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Articles 19051 - 19080 of 27485

Full-Text Articles in Physical Sciences and Mathematics

Solving The P-Median Problem With Insights From Discrete Vector Quantization, Gino J. Lim, Allen Holder, Josh Reese Aug 2009

Solving The P-Median Problem With Insights From Discrete Vector Quantization, Gino J. Lim, Allen Holder, Josh Reese

Mathematical Sciences Technical Reports (MSTR)

The goals of this paper are twofold. First, we formally equate the p-median problem from facility location to the optimal design of a vector quantizer. Second, we use the equivalence to show that the Maranzana Algorithm can be interpreted as a projected Lloyd Algorithm, a fact that improves complexity. Numerical results verify significant improvements in run-time.

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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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A Decomposition Of The Pure Parsimony Problem, Allen Holder, Thomas M. Langley Aug 2009

A Decomposition Of The Pure Parsimony Problem, Allen Holder, Thomas M. Langley

Mathematical Sciences Technical Reports (MSTR)

We partially order a collection of genotypes so that we can represent the problem of inferring the least number of haplotypes in terms of substructures we call g-lattices. This representation allows us to prove that if the genotypes partition into chains with certain structure, then the NP-Hard problem can be solved efficiently. Even without the specified structure, the decomposition shows how to separate the underlying integer programming model into smaller models.

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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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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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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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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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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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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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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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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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An Economical Model With Allee Effect, Rafael Luís, Saber Elaydi, Henrique Oliveira Aug 2009

An Economical Model With Allee Effect, Rafael Luís, Saber Elaydi, Henrique Oliveira

Mathematics Faculty Research

The Marx model for the profit rate r depending on the exploitation rate e and on the organic composition of the capital k is studied using a dynamical approach. Supposing both e(t) and k(t) are continuous functions of time we derive a law for r(t) in the long term. Depending upon the hypothesis set on the growth of k(t) and e(t) in the long term, r(t) can fall to zero or remain constant. This last case contradicts the classical hypothesis of Marx …

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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

Department of 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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A Clustering Approach For Optimizing Beam Angles In Imrt Planning, Gino J. Lim, Allen Holder, Josh Reese Aug 2009

A Clustering Approach For Optimizing Beam Angles In Imrt Planning, Gino J. Lim, Allen Holder, Josh Reese

Mathematical Sciences Technical Reports (MSTR)

In this paper we introduce a p-median problem based clustering heuristic for selecting efficient beam angles for intensity-modulated radiation therapy. The essence of the method described here is the clustering of beam angles according to probability that an angle will be observed in the final solution and similarities among different angles and the selection of a representative angle from each of the p resulting cluster cells. We conduct experiments using several combinations of modeling parameters to find the conditions where the heuristic best performs. We found a combination of such parameters that outperformed all other parameters on three of the …

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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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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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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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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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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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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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Some Congruence Modulo 2 Statements Of Primitive Conway Vassiliev Invariants., James M. Dawson Aug 2009

Some Congruence Modulo 2 Statements Of Primitive Conway Vassiliev Invariants., James M. Dawson

Masters Theses

Polynomial knot invariants can often be used to define Vassiliev invariants on singu- lar knots. Here Vassiliev invariants form the Conway, Jones, HOMFLY, and Kauffman polynomials are explored. Also, some explanation is given about how symbols of the Jones and Conway polynomial can evaluated on suitable chord diagrams. These in- variants are further used to find expressions that are congruent modulo 2 to some low degree invariants derived from the Primitive Conway polynomial.

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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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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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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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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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Small And Large Scale Limits Of Multifractal Stochastic Processes With Applications, Jennifer Laurie Sinclair Aug 2009

Small And Large Scale Limits Of Multifractal Stochastic Processes With Applications, Jennifer Laurie Sinclair

Doctoral Dissertations

Various classes of multifractal processes, that is processes that display different properties at different scales, are studied. Most of the processes examined in this work exhibit stable trends at small scales and Gaussian trends at large scales, although the opposite can also occur. Many natural phenomena exhibit a fractal structure depending on some scaling factor, such as space or time. Thus, these types of processes have many useful modeling applications, including Biology and Economics. First, generalized tempered stable processes are defined and studied, following the original work on tempered stable processes by Jan Rosinski [16]. Generalized tempered stable processes encompass …

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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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