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2009

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Articles 151 - 180 of 693

Full-Text Articles in Mathematics

On The Naturality Of The Spectral Sequence From Khovanov Homology To Heegaard Floer Homology, J. Elisenda Grigsby, Stephan M. Wehrli Jul 2009

On The Naturality Of The Spectral Sequence From Khovanov Homology To Heegaard Floer Homology, J. Elisenda Grigsby, Stephan M. Wehrli

Mathematics - All Scholarship

Ozsvath and Szabo have established an algebraic relationship, in the form of a spectral sequence, between the reduced Khovanov homology of (the mirror of) a link L in S3 and the Heegaard Floer homology of its double-branched cover. This relationship has since been recast by the authors as a specific instance of a broader connection between Khovanov- and Heegaard Floer-type homology theories, using a version of Heegaard Floer homology for sutured manifolds developed by Juhasz. In the present work we prove the naturality of the spectral sequence under certain elementary TQFT operations, using a generalization of Juhasz's surface decomposition …

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Khovanov Homology, Sutured Floer Homology, And Annular Links, J. Elisenda Grigsby, Stephan M. Wehrli Jul 2009

Khovanov Homology, Sutured Floer Homology, And Annular Links, J. Elisenda Grigsby, Stephan M. Wehrli

Mathematics - All Scholarship

Lawrence Roberts, extending the work of Ozsvath-Szabo, showed how to associate to a link, L, in the complement of a fixed unknot, B in S3, a spectral sequence from the Khovanov homology of a link in a thickened annulus to the knot Floer homology of the preimage of B inside the double-branched cover of L. In a previous paper, we extended Ozsvath-Szabo's spectral sequence in a different direction, constructing for each knot K in S3 and each positive integer n, a spectral sequence from Khovanov's categorification of the reduced, n-colored Jones polynomial to the sutured Floer homology …

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Using Works Of Visual Art To Teach Matrix Transformations, James Luke Akridge, Rachel Bowman, Peter Hamburger, Bruce Kessler Jul 2009

Using Works Of Visual Art To Teach Matrix Transformations, James Luke Akridge, Rachel Bowman, Peter Hamburger, Bruce Kessler

Mathematics Faculty Publications

The authors present a modern technique for teaching matrix transformations on $\R^2$ that incorporates works of visual art and computer programming. Two of the authors were undergraduate students in Dr. Hamburger's linear algebra class, where this technique was implemented as a special project for the students. The two students generated the images seen in this paper, and the movies that can be found on the accompanying webpage www.wku.edu/\~{\space}bruce.kessler/.

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Quasiplurisubharmonic Green Functions, Dan Coman, Vincent Guedj Jul 2009

Quasiplurisubharmonic Green Functions, Dan Coman, Vincent Guedj

Mathematics - All Scholarship

Given a compact Kahler manifold X, a quasiplurisubharmonic function is called a Green function with pole at p in X if its Monge-Ampere measure is supported at p. We study in this paper the existence and properties of such functions, in connection to their singularity at p. A full characterization is obtainedin concrete cases, such as (multi)projective spaces.

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Period-Doubling Bifurcation In An Array Of Coupled Stochastically Excitable Elements Subjected To Global Periodic Forcing, Robert Rovetti Jul 2009

Period-Doubling Bifurcation In An Array Of Coupled Stochastically Excitable Elements Subjected To Global Periodic Forcing, Robert Rovetti

Mathematics, Statistics and Data Science Faculty Works

The collective behaviors of coupled, stochastically excitable elements subjected to global periodic forcing are investigated numerically and analytically. We show that the whole system undergoes a period-doubling bifurcation as the driving period decreases, while the individual elements still exhibit random excitations. Using a mean-field representation, we show that this macroscopic bifurcation behavior is caused by interactions between the random excitation, the refractory period, and recruitment (spatial cooperativity) of the excitable elements.

