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Articles 361 - 390 of 465

Full-Text Articles in Mathematics

An Adaptive Method For Calculating Blow-Up Solutions, Charles F. Touron Jul 2009

An Adaptive Method For Calculating Blow-Up Solutions, Charles F. Touron

Mathematics & Statistics Theses & Dissertations

Reactive-diffusive systems modeling physical phenomena in certain situations develop a singularity at a finite value of the independent variable referred to as "blow-up." The attempt to find the blow-up time analytically is most often impossible, thus requiring a numerical determination of the value. The numerical methods often use a priori knowledge of the blow-up solution such as monotonicity or self-similarity. For equations where such a priori knowledge is unavailable, ad hoc methods were constructed. The object of this research is to develop a simple and consistent approach to find numerically the blow-up solution without having a priori knowledge or resorting …

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Circular Nonlinear Subdivision Schemes For Curve Design, Jian-Ao Lian, Yonghui Wang, Yonggao Yang Jun 2009

Circular Nonlinear Subdivision Schemes For Curve Design, Jian-Ao Lian, Yonghui Wang, Yonggao Yang

Applications and Applied Mathematics: An International Journal (AAM)

Two new families of nonlinear 3-point subdivision schemes for curve design are introduced. The first family is ternary interpolatory and the second family is binary approximation. All these new schemes are circular-invariant, meaning that new vertices are generated from local circles formed by three consecutive old vertices. As consequences of the nonlinear schemes, two new families of linear subdivision schemes for curve design are established. The 3-point linear binary schemes, which are corner-cutting depending on the choices of the tension parameter, are natural extensions of the Lane-Riesenfeld schemes. The four families of both nonlinear and linear subdivision schemes are implemented …

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Fractional Calculus: Definitions And Applications, Joseph M. Kimeu Apr 2009

Fractional Calculus: Definitions And Applications, Joseph M. Kimeu

Masters Theses & Specialist Projects

No abstract provided.

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The Universal Coefficient Theorem For Cohomology, Michael Anthony Rosas Jan 2009

The Universal Coefficient Theorem For Cohomology, Michael Anthony Rosas

Theses Digitization Project

This project is an expository survey of the Universal Coefficient Theorem for Cohomology. Algebraic preliminaries, homology, and cohomology are discussed prior to the proof of the theorem.

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The Fundamental Group And Van Kampen's Theorem, Aaron Christopher Thomas Jan 2009

The Fundamental Group And Van Kampen's Theorem, Aaron Christopher Thomas

Theses Digitization Project

This thesis deals with the field of algebraic topology. Basic topological facts are addressed including open and closed sets, continuity, homeomorphisms, and path connectedness as well as discussing Van Kampen's Theorem in detail.

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Geometric Theorem Proving Using The Groebner Basis Algorithm, Karla Friné Rivas Jan 2009

Geometric Theorem Proving Using The Groebner Basis Algorithm, Karla Friné Rivas

Theses Digitization Project

The purpose fo this project is to study ideals in polynomial rings and affine varieties in order to establish a connection between these two different concepts. Doing so will lead to an in depth examination of Groebner bases. Once this has been defined, step will be outlined that will enable the application of the Groebner Basis Algorithm to geometric problems.

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On A Symmetric Presentation Of The Double Cover Of M₂₂: 2, Gabriela Laura Maerean Jan 2009

On A Symmetric Presentation Of The Double Cover Of M₂₂: 2, Gabriela Laura Maerean

Theses Digitization Project

The purpose of this project is to construct finite homomorphic images of infinite semi-direct products. We will construct two finite homomorphic images, L₂ (8) and PGL₂ (9) of the infinite semi-direct product 2*³ : S₃. The main part of this project is to construct the double cover 2 - M₂₂ : 2 and the automorphism group M₂₂ : 2 of the Matheiu sporadic group M₂₂ as a homomorphic image of the progenitor 2*⁷ : L₃ (2).

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On The Number Of K-Gons In Finite Projective Planes, Felix Lazebnik, Keith Mellinger, Oscar Vega Jan 2009

On The Number Of K-Gons In Finite Projective Planes, Felix Lazebnik, Keith Mellinger, Oscar Vega

Mathematics Articles

Let π = πq denote a finite projective plane of order q, and let G = Levi(π) be the bipartite point-line incidence graph of π. For k ≥ 3, let c2k(π) denote the number of cycles of length 2k in G. Are the numbers c2k(π) the same for all πq? We prove that this is the case for k = 3, 4, 5, 6 by computing these numbers.

