New Research On Neutrosophic Algebraic Structures,
2014
University of New Mexico
New Research On Neutrosophic Algebraic Structures, Florentin Smarandache, Mumtaz Ali, Muhammad Shabir
Branch Mathematics and Statistics Faculty and Staff Publications
In this book, we define several new neutrosophic algebraic structures and their related properties. The main focus of this book is to study the important class of neutrosophic rings such as neutrosophic LA-semigroup ring, neutrosophic loop ring, neutrosophic groupoid ring and so on. We also construct their generalization in each case to study these neutrosophic algebraic structures in a broader sense. The indeterminacy element “ I “ gives rise to a more bigger algebraic structure than the classical algebraic structures. It mainly classifies the algebraic structures in three categories: such as neutrosophic algebraic structures, strong neutrosophic algebraic structures, and classical …
Groupoids Of Type I And Ii Using [0, N),
2014
University of New Mexico
Groupoids Of Type I And Ii Using [0, N), Florentin Smarandache, W.B. Vasantha Kandasamy
Branch Mathematics and Statistics Faculty and Staff Publications
Study of algebraic structures built using [0, n) happens to be one of an interesting and innovative research. Here in this book authors define non associative algebraic structures using the interval [0, n). Here we define two types of groupoids using [0, n) both of them are of infinite order. It is an open conjecture to find whether these new class of groupoids satisfy any of the special identities like Moufang identity or Bol identity or Bruck identity or so on. We know on [0, n) we cannot build rings only pseudo rings, however in this book we use these …
Special Pseudo Linear Algebras Using [0,N),
2014
University of New Mexico
Special Pseudo Linear Algebras Using [0,N), Florentin Smarandache, W.B. Vasantha Kandasamy
Branch Mathematics and Statistics Faculty and Staff Publications
In this book we introduce some special type of linear algebras called pseudo special linear algebras using the interval [0, n). These new types of special pseudo interval linear algebras has several interesting properties. Special pseudo interval linear algebras are built over the subfields in Zn where Zn is a S-ring. We study the substructures of them. The notion of Smarandache special interval pseudo linear algebras and Smarandache strong special pseudo interval linear algebras are introduced. The former Sspecial interval pseudo linear algebras are built over the Sring itself. Study in this direction has yielded several interesting results. S-strong special …
Soft Neutrosophic Algebraic Structures And Their Generalization - Vol. 2,
2014
University of New Mexico
Soft Neutrosophic Algebraic Structures And Their Generalization - Vol. 2, Florentin Smarandache, Mumtaz Ali, Muhammad Shabir
Branch Mathematics and Statistics Faculty and Staff Publications
In this book we define some new notions of soft neutrosophic algebraic structures over neutrosophic algebraic structures. We define some different soft neutrosophic algebraic structures but the main motivation is two-fold. Firstly the classes of soft neutrosophic group ring and soft neutrosophic semigroup ring defined in this book is basically the generalization of two classes of rings: neutrosophic group rings and neutrosophic semigroup rings. These soft neutrosophic group rings and soft neutrosophic semigroup rings are defined over neutrosophic group rings and neutrosophic semigroup rings respectively. This is basically the collection of parameterized subneutrosophic group ring and subneutrosophic semigroup ring of …
Algebraic Structures On The Fuzzy Interval [0, 1),
2014
University of New Mexico
Algebraic Structures On The Fuzzy Interval [0, 1), Florentin Smarandache, W.B. Vasantha Kandasamy
Branch Mathematics and Statistics Faculty and Staff Publications
In this book we introduce several algebraic structures on the special fuzzy interval [0, 1). This study is different from that of the algebraic structures using the interval [0, n) n ≠ 1, as these structures on [0, 1) has no idempotents or zero divisors under ×. Further [0, 1) under product × is only a semigroup. However by defining min(or max) operation in [0, 1); [0, 1) is made into a semigroup. The semigroup under × has no finite subsemigroups but under min or max we have subsemigroups of order one, two and so on. [0, 1) under + …
Pseudo Lattice Graphs And Their Applications To Fuzzy And Neutrosophic Models,
2014
University of New Mexico
Pseudo Lattice Graphs And Their Applications To Fuzzy And Neutrosophic Models, Florentin Smarandache, W.B. Vasantha Kandasamy, K. Ilanthenral
Branch Mathematics and Statistics Faculty and Staff Publications
