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2009

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Articles 121 - 150 of 693

Full-Text Articles in Mathematics

Compression Theorems For Periodic Tilings And Consequences, Arthur T. Benjamin, Alex K. Eustis '06, Mark A. Shattuck Aug 2009

Compression Theorems For Periodic Tilings And Consequences, Arthur T. Benjamin, Alex K. Eustis '06, Mark A. Shattuck

All HMC Faculty Publications and Research

We consider a weighted square-and-domino tiling model obtained by assigning real number weights to the cells and boundaries of an n-board. An important special case apparently arises when these weights form periodic sequences. When the weights of an nm-tiling form sequences having period m, it is shown that such a tiling may be regarded as a meta-tiling of length n whose weights have period 1 except for the first cell (i.e., are constant). We term such a contraction of the period in going from the longer to the shorter tiling as "period compression". It turns out that …

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Markovian Systems Of Transition Expectations, Volkmar Liebscher, Michael Skeide Aug 2009

Markovian Systems Of Transition Expectations, Volkmar Liebscher, Michael Skeide

Communications on Stochastic Analysis

No abstract provided.

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Using Weights For The Description Of States Of Boson Systems, Volkmar Liebscher Aug 2009

Using Weights For The Description Of States Of Boson Systems, Volkmar Liebscher

Communications on Stochastic Analysis

No abstract provided.

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Generating Functions Of Jacobi Polynomials, Izumi Kubo Aug 2009

Generating Functions Of Jacobi Polynomials, Izumi Kubo

Communications on Stochastic Analysis

No abstract provided.

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Generalized Cauchy-Stieltjes Transforms Of Some Beta Distributions, Nizar Demni Aug 2009

Generalized Cauchy-Stieltjes Transforms Of Some Beta Distributions, Nizar Demni

Communications on Stochastic Analysis

No abstract provided.

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Unbounded Positive Solutions Of Nonlinear Parabolic Itô Equations, Pao-Liu Chow Aug 2009

Unbounded Positive Solutions Of Nonlinear Parabolic Itô Equations, Pao-Liu Chow

Communications on Stochastic Analysis

No abstract provided.

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Manipulatives In Mathematics Instruction, Jessica Strom Aug 2009

Manipulatives In Mathematics Instruction, Jessica Strom

Mathematics Graduate Theses

This paper is a review of research pertaining to the use of manipulatives in middle and secondary school mathematics instruction. It covers the research on the rationale for using manipulatives, the psychology behind learning with manipulatives, the common mistakes when teaching with manipulatives, and the suggested process to follow when using manipulatives in the classroom. There is a large amount of research and information on manipulatives in the classroom. One of the most prevalent topics addresses that the concrete characteristics of manipulatives allow students to progress through a natural learning process on their way to an abstract understanding of mathematical …

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Markovian Properties Of The Pauli-Fierz Model, Ameur Dhahri Aug 2009

Markovian Properties Of The Pauli-Fierz Model, Ameur Dhahri

Communications on Stochastic Analysis

No abstract provided.

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Representations Of The Gegenbauer Oscillator Algebra And The Overcompleteness Of Sequences Of Nonlinear Coherent States, Abdessatar Barhoumi Aug 2009

Representations Of The Gegenbauer Oscillator Algebra And The Overcompleteness Of Sequences Of Nonlinear Coherent States, Abdessatar Barhoumi

Communications on Stochastic Analysis

No abstract provided.

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Local Time For Gaussian Processes As An Element Of Sobolev Space, Alexey Rudenko Aug 2009

Local Time For Gaussian Processes As An Element Of Sobolev Space, Alexey Rudenko

Communications on Stochastic Analysis

No abstract provided.

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Infimal Convolutions And Lipschitzian Properties Of Subdifferentials For Prox-Regular Functions In Hilbert Spaces, Miroslav Bačák, Jonathan M. Borwein, Andrew Eberhard, Boris S. Mordukhovich Aug 2009

Infimal Convolutions And Lipschitzian Properties Of Subdifferentials For Prox-Regular Functions In Hilbert Spaces, Miroslav Bačák, Jonathan M. Borwein, Andrew Eberhard, Boris S. Mordukhovich