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Groups As Graphs, Florentin Smarandache, W.B. Vasantha Kandasamy Jan 2009

Groups As Graphs, Florentin Smarandache, W.B. Vasantha Kandasamy

Branch Mathematics and Statistics Faculty and Staff Publications

Through this book, for the first time we represent every finite group in the form of a graph. The authors choose to call these graphs as identity graph, since the main role in obtaining the graph is played by the identity element of the group. This study is innovative because through this description one can immediately look at the graph and say the number of elements in the group G which are self-inversed. Also study of different properties like the subgroups of a group, normal subgroups of a group, p-sylow subgroups of a group and conjugate elements of a group …

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On A-Ary Subdivision For Curve Design Ii. 3-Point And 5-Point Interpolatory Schemes, Jian-Ao Lian Dec 2008

On A-Ary Subdivision For Curve Design Ii. 3-Point And 5-Point Interpolatory Schemes, Jian-Ao Lian

Applications and Applied Mathematics: An International Journal (AAM)

The a-ary 3-point and 5-point interpolatery subdivision schemes for curve design are introduced for arbitrary odd integer a greater than or equal to 3. These new schemes further extend the family of the classical 4- and 6-point interpolatory schemes.

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An Exploration Of A Discrete Rhombohedral Lattice Of Possible Engineering Or Physical Relevance (Revised Version) 2008, Jim Mcgovern Jun 2008

An Exploration Of A Discrete Rhombohedral Lattice Of Possible Engineering Or Physical Relevance (Revised Version) 2008, Jim Mcgovern

Conference Papers

A particular discrete rhombohedral lattice consisting of four symmetrically interlaced cuboctahedral point lattices is described that is interesting because of the high degree of symmetry it exhibits. The four constituent cuboctahedral lattices are denoted by four colours and the composite lattice is referred to as a 4-colour rhombohedral lattice. Each point of the 4-colour lattice can be referenced by an integer 4-tuple containing only the positive non-zero integers (the counting numbers). The relationship between the discrete rhombohedral lattice and a discrete Cartesian lattice is explained. Some interesting aspects of the lattice and of the counting-number 4-tuple coordinate system are pointed …

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An Exploration Of A Discrete Rhombohedral Lattice Of Possible Engineering Or Physical Relevance, Jim Mcgovern Jun 2008

An Exploration Of A Discrete Rhombohedral Lattice Of Possible Engineering Or Physical Relevance, Jim Mcgovern

Conference Papers

A particular discrete rhombohedral lattice consisting of four symmetrically interlaced cuboctahedral or cubic point lattices is described that is interesting because of the high degree of symmetry it exhibits. The four constituent lattices are denoted by four colours and the composite lattice is referred to as a 4-colour rhombohedral lattice. Each point of the 4-colour lattice can be referenced by an integer 4-tuple containing only the positive non-zero integers (the counting numbers). The relationship between the discrete rhombohedral lattice and a discrete Cartesian lattice is explained. Some interesting aspects of the lattice and of the counting-number 4-tuple coordinate system are …

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On A-Ary Subdivision For Curve Design: I. 4-Point And 6-Point Interpolatory Schemes, Jian-Ao Lian Jun 2008

On A-Ary Subdivision For Curve Design: I. 4-Point And 6-Point Interpolatory Schemes, Jian-Ao Lian

Applications and Applied Mathematics: An International Journal (AAM)

The classical binary 4-point and 6-point interpolatery subdivision schemes are generalized to a-ary setting for any integer a greater than or equal to 3. These new a-ary subdivision schemes for curve design are derived easily from their corresponding two-scale scaling functions, a notion from the context of wavelets.

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Rethinking Pythagorean Triples, William J. Spezeski Jun 2008

Rethinking Pythagorean Triples, William J. Spezeski

Applications and Applied Mathematics: An International Journal (AAM)

It has been known for some 2000 years how to generate Pythagorean Triples. While the classical formulas generate all of the primitive triples, they do not generate all of the triples. For example, the triple (9, 12, 15) can’t be generated from the formulas, but it can be produced by introducing a multiplier to the primitive triple (3, 4, 5). And while the classical formulas produce the triple (3, 4, 5), they don’t produce the triple (4, 3, 5); a transposition is needed. This paper explores a new set of formulas that, in fact, do produce all of the triples …

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Fiber Bundle Description Of Flow And Nonlinear Hydrodynamics On Circles, Andrei Ludu Apr 2008

Fiber Bundle Description Of Flow And Nonlinear Hydrodynamics On Circles, Andrei Ludu

Publications

We introduce a differential geometry description of the path lines, stream lines and particles contours in hydrodynamics. We present a generalized form of a Korteweg-de Vries type of equation for the exterior of a circle. Nonlinearities from the boundary conditions, surface tension and the Euler equations are taken into account, but the flow is considered inviscid and irrotational. For the circular case we describe the traveling waves shapes, solitons and the particles trajectories.