In this book for the first time authors introduce the concept of merged lattice, which gives a lattice or a graph. The resultant lattice or graph is defined as the pseudo lattice graph of type I. Here we also merge a graph with a lattice or two or more graphs which call as the pseudo lattice graph of type II. We merge either edges or vertices or both of a lattice and a graph or a lattice and a lattice or graph with itself. Such study is innovative and these mergings are adopted on all fuzzy and neutrosophic models which …
Algebraic Structures On Finite Complex Modulo Integer Interval C([0, N)),
2014
University of New Mexico
Algebraic Structures On Finite Complex Modulo Integer Interval C([0, N)), Florentin Smarandache, W.B. Vasantha Kandasamy
Branch Mathematics and Statistics Faculty and Staff Publications
In this book authors introduce the notion of finite complex modulo integer intervals. Finite complex modulo integers was introduced by the authors in 2011. Now using this finite complex modulo integer intervals several algebraic structures are built. Further the concept of finite complex modulo integers itself happens to be new and innovative for in case of finite complex modulo integers the square value of the finite complex number varies with varying n of Zn. In case of finite complex modulo integer intervals also we can have only pseudo ring as the distributive law is not true, in general in C([0, …
Algebraic Generalization Of Venn Diagram,
2014
University of New Mexico
Algebraic Generalization Of Venn Diagram, Florentin Smarandache
Branch Mathematics and Statistics Faculty and Staff Publications
It is easy to deal with a Venn Diagram for 1 ≤ n ≤ 3 sets. When n gets larger, the picture becomes more complicated, that's why we thought at the following codification. That’s why we propose an easy and systematic algebraic way of dealing with the representation of intersections and unions of many sets.
Early Investigations In Conformal And Differential Geometry,
2014
University of Arkansas, Fayetteville
Early Investigations In Conformal And Differential Geometry, Raymond T. Walter
Inquiry: The University of Arkansas Undergraduate Research Journal
The present article introduces fundamental notions of conformal and differential geometry, especially where such notions are useful in mathematical physics applications. Its primary achievement is a nontraditional proof of the classic result of Liouville that the only conformal transformations in Euclidean space of dimension greater than two are Möbius transformations. The proof is nontraditional in the sense that it uses the standard Dirac operator on Euclidean space and is based on a representation of Möbius transformations using 2x2 matrices over a Clifford algebra. Clifford algebras and the Dirac operator are important in other applications of pure mathematics and mathematical physics, …
Tropical Convexity Over Max-Min Semiring,
2014
West Chester University of Pennsylvania
Tropical Convexity Over Max-Min Semiring, Viorel Nitica, Sergei Sergeev
Mathematics Faculty Publications
No abstract provided.
A Metric On Max-Min Algebra,
2014
University of Oregon
A Metric On Max-Min Algebra, Jonathan Eskeldson, Miriam Jaffe, Viorel Nitica
Mathematics Faculty Publications
No abstract provided.
Function Of Several Variable,
2014
Parkland College
Function Of Several Variable, Weiting Li
A with Honors Projects
This Parkland A with Honors project discusses the function of several variables, it's limits and partial derivatives.
Geometry Of Optimal Control For Control-Affine Systems,
2013
University of Colorado Boulder
Geometry Of Optimal Control For Control-Affine Systems, Jeanne N. Clelland, Christopher G. Moseley, George R. Wilkens
University Faculty Publications and Creative Works
Motivated by the ubiquity of control-affine systems in optimal control theory, we investigate the geometry of point-affine control systems with metric structures in dimensions two and three. We compute local isometric invariants for point-affine distributions of constant type with metric structures for systems with 2 states and 1 control and systems with 3 states and 1 control, and use Pontryagin's maximum principle to find geodesic trajectories for homogeneous examples. Even in these low dimensions, the behavior of these systems is surprisingly rich and varied.
Geometry Of Optimal Control For Control-Affine Systems,
2013
University of Colorado Boulder
Geometry Of Optimal Control For Control-Affine Systems, Jeanne N. Clelland, Christopher G. Moseley, George R. Wilkens
University Faculty Publications and Creative Works
Motivated by the ubiquity of control-affine systems in optimal control theory, we investigate the geometry of point-affine control systems with metric structures in dimensions two and three. We compute local isometric invariants for point-affine distributions of constant type with metric structures for systems with 2 states and 1 control and systems with 3 states and 1 control, and use Pontryagin's maximum principle to find geodesic trajectories for homogeneous examples. Even in these low dimensions, the behavior of these systems is surprisingly rich and varied.