Mathematics Research Reports

In this paper we study infimal convolutions of extended-real-valued functions in Hilbert spaces paying a special attention to a rather broad and remarkable class of prox-regular functions. Such functions have been well recognized as highly important in many aspects of variational analysis and its applications in both finite-dimensional and infinite-dimensional settings. Based on advanced variational techniques, we discover some new sub differential properties of infima! convolutions and apply them to the study of Lipschitzian behavior of subdifferentials for prox-regular functions in Hilbert spaces. It is shown, in particular, that the fulfillment of a natural Lipschitz-like property for (set-valued) sub differentials …

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Fan Cohomology And Equivariant Chow Rings Of Toric Varieties, Mu-Wan Huang Aug 2009

Fan Cohomology And Equivariant Chow Rings Of Toric Varieties, Mu-Wan Huang

Department of Mathematics: Dissertations, Theses, and Student Research

Toric varieties are varieties equipped with a torus action and constructed from cones and fans. In the joint work with Suanne Au and Mark E. Walker, we prove that the equivariant K-theory of an affine toric variety constructed from a cone can be identified with a group ring determined by the cone. When a toric variety X(Δ) is smooth, we interpret equivariant K-groups as presheaves on the associated fan space Δ. Relating the sheaf cohomology groups to equivariant K-groups via a spectral sequence, we provide another proof of a theorem of Vezzosi and Vistoli: equivariant K …

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Some Implications Of The Wp-Bailey Tree, James Mclaughlin, Peter Zimmer Aug 2009

Some Implications Of The Wp-Bailey Tree, James Mclaughlin, Peter Zimmer

Mathematics Faculty Publications

We consider a special case of a WP-Bailey chain of George Andrews, and use it to derive a number of curious transformations of basic hypergeometric series. We also derive two new WP-Bailey pairs, and use them to derive some new transformations for basic hypergeometric series. Finally, we briefly consider the implications of WP-Bailey pairs (αn(a, k), βn(a, k)), in which αn(a, k) is independent of k, for generalizations of identities of the Rogers-Ramanujan type.

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Cyclic Shifts Of The Van Der Corput Set, Dmitriy Bilyk Aug 2009

Cyclic Shifts Of The Van Der Corput Set, Dmitriy Bilyk

Faculty Publications

In 1980, K. Roth showed that the expected value of the L2 discrepancy of the cyclic shifts of the N-point van der Corput set is bounded by a constant multiple of √logN, thus guaranteeing the existence of a shift with asymptotically minimal L2 discrepancy. In the present paper, we construct a specific example of such a shift.

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Grades 7-8 Mean, Median, And Mode, Rich Miller Iii Aug 2009

Grades 7-8 Mean, Median, And Mode, Rich Miller Iii

Math

This lesson is a math lesson for seventh and eighth grade students on mean, medium, and mode. Through this lesson students will be able to understand the measures of central tendency and their definitions, how to calculate them and what steps are involved, and how the theories can be applied on real life. In this lesson, students are tiered by ability and are able to pick a project based off of their interest and the math concept they are working on. Each activity has a tiered task card to guide the students.

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Transparency In Formal Proof, Cap Petschulat Aug 2009

Transparency In Formal Proof, Cap Petschulat

Boise State University Theses and Dissertations

The oft-emphasized virtue of formal proof is correctness; a machine-checked proof adds greatly to our confidence in a result. But the rigors of formalization give rise to another possible virtue, namely clarity. Given the state of the art, clarity and formality are at odds: complexity of formalization obscures the content of proof. To address this, we develop a notion of proof strategies which extend the well-known notion of proof tactics. Beginning with the foundations of logic, we describe the methods and structures necessary to implement proof strategies, concluding with a proof-of-concept implementation in CheQED, a web-based proof assistant.

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Solvability Characterizations Of Pell Like Equations, Jason Smith Aug 2009

Solvability Characterizations Of Pell Like Equations, Jason Smith

Boise State University Theses and Dissertations

Pell's equation has intrigued mathematicians for centuries. First stated as Archimedes' Cattle Problem, Pell's equation, in its most general form, X2 – P • Y2 = 1, where P is any square free positive integer and solutions are pairs of integers, has seen many approaches but few general solutions. The eleventh century Indian mathematician Bhaskara solved X2 – 61 • Y2 = 1 and, in response to Fermat's challenge, Wallis and Brouncker gave solutions to X2 – 151 • Y2 = 1 and X2 –313 • Y2 = 1. Fermat claimed to …

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Generalized Mean Curvature Flow In Carnot Groups, Luca Capogna, Giovanna Citti Aug 2009

Generalized Mean Curvature Flow In Carnot Groups, Luca Capogna, Giovanna Citti

Mathematics Sciences: Faculty Publications

In this paper we study the generalized mean curvature flow of sets in the sub-Riemannian geometry of Carnot groups. We extend to our context the level sets method and the weak (viscosity) solutions introduced in the Euclidean setting in [4] and [12]. We establish two special cases of the comparison principle, existence, uniqueness and basic geometric properties of the flow.

