Neutrosophic Bilinear Algebras And Their Generalizations, 2010 University of New Mexico

#### Neutrosophic Bilinear Algebras And Their Generalizations, Florentin Smarandache, W.B. Vasantha Kandasamy

*Branch Mathematics and Statistics Faculty and Staff Publications*

This book introduces the concept of neutrosophic bilinear algebras and their generalizations to n-linear algebras, n>2. This book has five chapters. The reader should be well-versed with the notions of linear algebras as well as the concepts of bilinear algebras and n- linear algebras. Further the reader is expected to know about neutrosophic algebraic structures as we have not given any detailed literature about it. The first chapter is introductory in nature and gives a few essential definitions and references for the reader to make use of the literature in case the reader is not thorough with the basics. …

Proposed Problems Of Mathematics (Vol. Ii), 2010 University of New Mexico

#### Proposed Problems Of Mathematics (Vol. Ii), Florentin Smarandache

*Branch Mathematics and Statistics Faculty and Staff Publications*

The first book of “Problèmes avec et sans … problèmes!” was published in Morocco in 1983. I collected these problems that I published in various Romanian or foreign magazines (amongst which: “Gazeta Matematică”, magazine which formed me as problem solver, “American Mathematical Monthly”, “Crux Mathematicorum” (Canada), “Elemente der Mathematik” (Switzerland), “Gaceta Matematica” (Spain), “Nieuw voor Archief” (Holland), etc. while others are new proposed problems in this second volume.

These have been created in various periods: when I was working as mathematics professor in Romania (1984-1988), or co-operant professor in Morocco (1982-1984), or emigrant in the USA (1990-1997). I thank to …

Recognizing Graph Theoretic Properties With Polynomial Ideals, 2010 University of California - Davis

#### Recognizing Graph Theoretic Properties With Polynomial Ideals, Jesus A. De Loera, Christopher J. Hillar, Peter N. Malkin, Mohamed Omar

*All HMC Faculty Publications and Research*

Many hard combinatorial problems can be modeled by a system of polynomial equations. N. Alon coined the term *polynomial method* to describe the use of nonlinear polynomials when solving combinatorial problems. We continue the exploration of the polynomial method and show how the algorithmic theory of polynomial ideals can be used to detect k-colorability, unique Hamiltonicity, and automorphism rigidity of graphs. Our techniques are diverse and involve Nullstellensatz certificates, linear algebra over finite fields, Gröbner bases, toric algebra, convex programming, and real algebraic geometry.

Epimorphisms And Boundary Slopes Of 2–Bridge Knots, 2010 Pitzer College

#### Epimorphisms And Boundary Slopes Of 2–Bridge Knots, Jim Hoste, Patrick D. Shanahan

*Mathematics Faculty Works*

In this article we study a partial ordering on knots in S^{3} where K_{1}≥K_{2} if there is an epimorphism from the knot group of K_{1} onto the knot group of K_{2} which preserves peripheral structure. If K_{1} is a 2–bridge knot and K_{1}≥K_{2}, then it is known that K_{2} must also be 2–bridge. Furthermore, Ohtsuki, Riley and Sakuma give a construction which, for a given 2–bridge knot K_{p∕q}, produces infinitely many 2–bridge knots K_{p′/q′} with K_{p′∕q′}≥K_{p∕q}. After characterizing all 2–bridge knots …

Symmetric Generation, 2010 California State University, San Bernardino

#### Symmetric Generation, Dung Hoang Tri

*Theses Digitization Project*

In this thesis we construct finite homorphic images of infinite semi-direct products, 2*n : N, where 2*n is a free product of n copies the cyclic group of permutations on n letter.

An Investigation Of Kurosh's Theorem, 2010 California State University, San Bernardino

#### An Investigation Of Kurosh's Theorem, Keith Anthony Earl

*Theses Digitization Project*

The purpose of this project will be an exposition of the Kurosh Theorem and the necessary and suffcient condition that A must be algebraic and satisfy a P.I. to be locally finite.

Symmetric Generators Of Order 3, 2010 California State University, San Bernardino

#### Symmetric Generators Of Order 3, Stewart Contreras

*Theses Digitization Project*

The main purpose of this project is to construct finite homomorphic images of infinite semi-direct products.