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Z-Transform Methods For The Optimal Design Of One-Dimensional Layered Elastic Media, Ani P. Velo, George A. Gazonas, Takanobu Ameya Jul 2009

Z-Transform Methods For The Optimal Design Of One-Dimensional Layered Elastic Media, Ani P. Velo, George A. Gazonas, Takanobu Ameya

Mathematics: Faculty Scholarship

In this work, we develop a finite trigonometric series representation for the stress in a multilayered Goupillaud-type elastic strip subjected to transient Heaviside loading on one end while the other end is held fixed. This representation is achieved by means of the z-transform method and involves the so-called base angles. Generally, different layered designs could share the same set of base angles, and the more layers the design has, the more base angles are expected. Necessary conditions for the base angles and design parameters for any given design are described. As a result of the stress representation, we are able …

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Four-Body Problem With Collision Singularity, Duokui Yan Jul 2009

Four-Body Problem With Collision Singularity, Duokui Yan

Theses and Dissertations

In this dissertation, regularization of simultaneous binary collision, existence of a Schubart-like periodic orbit, existence of a planar symmetric periodic orbit with multiple simultaneous binary collisions, and their linear stabilities are studied. The detailed background of those problems is introduced in chapter 1. The singularities of simultaneous binary collision in the collinear four-body problem is regularized in chapter 2. We use canonical transformations to collectively analytically continue the singularities of the simultaneous binary collision solutions in both the decoupled case and the coupled case. All the solutions are found and more importantly, we find a crucial first integral which describes …

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Fixed Point Theory For Admissible Type Maps With Applications, Ravi P. Agarwal, Donal O'Regan Jul 2009

Fixed Point Theory For Admissible Type Maps With Applications, Ravi P. Agarwal, Donal O'Regan

Mathematics and System Engineering Faculty Publications

We present new Leray-Schauder alternatives, Krasnoselskii and Lefschetz fixed point theory for multivalued maps between Fréchet spaces. As an application we show that our results are directly applicable to establish the existence of integral equations over infinite intervals. Copyright © 2009 R. P. Agarwal and D. O'Regan

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The Research On Optimization Of Liner Route Between China To Middle East, Tingyi Chen Jul 2009

The Research On Optimization Of Liner Route Between China To Middle East, Tingyi Chen

World Maritime University Dissertations

No abstract provided.

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Marketing Analysis Of The Chinese Coffee Market : Suggestions For A Logistic System For The Colombian Coffee Exporters, Soraya Margarita Herrera Jaramillo Jul 2009

Marketing Analysis Of The Chinese Coffee Market : Suggestions For A Logistic System For The Colombian Coffee Exporters, Soraya Margarita Herrera Jaramillo

World Maritime University Dissertations

No abstract provided.

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The Research On Risk Evaluation Of Shanghai Lng Import Program, Chao Lin Jul 2009

The Research On Risk Evaluation Of Shanghai Lng Import Program, Chao Lin

World Maritime University Dissertations

No abstract provided.

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The Construction And Development Of Shanghai International Shipping Center, Shimin Wang Jul 2009

The Construction And Development Of Shanghai International Shipping Center, Shimin Wang

World Maritime University Dissertations

No abstract provided.

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The Feasibility Analysis Of The Third Euro-Asia Continental Bridge, Tongyou Weng Jul 2009

The Feasibility Analysis Of The Third Euro-Asia Continental Bridge, Tongyou Weng

World Maritime University Dissertations

No abstract provided.

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New Eurasian Continental Bridgehead Lianyungang, Qiaoqiao Wu Jul 2009

New Eurasian Continental Bridgehead Lianyungang, Qiaoqiao Wu

World Maritime University Dissertations

No abstract provided.

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Research On Value-At-Risk In International Crude Oil Shipping Market, Xiaoyin Cui Jul 2009

Research On Value-At-Risk In International Crude Oil Shipping Market, Xiaoyin Cui

World Maritime University Dissertations

No abstract provided.

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Research On Brand Strategies Of Cdl Company, Wei Gu Jul 2009

Research On Brand Strategies Of Cdl Company, Wei Gu

World Maritime University Dissertations

No abstract provided.

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Economic Approach Of Piracy Along The Maritime Silk Road And Cost Analysis Of The Northern Sea Route, Petros Kelaiditis Jul 2009

Economic Approach Of Piracy Along The Maritime Silk Road And Cost Analysis Of The Northern Sea Route, Petros Kelaiditis

World Maritime University Dissertations

No abstract provided.