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Analytical And Computational Studies Of Magneto-Convection In Solidifying Mushy Layer, Mallikarjunaiah Siddapura Muddamallappa Aug 2009

Analytical And Computational Studies Of Magneto-Convection In Solidifying Mushy Layer, Mallikarjunaiah Siddapura Muddamallappa

Theses and Dissertations - UTB/UTPA

Natural convection in solidifying binary media is of great interest due to it's applications in material processing and crystal growth industries. Convective flows between the layers of melt during alloy solidification is known to produce mechanical imperfections such as freckle's. Hence it is important to investigate the criterion for freckling and discover the means of suppressing it. A mushy layer, which has both solid and fluid components and is formed between underlying solid and overlying liquid, is known to produce chimneys, which are narrow, vertical vents, devoid of solid. We consider the problem of magneto-convection in a horizontal mushy layer …

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Two-Dimensional Wigner-Ville Transforms And Their Basic Properties, Bheemaiah Veena Shankara Narayana Rao Aug 2009

Two-Dimensional Wigner-Ville Transforms And Their Basic Properties, Bheemaiah Veena Shankara Narayana Rao

Theses and Dissertations - UTB/UTPA

This thesis deals with Wigner-Ville transforms and their basic properties. The Wigner-Ville transforms are a non-linear transform which constitute an important tool in nonstationary signal analysis. Wigner-Ville transforms in one dimension and their basic properties are discussed here. Special attention is given to formulation of two dimensional Wigner-Ville transform, its inversion formula and some of their basic properties. Some applications of Wigner-Ville transforms are also briefly discussed.

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Reaction-Diffusion Systems With A Nonlinear Rate Of Growth, Yubing Wan Aug 2009

Reaction-Diffusion Systems With A Nonlinear Rate Of Growth, Yubing Wan

Theses and Dissertations - UTB/UTPA

In the literature there are quite a few elegant approaches which have been proposed to find (he first integrals of nonlinear differential equations. Recently, the modified Prelle-Singer method for finding the first integrals of second-order nonlinear ordinary differential equations (ODEs) has attracted considerable attention. Many researchers used this method to derive the first integrals to various systems. In this thesis, we are concerned with the first integrals for reaction-diffusion systems with a nonlinear rate of growth. Under certain parametric conditions we express the first integrals explicitly by applying an analytical method as well as the modified Prelle-Singer method.

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Rogers-Ramanujan Computer Searches, James Mclaughlin, Andrew Sills, Peter Zimmer Aug 2009

Rogers-Ramanujan Computer Searches, James Mclaughlin, Andrew Sills, Peter Zimmer

Mathematical Sciences: Faculty Publications

We describe three computer searches (in PARI/GP, Maple, and Mathematica, respectively) which led to the discovery of a number of identities of Rogers–Ramanujan type and identities of false theta functions.

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Integrable Equations With Non-Smooth Solitons, Xianqi Li Aug 2009

Integrable Equations With Non-Smooth Solitons, Xianqi Li

Theses and Dissertations - UTB/UTPA

In this thesis, we present a class of integrable equations with non-smooth soliton solutions. In particular, we derive the bi-Hamiltonian structure and Lax pair of the equation pt = bux + \[{u2 — u1)p]x,p = u — uxx, which guarantee its integrability. Another interesting integrable equation we study is (=Jff!i)t = 2uux, which is exactly the first member of the negative KdV hierarchy. Through traveling wave setting arid phase step analysis, we obtain non-smooth soliton solutions of these integrable equations under different boundary condition at infinities. These equations were shown to have peaked soliton (peakon), "W/M-shape" peakon or cusped soliton …

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Structure And Properties Of Maximal Outerplanar Graphs., Benjamin Allgeier Aug 2009

