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Articles 1 - 17 of 17
Full-Text Articles in Algebraic Geometry
Continuous Dependence Of Solutions Of Equations On Parameters, Sean A. Broughton
Continuous Dependence Of Solutions Of Equations On Parameters, Sean A. Broughton
Mathematical Sciences Technical Reports (MSTR)
It is shown under very general conditions that the solutions of equations depend continuously on the coefficients or parameters of the equations. The standard examples are solutions of monic polynomial equations and the eigenvalues of a matrix. However, the proof methods apply to any finite map T : Cn -> Cn.
Light Pollution Research Through Citizen Science, John Kanemoto
Light Pollution Research Through Citizen Science, John Kanemoto
STAR Program Research Presentations
Light pollution (LP) can disrupt and/or degrade the health of all living things, as well as, their environments. The goal of my research at the NOAO was to check the accuracy of the citizen science LP reporting systems entitled: Globe at Night (GaN), Dark Sky Meter (DSM), and Loss of the Night (LoN). On the GaN webpage, the darkness of the night sky (DotNS) is reported by selecting a magnitude chart. Each magnitude chart has a different density/number of stars around a specific constellation. The greater number of stars implies a darker night sky. Within the DSM iPhone application, a …
The Neural Ring: Using Algebraic Geometry To Analyze Neural Codes, Nora Youngs
The Neural Ring: Using Algebraic Geometry To Analyze Neural Codes, Nora Youngs
Department of Mathematics: Dissertations, Theses, and Student Research
Neurons in the brain represent external stimuli via neural codes. These codes often arise from stimulus-response maps, associating to each neuron a convex receptive field. An important problem confronted by the brain is to infer properties of a represented stimulus space without knowledge of the receptive fields, using only the intrinsic structure of the neural code. How does the brain do this? To address this question, it is important to determine what stimulus space features can - in principle - be extracted from neural codes. This motivates us to define the neural ring and a related neural ideal, algebraic objects …
The Dual Gromov-Hausdorff Propinquity, Frédéric Latrémolière
The Dual Gromov-Hausdorff Propinquity, Frédéric Latrémolière
Mathematics Preprint Series
Motivated by the quest for an analogue of the Gromov-Hausdorff distance in noncommutative geometry which is well-behaved with respect to C*- algebraic structures, we propose a complete metric on the class of Leibniz quantum compact metric spaces, named the dual Gromov-Hausdorff propinquity, which resolves several important issues raised by recent research in noncommutative metric geometry: our new metric makes *-isomorphism a necessary condition for distance zero, is well-adapted to Leibniz seminorms, and — very importantly — is complete, unlike the quantum propinquity which we introduced earlier. Thus our new metric provides a new tool for noncommutative metric geometry which offers …
Function Of Several Variable, Weiting Li
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.
Tropical Convexity Over Max-Min Semiring, Viorel Nitica, Sergei Sergeev
Tropical Convexity Over Max-Min Semiring, Viorel Nitica, Sergei Sergeev
Mathematics Faculty Publications
No abstract provided.
A Metric On Max-Min Algebra, Jonathan Eskeldson, Miriam Jaffe, Viorel Nitica
A Metric On Max-Min Algebra, Jonathan Eskeldson, Miriam Jaffe, Viorel Nitica
Mathematics Faculty Publications
No abstract provided.
Split Strongly Abelian P-Chief Factors And First Degree Restricted Cohomology, Jorg Feldvoss, Salvatore Siciliano, Thomas Weigel
Split Strongly Abelian P-Chief Factors And First Degree Restricted Cohomology, Jorg Feldvoss, Salvatore Siciliano, Thomas Weigel
University Faculty and Staff Publications
In this paper we investigate the relation between the multiplicities of split strongly abelian p-chief factors of finite-dimensional restricted Lie algebras and first degree restricted cohomology. As an application we obtain a characterization of solvable restricted Lie algebras in terms of the multiplicities of split strongly abelian p-chief factors. Moreover, we derive some results in the representation theory of restricted Lie algebras related to the principal block and the projective cover of the trivial irreducible module of a finite-dimensional restricted Lie algebra. In particular, we obtain a characterization of finite-dimensional solvable restricted Lie algebras in terms of the second Loewy …
Soft Neutrosophic Algebraic Structures And Their Generalization - Vol. 2, Florentin Smarandache, Mumtaz Ali, Muhammad Shabir
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 …
Some Properties Of The Harmonic Quadrilateral, Florentin Smarandache
Some Properties Of The Harmonic Quadrilateral, Florentin Smarandache
Branch Mathematics and Statistics Faculty and Staff Publications
In this article, we review some properties of the harmonic quadrilateral related to triangle simedians and to Apollonius circles.
Algebraic Structures On The Fuzzy Interval [0, 1), Florentin Smarandache, W.B. Vasantha Kandasamy
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 + …
Algebraic Structures On Finite Complex Modulo Integer Interval C([0, N)), Florentin Smarandache, W.B. Vasantha Kandasamy
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, Florentin Smarandache
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.
Special Pseudo Linear Algebras Using [0,N), Florentin Smarandache, W.B. Vasantha Kandasamy
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 …
Groupoids Of Type I And Ii Using [0, N), Florentin Smarandache, W.B. Vasantha Kandasamy
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 …
Pseudo Lattice Graphs And Their Applications To Fuzzy And Neutrosophic Models, Florentin Smarandache, W.B. Vasantha Kandasamy, K. Ilanthenral
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 …
New Research On Neutrosophic Algebraic Structures, Florentin Smarandache, Mumtaz Ali, Muhammad Shabir
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 …