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Studies In Free Module And It's Basis, Hsu-Chia Chen Jan 2008

Studies In Free Module And It's Basis, Hsu-Chia Chen

Theses Digitization Project

The purpose of this project was to study some basic properties of free modules over a ring. A module with a basis is called a free module and a free module over a division ring (or field) is called a vector space. We show every vector has a basis and any two bases of a vector space have same cardinality. However, a free module over an arbitrary ring (with identity) does not have this property.

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The Bar-Natan Skein Module Of The Solid Torus And The Homology Of (N,N) Springer Varieties, Heather M. Russell Jan 2008

The Bar-Natan Skein Module Of The Solid Torus And The Homology Of (N,N) Springer Varieties, Heather M. Russell

Department of Math & Statistics Faculty Publications

This paper establishes an isomorphism between the Bar-Natan skein module of the solid torus with a particular boundary curve system and the homology of the (n, n) Springer variety. The results build on Khovanov's work with crossingless matchings and the cohomology of the (n, n) Springer variety. We also give a formula for comultiplication in the Bar-Natan skein module for this specific three-manifold and boundary curve system.

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Super Linear Algebra, Florentin Smarandache, W.B. Vasantha Kandasamy Jan 2008

Super Linear Algebra, Florentin Smarandache, W.B. Vasantha Kandasamy

Branch Mathematics and Statistics Faculty and Staff Publications

In this book, the authors introduce the notion of Super linear algebra and super vector spaces using the definition of super matrices defined by Horst (1963). This book expects the readers to be well-versed in linear algebra. Many theorems on super linear algebra and its properties are proved. Some theorems are left as exercises for the reader. These new class of super linear algebras which can be thought of as a set of linear algebras, following a stipulated condition, will find applications in several fields using computers. The authors feel that such a paradigm shift is essential in this computerized …

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N-Linear Algebra Of Type Ii, Florentin Smarandache, W.B. Vasantha Kandasamy Jan 2008

N-Linear Algebra Of Type Ii, Florentin Smarandache, W.B. Vasantha Kandasamy

Branch Mathematics and Statistics Faculty and Staff Publications

This book is a continuation of the book n-linear algebra of type I and its applications. Most of the properties that could not be derived or defined for n-linear algebra of type I is made possible in this new structure: n-linear algebra of type II which is introduced in this book. In case of n-linear algebra of type II, we are in a position to define linear functionals which is one of the marked difference between the n-vector spaces of type I and II. However all the applications mentioned in n-linear algebras of type I can be appropriately extended to …

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N- Linear Algebra Of Type I And Its Applications, Florentin Smarandache, W.B. Vasantha Kandasamy Jan 2008

N- Linear Algebra Of Type I And Its Applications, Florentin Smarandache, W.B. Vasantha Kandasamy

Branch Mathematics and Statistics Faculty and Staff Publications

With the advent of computers one needs algebraic structures that can simultaneously work with bulk data. One such algebraic structure namely n-linear algebras of type I are introduced in this book and its applications to n-Markov chains and n-Leontief models are given. These structures can be thought of as the generalization of bilinear algebras and bivector spaces. Several interesting n-linear algebra properties are proved. This book has four chapters. The first chapter just introduces n-group which is essential for the definition of nvector spaces and n-linear algebras of type I. Chapter two gives the notion of n-vector spaces and several …

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How Geometer’S Sketchpad Improves Student Learning, William George Awe Oct 2007

How Geometer’S Sketchpad Improves Student Learning, William George Awe

Mathematics Graduate Theses

This study investigated whether dynamic software improves learning and reviews different types of dynamic software. The study then narrows its focus to one type of dynamic software, Geometer’s Sketchpad and studies how Geometer’s Sketchpad, in itself, improves student learning. The researcher identified what dynamic software is, the importance of dynamic software and different types of dynamic software. The researcher also identifies how dynamic software is utilized in schools and researches how to improve the use of dynamic software in schools. Dynamic software, and Geometer’s Sketchpad, In particular, was found to improve learning across grade levels and with different levels of …

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Isomorphisms Of Elliptic Curves Over Extensions Of Finite Fields, Mathew Niemerg Jul 2007

Isomorphisms Of Elliptic Curves Over Extensions Of Finite Fields, Mathew Niemerg

Mathematical Sciences Technical Reports (MSTR)

Our main interest lies in exploring isomorphisms of elliptic curves. In particular, we focus on two curves defined over a base field and look at which extension fields the curves are isomorphic over. Elliptic curves have a fascinating structure behind them. This structure allows for much to be explored and studied.

