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Some Necessary Conditions Of Boolean Functions To Resist Algebraic Attacks., Deepak Dalai Dr.
Some Necessary Conditions Of Boolean Functions To Resist Algebraic Attacks., Deepak Dalai Dr.
Doctoral Theses
No abstract provided.
Polynomial Functions Over Rings Of Residue Classes Of Integers, M Brandon Meredith
Polynomial Functions Over Rings Of Residue Classes Of Integers, M Brandon Meredith
Mathematics Theses
In this thesis we discuss how to find equivalent representations of polynomial functions over the ring of integers modulo a power of a prime. Specifically, we look for lower degree representations and representations with fewer variables for which important applications in electrical and computer engineering exist. We present several algorithms for finding these compact formulations.
Infinite Product Group, Keith G. Penrod
Infinite Product Group, Keith G. Penrod
Theses and Dissertations
The theory of infinite multiplication has been studied in the case of the Hawaiian earring group, and has been seen to simplify the description of that group. In this paper we try to extend the theory of infinite multiplication to other groups and give a few examples of how this can be done. In particular, we discuss the theory as applied to symmetric groups and braid groups. We also give an equivalent definition to K. Eda's infinitary product as the fundamental group of a modified wedge product.
Structural Properties Of Formal Polynomial Algebras In Noncommuting Or Nonassociating Indeterminates, Serge C. Ballif
Structural Properties Of Formal Polynomial Algebras In Noncommuting Or Nonassociating Indeterminates, Serge C. Ballif
All Graduate Theses and Dissertations, Spring 1920 to Summer 2023
In order to enlarge the class of equations provided by traditional polynomials over a binary algebra A to a more useful class of equations, we introduce polynomials in noncommuting or nonassociating indeterminates. We discuss algebraic properties of these formal polynomial algebras and their accompanying polynomial function algebras. We present certain basis results for polynomial algebras, which are used to address the question of zero divisors in a polynomial algebra. We give an analog of the remainder theorem and the factor theorem for polynomials. Particular emphasis is placed on showing the difference between polynomials and polynomial functions. We also provide a …
Reality Properties Of Conjugacy Classes In Algebraic Groups., Anupam Kumar Singh Dr.
Reality Properties Of Conjugacy Classes In Algebraic Groups., Anupam Kumar Singh Dr.
Doctoral Theses
In this thesis we denote a field by k. We consider fields of characteristic not 2 unless stated otherwise. The notation ¯k and ks denotes an algebraic closure and separable closure of k respectively. The symbols Q, R, C will denote fields of rational, real, complex numbers respectively. The symbol Z will denote the set of integers. We denote by cd(k) the cohomological dimension of k.We use G to denote an algebraic group and G(k) to denote the group of k rational points of G. Sometimes we abuse notation and denote the group of ¯k points of G by G. …
Some Geometrical Aspects Of The Cone Linear Complementarity Problem., Madhur Malik Dr.
Some Geometrical Aspects Of The Cone Linear Complementarity Problem., Madhur Malik Dr.
Doctoral Theses
Cone Linear Complementarity ProblemLet V be a finite dimensional real inner product space and K be a closed convex cone in V. Given a linear transformation L : V → V and a vector q ∈ V the cone linear complementarity problem or linear complementarity problem over K, denoted as LCP(K, L, q), is to find a vector x ∈ K such thatL(x) + q ∈ K+ and hx, L(x) + qi = 0,where h., .i denotes an inner product on V and K is the dual cone of K defined as:K∗ := {y ∈ V : hx, yi ≥ …