Results On Containments And Resurgences, With A Focus On Ideals Of Points In The Plane,
2013
University of Nebraska-Lincoln
Results On Containments And Resurgences, With A Focus On Ideals Of Points In The Plane, Annika Denkert
Department of Mathematics: Dissertations, Theses, and Student Research
Let K be an algebraically closed field and I ⊆ R=K[PN] a nontrivial homogeneous ideal. We can describe ordinary powers Ir and symbolic powers I(m) of I. One question that has been of interest over the past couple of years is that of when we have containment of I(m) in Ir. Bocci and Harbourne defined the resurgence of I as rho(I)=supm,r{m/r | I(m) is not contained in Ir}. Hence in particular I(m) ⊆ Ir whenever m/r is at least …
Geometric Study Of The Category Of Matrix Factorizations,
2013
University of Nebraska-Lincoln
Geometric Study Of The Category Of Matrix Factorizations, Xuan Yu
Department of Mathematics: Dissertations, Theses, and Student Research
We study the geometry of matrix factorizations in this dissertation.
It contains two parts. The first one is a Chern-Weil style
construction for the Chern character of matrix factorizations; this
allows us to reproduce the Chern character in an explicit,
understandable way. Some basic properties of the Chern character are
also proved (via this construction) such as functoriality and that
it determines a ring homomorphism from the Grothendieck group of
matrix factorizations to its Hochschild homology. The second part is
a reconstruction theorem of hypersurface singularities. This is
given by applying a slightly modified version of Balmer's tensor
triangular geometry …
On Cyclic Fixed Points Of Spectra,
2013
Aarhus University, Denmark
On Cyclic Fixed Points Of Spectra, Marcel Bökstedt, Robert R. Bruner, Sverre Lunøe-Nielsen, John Rognes
Mathematics Faculty Research Publications
For a finite ��-group �� and a bounded below ��-spectrum �� of finite type mod ��, the ��-equivariant Segal conjecture for �� asserts that the canonical map ��^��→��^ℎ��, from ��-fixed points to ��-homotopy fixed points, is a ��-adic equivalence. Let ��_(��^��) be the cyclic group of order ��^��. We show that if the ��_��-equivariant Segal conjecture holds for a ��_(��^��)-spectrum ��, as well as for each of its geometric fixed point spectra Φ^(��_(��^��))(��) for 0<��<��, then the ��_(��^��)-equivariant Segal conjecture holds for ��. Similar results also hold for weaker forms of the Segal conjecture, asking only that the canonical map induces an equivalence in sufficiently high degrees, on homotopy groups with suitable finite coefficients.
Projected Surface Finite Elements For Elliptic Equations,
2013
University of Tulsa
Projected Surface Finite Elements For Elliptic Equations, Necibe Tuncer
Applications and Applied Mathematics: An International Journal (AAM)
In this article, we define a new finite element method for numerically approximating solutions of elliptic partial differential equations defined on “arbitrary” smooth surfaces S in RN+1. By “arbitrary” smooth surfaces, we mean surfaces that can be implicitly represented as level sets of smooth functions. The key idea is to first approximate the surface S by a polyhedral surface Sh, which is a union of planar triangles whose vertices lie on S; then to project Sh onto S. With this method, we can also approximate the eigenvalues and eigenfunctions of th Laplace-Beltrami operator on these “arbitrary” surfaces.
Chip Firing Games And Riemann-Roch Properties For Directed Graphs,
2013
Harvey Mudd College
Chip Firing Games And Riemann-Roch Properties For Directed Graphs, Joshua Z. Gaslowitz
HMC Senior Theses
The following presents a brief introduction to tropical geometry, especially tropical curves, and explains a connection to graph theory. We also give a brief summary of the Riemann-Roch property for graphs, established by Baker and Norine (2007), as well as the tools used in their proof. Various generalizations are described, including a more thorough description of the extension to strongly connected directed graphs by Asadi and Backman (2011). Building from their constructions, an algorithm to determine if a directed graph has Row Riemann-Roch Property is given and thoroughly explained.
Split Abelian Chief Factors And First Degree Cohomology For Lie Algebras,
2013
University of South Alabama
Split Abelian Chief Factors And First Degree Cohomology For Lie Algebras, Jorg Feldvoss, Salvatore Siciliano, Thomas Weigel
University Faculty and Staff Publications
In this paper we investigate the relation between the multiplicities of split abelian chief factors of finite-dimensional Lie algebras and first degree cohomology. In particular, we obtain a characterization of modular solvable Lie algebras in terms of the vanishing of first degree cohomology or in terms of the multiplicities of split abelian chief factors. The analogues of these results are well known in the modular representation theory of finite groups. An important tool in the proof of these results is a refinement of a non-vanishing theorem of Seligman for the first degree cohomology of non-solvable finite-dimensional Lie algebras in prime …