Structure And Properties Of Maximal Outerplanar Graphs., Benjamin Allgeier

Electronic Theses and Dissertations

Outerplanar graphs are planar graphs that have a plane embedding in which each vertex lies on the boundary of the exterior region. An outerplanar graph is maximal outerplanar if the graph obtained by adding an edge is not outerplanar. Maximal outerplanar graphs are also known as triangulations of polygons. The spine of a maximal outerplanar graph G is the dual graph of G without the vertex that corresponds to the exterior region. In this thesis we study metric properties involving geodesic intervals, geodetic sets, Steiner sets, different concepts of boundary, and also relationships between the independence numbers and domination numbers …

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A Dna Approach To The Road-Coloring Problem, Arindam Roy Aug 2009

A Dna Approach To The Road-Coloring Problem, Arindam Roy

Theses and Dissertations - UTB/UTPA

The Road-Coloring Problem in graph theory can be stated as follows: Is any irreducible aperiodic directed graph with constant outdegree 2 road-colorable? In other words, does such a graph have a synchronizing instruction? That is to say: can we label (or color) the two outgoing edges at each vertex, one with “b” or blue color and the other with “r” or red color, in such a manner that there will be an instruction in the form of a finite sequence in “b”s and “r”s (example: rrbrbbbr) such that this instruction will lead each vertex to the same “target” vertex? This …

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Statistical Investigation Of Structure In The Discrete Logarithm, Andrew Hoffman Jul 2009

Statistical Investigation Of Structure In The Discrete Logarithm, Andrew Hoffman

Mathematical Sciences Technical Reports (MSTR)

The absence of an efficient algorithm to solve the Discrete Logarithm Problem is often exploited in cryptography. While exponentiation with a modulus is extremely fast with a modern computer, the inverse is decidedly not. At the present time, the best algorithms assume that the inverse mapping is completely random. Yet there is at least some structure, and to uncover additional structure that may be useful in constructing or refining algorithms, statistical methods are employed to compare modular exponential mappings to random mappings. More concretely, structure will be defined by representing the mappings as functional graphs and using parameters from graph …

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Discrete Logarithm Over Composite Moduli, Marcus L. Mace Jul 2009

Discrete Logarithm Over Composite Moduli, Marcus L. Mace

Mathematical Sciences Technical Reports (MSTR)

In an age of digital information, security is of utmost importance. Many encryption schemes, such as the Diffie-Hellman Key Agreement and RSA Cryptosystem, use a function which maps x to y by a modular power map with generator g. The inverse of this function - trying to find x from y - is called the discrete logarithm problem. In most cases, n is a prime number. In some cases, however, n may be a composite number. In particular, we will look at when n = p^b for a prime p. We will show different techniques of obtaining graphs of this …

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Structural Properties Of Power Digraphs Modulo N, Joseph Kramer-Miller Jul 2009

Structural Properties Of Power Digraphs Modulo N, Joseph Kramer-Miller

Mathematical Sciences Technical Reports (MSTR)

We define G(n, k) to be a directed graph whose set of vertices is {0, 1, ..., n−1} and whose set of edges is defined by a modular relation. We say that G(n, k) is symmetric of order m if we can partition G(n, k) into subgraphs, each containing m components, such that all the components in a subgraph are isomorphic. We develop necessary and sufficient conditions for G(n, k) to contain symmetry when n is odd and square-free. Additionally, we use group theory to describe the structural properties of the subgraph of G(n, k) containing only those vertices relatively …

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Versal Deformations Of Leibniz Algebra., Ashis Mandal Dr. Jul 2009

Versal Deformations Of Leibniz Algebra., Ashis Mandal Dr.

Doctoral Theses

No abstract provided.

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Isomorphism Of Schwartz Spaces Under Fourier Transform., Joydip Jana Dr. Jul 2009

Isomorphism Of Schwartz Spaces Under Fourier Transform., Joydip Jana Dr.

Doctoral Theses

Classical Fourier analysis derives much of its power from the fact that there are three function spaces whose images under the Fourier transform can be exactly determined. They are the Schwartz space, the L2 space and the space of all C ∞ functions of compact support. The determination of the image is obtained from the definition in the case of Schwartz space, through the Plancherel theorem for the L 2space and through the Paley-Wiener theorem for the other space.In harmonic analysis of semisimple Lie groups, function spaces on various restricted set-ups are of interest. Among the multitude of these spaces …

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