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Asymptotic Dynamics Of Attractive-Repulsive Swarms, Andrew J. Leverentz '08, Chad M. Topaz, Andrew J. Bernoff Jul 2009

Asymptotic Dynamics Of Attractive-Repulsive Swarms, Andrew J. Leverentz '08, Chad M. Topaz, Andrew J. Bernoff

All HMC Faculty Publications and Research

We classify and predict the asymptotic dynamics of a class of swarming models. The model consists of a conservation equation in one dimension describing the movement of a population density field. The velocity is found by convolving the density with a kernel describing attractive-repulsive social interactions. The kernel’s first moment and its limiting behavior at the origin determine whether the population asymptotically spreads, contracts, or reaches steady state. For the spreading case, the dynamics approach those of the porous medium equation. The widening, compactly supported population has edges that behave like traveling waves whose speed, density, and slope we calculate. …

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Almost Avoiding Permutations, Robert Brignall, Shalosh B. Ekhad, Rebecca Smith, Vincent Vatter Jul 2009

Almost Avoiding Permutations, Robert Brignall, Shalosh B. Ekhad, Rebecca Smith, Vincent Vatter

Dartmouth Scholarship

The permutation π of length n, written in one-line notation as π (1)π (2)· · · π (n), is said to contain the permutation σ if π has a subsequence that is order isomorphic to σ, and each such subsequence is said to be an occurrence of σ in π or simply a σ pattern. For example, π = 491867532 contains σ = 51342 because of the subsequence π (2)π (3)π (5)π (6)π (9) = 91672. Permutation containment is easily seen to be a partial order on the set of all (finite) permutations, which we simply denote by ≤. If …

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The Expectation Of Transition Events On Finite-State Markov Chains, Jeremy Michael West Jul 2009

The Expectation Of Transition Events On Finite-State Markov Chains, Jeremy Michael West

Theses and Dissertations

Markov chains are a fundamental subject of study in mathematical probability and have found wide application in nearly every branch of science. Of particular interest are finite-state Markov chains; the representation of finite-state Markov chains by a transition matrix facilitates detailed analysis by linear algebraic methods. Previous methods of analyzing finite-state Markov chains have emphasized state events. In this thesis we develop the concept of a transition event and define two types of transition events: cumulative events and time-average events. Transition events generalize state events and provide a more flexible framework for analysis. We derive computable, closed-form expressions for the …

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Submodular Percolation, Graham R. Brightwell, Peter Winkler Jul 2009

Submodular Percolation, Graham R. Brightwell, Peter Winkler

Dartmouth Scholarship

Let $f:{\cal L}\to\mathbb{R}$ be a submodular function on a modular lattice ${\cal L}$; we show that there is a maximal chain ${\cal C}$ in ${\cal L}$ on which the sequence of values of f is minimal among all paths from 0 to 1 in the Hasse diagram of ${\cal L}$, in a certain well-behaved partial order on sequences of reals. One consequence is that the maximum value of f on ${\cal C}$ is minimized over all such paths—i.e., if one can percolate from 0 to 1 on lattice points X with $f(X)\le b$, then one can do so along a …

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The Orbifold Landau-Ginzburg Conjecture For Unimodal And Bimodal Singularities, Natalie Wilde Bergin Jul 2009

The Orbifold Landau-Ginzburg Conjecture For Unimodal And Bimodal Singularities, Natalie Wilde Bergin

Theses and Dissertations

The Orbifold Landau-Ginzburg Mirror Symmetry Conjecture states that for a quasihomogeneous singularity W and a group G of symmetries of W, there is a dual singularity WT and dual group GT such that the orbifold A-model of W/G is isomorphic to the orbifold B-model of WT/GT. The Landau-Ginzburg A-model is the Frobenius algebra HW,G constructed by Fan, Jarvis, and Ruan, and the B-model is the Orbifold Milnor ring of WT . The unorbifolded conjecture has been verified for Arnol'd's list of simple, unimodal and bimodal quasi-homogeneous singularities with G the maximal diagonal symmetry group by Priddis, Krawitz, Bergin, Acosta, et …

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Development Of Scoring Rubrics And Pre-Service Teachers Ability To Validate Mathematical Proofs, Timothy J. Middleton Jul 2009

Development Of Scoring Rubrics And Pre-Service Teachers Ability To Validate Mathematical Proofs, Timothy J. Middleton

Mathematics & Statistics ETDs

The basic aim of this exploratory research study was to determine if a specific instructional strategy, that of developing scoring rubrics within a collaborative classroom setting, could be used to improve pre-service teachers facility with proofs. During the study, which occurred in a course for secondary mathematics teachers, the primary focus was on creating and implementing a scoring rubric, rather than on direct instruction about proofs. In general, the study had very mixed results. Statistically, the quantitative data indicated no significant improvement occurred in participants' ability to validate proofs. However, the qualitative results and the considerable improvement by some participants …

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Some Congruence Properties Of Pell's Equation, Nathan C. Priddis Jul 2009

Some Congruence Properties Of Pell's Equation, Nathan C. Priddis

Theses and Dissertations

In this thesis I will outline the impact of Pell's equation on various branches of number theory, as well as some of the history. I will also discuss some recently discovered properties of the solutions of Pell's equation.

