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Applied Mathematics Commons™

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2001

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Articles 61 - 66 of 66

Full-Text Articles in Applied Mathematics

Bounding The Wild Set (Counting The Minimum Number Of Wild Primes In Hilbert Symbol Equivalent Number Fields), Marius M. Somodi Jan 2001

Bounding The Wild Set (Counting The Minimum Number Of Wild Primes In Hilbert Symbol Equivalent Number Fields), Marius M. Somodi

LSU Doctoral Dissertations

This dissertation makes a contribution to the study of Witt rings of quadratic forms over number fields. To every pair of algebraic number fields with isomorphic Witt rings one can associate a number, called the minimum number of wild primes. The situation is particularly nice when this number is 0; often it is not 0. Earlier investigations have established lower bounds for this number. In this dissertation an analysis is presented that expresses the minimum number of wild primes in terms of the number of wild dyadic primes. This formula not only gives immediate upper bounds, but can be considered …

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Artin-Schreier Families And 2-D Cycle Codes, Cem Guneri Jan 2001

Artin-Schreier Families And 2-D Cycle Codes, Cem Guneri

LSU Doctoral Dissertations

We start with the study of certain Artin-Schreier families. Using coding theory techniques, we determine a necessary and sufficient condition for such families to have a nontrivial curve with the maximum possible number of rational points over the finite field in consideration. This result produces several nice corollaries, including the existence of certain maximal curves; i.e., curves meeting the Hasse-Weil bound.We then present a way to represent two-dimensional (2-D) cyclic codes as trace codes starting from a basic zero set of its dual code. This representation enables us to relate the weight of a codeword to the number of rational …

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A New Compensating Element For A Femtosecond Photoelectron Gun, Bao-Liang Qian, Hani E. Elsayed-Ali Jan 2001

A New Compensating Element For A Femtosecond Photoelectron Gun, Bao-Liang Qian, Hani E. Elsayed-Ali

Electrical & Computer Engineering Faculty Publications

Design and analysis of a new compensating element for improving the electron pulse front and compressing the pulse duration in a femtosecond photoelectron gun are described. The compensating element is a small metallic cylindrical cavity in which an external voltage is applied in such a way that a special electric field forms and interacts with the electron pulse. This electric field reduces the distances between the faster and slower electrons inside the cavity and efficiently compensates for electron pulse broadening caused by the photoelectron energy spread and space charge effects. Poisson's equation and the equation of motion are solved to …

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Eddy Structures Induced Within A Wedge By A Honing Circular Arc, C. P. Hills Jan 2001

Eddy Structures Induced Within A Wedge By A Honing Circular Arc, C. P. Hills

Articles

In this paper we outline an expeditious numerical procedure to calculate the Stokes flow in a corner due to the rotation of a scraping circular boundary. The method is also applicable to other wedge geometries. We employ a collocation technique utilising a basis of eddy (similarity) functions introduced by Moffatt (1964) that allows us to satisfy automatically the governing equations for the streamfunction and all the boundary conditions on the surface of the wedge. The circular honing problem thereby becomes one-dimensional requiring only the satisfaction of conditions on the circular boundary. The advantage of using the Moffatt eddy functions as …

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Eddies Induced In Cylindrical Containers By A Rotating End Wall, Christopher Hills Jan 2001

Eddies Induced In Cylindrical Containers By A Rotating End Wall, Christopher Hills

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The flow generated in a viscous liquid contained in a cylindrical geometry by a rotating end wall is considered. Recent numerical and experimental work has established several distinct phases of the motion when fluid inertia plays a significant role. The current paper, however, establishes the nature of the flow in the thus far neglected low Reynolds number regime. Explicitly, by employing biorthogonality relations appropriate to the current geometry, it is shown that a sequence of exponentially decaying eddies extends outward from the rotating end wall. The cellular structure is a manifestation of the dominance of complex eigensolutions to the homogeneous …

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Efficient Traitor Tracing Algorithms Using List Decoding, Alice Silverberg, Jessica Staddon, Judy L. Walker Jan 2001

Efficient Traitor Tracing Algorithms Using List Decoding, Alice Silverberg, Jessica Staddon, Judy L. Walker

Department of Mathematics: Faculty Publications

We use powerful new techniques for list decoding error-correcting codes to efficiently trace traitors. Although much work has focused on constructing traceability schemes, the complexity of the tracing algorithm has received little attention. Because the TA tracing algorithm has a runtime of O(N) in general, where N is the number of users, it is inefficient for large populations.We produce schemes for which the TA algorithm is very fast. The IPP tracing algorithm, though less efficient, can list all coalitions capable of constructing a given pirate. We give evidence that when using an algebraic structure, the ability to …

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