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Mordell-Weil Theorem And The Rank Of Elliptical Curves, Hazem Khalfallah Jan 2007

Mordell-Weil Theorem And The Rank Of Elliptical Curves, Hazem Khalfallah

Theses Digitization Project

The purpose of this thesis is to give a detailed group theoretic proof of the rank formula in a more general setting. By using the proof of Mordell-Weil theorem, a formula for the rank of the elliptical curves in certain cases over algebraic number fields can be obtained and computable.

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Primary Decomposition Of Ideals In A Ring, Sola Oyinsan Jan 2007

Primary Decomposition Of Ideals In A Ring, Sola Oyinsan

Theses Digitization Project

The concept of unique factorization was first recognized in the 1840s, but even then, it was still fairly believed to be automatic. The error of this assumption was exposed largely through attempts to prove Pierre de Fermat's, 1601-1665, last theorem. Once mathematicians discovered that this property did not always hold, it was only natural for them to try to search for the strongest available alternative. Thus began the attempt to generalize unique factorization. Using the ascending chain condition on principle ideals, we will show the conditions under which a ring is a unique factorization domain.

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Collected Papers Vol. 1, Florentin Smarandache Jan 2007

Collected Papers Vol. 1, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

No abstract provided.

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The Elementary Theory Of Normed Linear Spaces And Linear Functionals, Suresh Eswarthasan May 2006

The Elementary Theory Of Normed Linear Spaces And Linear Functionals, Suresh Eswarthasan

Renée Crown University Honors Thesis Projects - All

Abstract not Included

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The Local Gromov–Witten Invariants Of Configurations Of Rational Curves, Dagan Karp, Chiu-Chu Melissa Liu, Marcos Mariño Mar 2006

The Local Gromov–Witten Invariants Of Configurations Of Rational Curves, Dagan Karp, Chiu-Chu Melissa Liu, Marcos Mariño

All HMC Faculty Publications and Research

We compute the local Gromov–Witten invariants of certain configurations of rational curves in a Calabi–Yau threefold. These configurations are connected subcurves of the “minimal trivalent configuration”, which is a particular tree of ℙ1’s with specified formal neighborhood. We show that these local invariants are equal to certain global or ordinary Gromov–Witten invariants of a blowup of ℙ3 at points, and we compute these ordinary invariants using the geometry of the Cremona transform. We also realize the configurations in question as formal toric schemes and compute their formal Gromov–Witten invariants using the mathematical and physical theories of the …

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Injective Modules And Prime Ideals Of Universal Enveloping Algebras, Jorg Feldvoss Jan 2006

Injective Modules And Prime Ideals Of Universal Enveloping Algebras, Jorg Feldvoss

University Faculty and Staff Publications

In this paper we study injective modules over universal enveloping algebras of finite-dimensional Lie algebras over fields of arbitrary characteristic. Most of our results are dealing with fields of prime characteristic but we also elaborate on some of their analogues for solvable Lie algebras over fields of characteristic zero. It turns out that analogous results in both cases are often quite similar and resemble those familiar from commutative ring theory.

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Intrinsic Linking And Knotting Of Graphs In Arbitrary 3–Manifolds, Erica Flapan, Hugh Howards, Don Lawrence, Blake Mellor Jan 2006

Intrinsic Linking And Knotting Of Graphs In Arbitrary 3–Manifolds, Erica Flapan, Hugh Howards, Don Lawrence, Blake Mellor

Pomona Faculty Publications and Research

We prove that a graph is intrinsically linked in an arbitrary 3–manifold M if and only if it is intrinsically linked in S3. Also, assuming the Poincaré Conjecture, we prove that a graph is intrinsically knotted in M if and only if it is intrinsically knotted in S3.

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Linked Exact Triples Of Triangulated Categories And A Calculus Of T-Structures, Michael Berg Jan 2006

Linked Exact Triples Of Triangulated Categories And A Calculus Of T-Structures, Michael Berg

Mathematics, Statistics and Data Science Faculty Works

We introduce a new formalism of exact triples of triangulated categories arranged in certain types of diagrams. We prove that these arrangements are well-behaved relative to the process of gluing and ungluing t-structures defined on the indicated categories and we connect our con. structs to· a problem (from number theory) involving derived categories. We also briefly address a possible connection with a result of R. Thomason.

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