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Evans Function Computation, Blake H. Barker Jul 2009

Evans Function Computation, Blake H. Barker

Theses and Dissertations

In this thesis, we review the stability problem for traveling waves and discuss the Evans function, an emerging tool in the stability analysis of traveling waves. We describe some recent developments in the numerical computation of the Evans function and discuss STABLAB, an interactive MATLAB based tool box that we developed. In addition, we verify the Evans function for shock layers in Burgers equation and the p-system with and without capillarity, as well as pulses in the generalized Kortweg-de Vries (gKdV) equation. We conduct a new study of parallel shock layers in isentropic magnetohydrodynamics (MHD) obtaining results consistent with stability.

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Numerical Solutions For Stochastic Differential Equations And Some Examples, Yi Luo Jul 2009

Numerical Solutions For Stochastic Differential Equations And Some Examples, Yi Luo

Theses and Dissertations

In this thesis, I will study the qualitative properties of solutions of stochastic differential equations arising in applications by using the numerical methods. It contains two parts. In the first part, I will first review some of the basic theory of the stochastic calculus and the Ito-Taylor expansion for stochastic differential equations (SDEs). Then I will discuss some numerical schemes that come from the Ito-Taylor expansion including their order of convergence. In the second part, I will use some schemes to solve the stochastic Duffing equation, the stochastic Lorenz equation, the stochastic pendulum equation, and the stochastic equations which model …

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Properties Of The Zero Forcing Number, Kayla Denise Owens Jul 2009

Properties Of The Zero Forcing Number, Kayla Denise Owens

Theses and Dissertations

The zero forcing number is a graph parameter first introduced as a tool for solving the minimum rank problem, which is: Given a simple, undirected graph G, and a field F, let S(F,G) denote the set of all symmetric matrices A=[a_{ij}] with entries in F such that a_{ij} doess not equal 0 if and only if ij is an edge in G. Find the minimum possible rank of a matrix in S(F,G). It is known that the zero forcing number Z(G) provides an upper bound for the maximum nullity of a graph. I investigate properties of the zero forcing number, …

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Weighted Composition Operators From Logarithmic Bloch-Type Spaces To Bloch-Type Spaces, Stevo Stevic, Ravi P. Agarwal Jul 2009

Weighted Composition Operators From Logarithmic Bloch-Type Spaces To Bloch-Type Spaces, Stevo Stevic, Ravi P. Agarwal

Mathematics and System Engineering Faculty Publications

The boundedness and compactness of the weighted composition operators from to Bloch-type spaces are studied here. © 2009 S. Stević and R. P. Agarwal.

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Harmonic Functions On R-Covered Foliations And Group Actions On The Circle, Sergio Fenley, Renato Feres, Kamlesh Parwani Jul 2009

Harmonic Functions On R-Covered Foliations And Group Actions On The Circle, Sergio Fenley, Renato Feres, Kamlesh Parwani

Faculty Research and Creative Activity

Let (M,F) be a compact codimension-one foliated manifold whose leaves are equipped with Riemannian metrics, and consider continuous functions on M that are harmonic along the leaves of F. If every such function is constant on leaves we say that (M,F) has the Liouville property. Our main result is that codimension-one foliated bundles over compact negatively curved manifolds satisfy the Liouville property. Related results for R-covered foliations, as well as for discrete group actions and discrete harmonic functions, are also established.

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Harmonic Functions On R-Covered Foliations And Group Actions On The Circle, Sergio Fenley, Renato Feres, Kamlesh Parwani Jul 2009

Harmonic Functions On R-Covered Foliations And Group Actions On The Circle, Sergio Fenley, Renato Feres, Kamlesh Parwani

Faculty Research and Creative Activity

Let (M,F) be a compact codimension-one foliated manifold whose leaves are equipped with Riemannian metrics, and consider continuous functions on M that are harmonic along the leaves of F. If every such function is constant on leaves we say that (M,F) has the Liouville property. Our main result is that codimension-one foliated bundles over compact negatively curved manifolds satisfy the Liouville property. Related results for R-covered foliations, as well as for discrete group actions and discrete harmonic functions, are also established.

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