman Transforms, Seung Jun Change, Chull Park, David Skough Jan 2000

Translation Theorems For Fourier-Feynman Transforms And Conditional Fourier-Feynman Transforms, Seung Jun Change, Chull Park, David Skough

Department of Mathematics: Faculty Publications

Translation theorems for Wiener integrals were given by Cameron and Martin in [3] and by Cameron and Graves in [2]. Translation theorems for analytic Feynman integrals were given by Cameron and Storvick in [4], [7] and translation theorems for Feynman integrals on abstract Wiener and Hilbert spaces were given by Chung and Kang in [12].