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Articles 5791 - 5820 of 7997

Full-Text Articles in Physical Sciences and Mathematics

Hamilton-Jacobi Theory For Optimal Control Problems On Stratified Domains, Richard Charles Barnard Jan 2010

Hamilton-Jacobi Theory For Optimal Control Problems On Stratified Domains, Richard Charles Barnard

LSU Doctoral Dissertations

This thesis studies optimal control problems on stratified domains. We first establish a known proximal Hamilton-Jacobi characterization of the value function for problems with Lipschitz dynamics. This background gives the motivation for our results for systems over stratified domains, which is a system with non-Lipschitz dynamics that were introduced by Bressan and Hong. We provide an example that shows their attempt to derive a Hamilton-Jacobi characterization of the value function is incorrect, and discuss the nature of their error. A new construction of a multifunction is introduced that possesses properties similar to those of a Lipschitz multifunction, and is used …

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Multigrid Methods For Maxwell's Equations, Jintao Cui Jan 2010

Multigrid Methods For Maxwell's Equations, Jintao Cui

LSU Doctoral Dissertations

In this work we study finite element methods for two-dimensional Maxwell's equations and their solutions by multigrid algorithms. We begin with a brief survey of finite element methods for Maxwell's equations. Then we review the related fundamentals, such as Sobolev spaces, elliptic regularity results, graded meshes, finite element methods for second order problems, and multigrid algorithms. In Chapter 3, we study two types of nonconforming finite element methods on graded meshes for a two-dimensional curl-curl and grad-div problem that appears in electromagnetics. The first method is based on a discretization using weakly continuous P1 vector fields. The second method uses …

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Perverse Poisson Sheaves On The Nilpotent Cone, Jared Lee Culbertson Jan 2010

Perverse Poisson Sheaves On The Nilpotent Cone, Jared Lee Culbertson

LSU Doctoral Dissertations

For a reductive complex algebraic group, the associated nilpotent cone is the variety of nilpotent elements in the corresponding Lie algebra. Understanding the nilpotent cone is of central importance in representation theory. For example, the nilpotent cone plays a prominent role in classifying the representations of finite groups of Lie type. More recently, the nilpotent cone has been shown to have a close connection with the affine flag variety and this has been exploited in the Geometric Langlands Program. We make use of the following important fact. The nilpotent cone is invariant under the coadjoint action of G on the …

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Basic Social Math: A Linguistic Upgrade For Decision Analysis And Social Dynamics Research., Jared Hanson Jan 2010

Basic Social Math: A Linguistic Upgrade For Decision Analysis And Social Dynamics Research., Jared Hanson

MA TESOL Collection

There are foundational errors in the mathematical frameworks currently used in Economic and Decision Theories. Recent systemic failures in the interdependent business and educational sectors also show that many practices based on these theories are unsustainable in the changing dynamics of the global economy. A new approach is needed in social science research and systems engineering. This paper examines how the new understandings of complex systems, the role of emotion in cognition, and the core dynamics of decision making can help us correct these errors and to create a general framework for systemic innovation. It argues for the development of …

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Voting In Agreeable Societies, Deborah E. Berg '06, Serguei Norine, Francis E. Su, Robin Thomas, Paul Wollan Jan 2010

Voting In Agreeable Societies, Deborah E. Berg '06, Serguei Norine, Francis E. Su, Robin Thomas, Paul Wollan

All HMC Faculty Publications and Research

No abstract provided in this article.

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Hybridization And Postprocessing Techniques For Mixed Eigenfunctions, Bernardo Cockburn, Jay Gopalakrishnan, F. Li, Ngoc Cuong Nguyen, Jaume Peraire Jan 2010

Hybridization And Postprocessing Techniques For Mixed Eigenfunctions, Bernardo Cockburn, Jay Gopalakrishnan, F. Li, Ngoc Cuong Nguyen, Jaume Peraire

Mathematics and Statistics Faculty Publications and Presentations

We introduce hybridization and postprocessing techniques for the Raviart–Thomas approximation of second-order elliptic eigenvalue problems. Hybridization reduces the Raviart–Thomas approximation to a condensed eigenproblem. The condensed eigenproblem is nonlinear, but smaller than the original mixed approximation. We derive multiple iterative algorithms for solving the condensed eigenproblem and examine their interrelationships and convergence rates. An element-by-element postprocessing technique to improve accuracy of computed eigenfunctions is also presented. We prove that a projection of the error in the eigenspace approximation by the mixed method (of any order) superconverges and that the postprocessed eigenfunction approximations converge faster for smooth eigenfunctions. Numerical experiments using …

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Advances And Applications Of Dsmt For Information Fusion (In Chinese), Florentin Smarandache, Jean Dezert Jan 2010

Advances And Applications Of Dsmt For Information Fusion (In Chinese), Florentin Smarandache, Jean Dezert

Branch Mathematics and Statistics Faculty and Staff Publications

No abstract provided.

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Neutrosophic Bilinear Algebras And Their Generalizations, Florentin Smarandache, W.B. Vasantha Kandasamy Jan 2010

Neutrosophic Bilinear Algebras And Their Generalizations, Florentin Smarandache, W.B. Vasantha Kandasamy

Branch Mathematics and Statistics Faculty and Staff Publications

This book introduces the concept of neutrosophic bilinear algebras and their generalizations to n-linear algebras, n>2. This book has five chapters. The reader should be well-versed with the notions of linear algebras as well as the concepts of bilinear algebras and n- linear algebras. Further the reader is expected to know about neutrosophic algebraic structures as we have not given any detailed literature about it. The first chapter is introductory in nature and gives a few essential definitions and references for the reader to make use of the literature in case the reader is not thorough with the basics. …

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An Amazing Mathematical Card Trick, Arthur T. Benjamin Jan 2010

An Amazing Mathematical Card Trick, Arthur T. Benjamin

All HMC Faculty Publications and Research

A magician gives a member of the audience 20 cards to shuffle. After the cards are thoroughly mixed, the magician goes through the deck two cards at a time, sometimes putting the two cards face to face, sometimes back to back, and sometimes in the same direction. Before dealing each pair of cards into a pile, he asks random members of the audience if the pair should be flipped over or not. He goes through the pile again four cards at a time and before each group of four is dealt to a pile, the audience gets to decide whether …

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Sex, Mixability, And Modularity, Adi Livnat, Christos Papadimitriou, Nicholas Pippenger, Marcus W. Feldman Jan 2010

Sex, Mixability, And Modularity, Adi Livnat, Christos Papadimitriou, Nicholas Pippenger, Marcus W. Feldman

All HMC Faculty Publications and Research

The assumption that different genetic elements can make separate contributions to the same quantitative trait was originally made in order to reconcile biometry and Mendelism and ever since has been used in population genetics, specifically for the trait of fitness. Here we show that sex is responsible for the existence of separate genetic effects on fitness and, more generally, for the existence of a hierarchy of genetic evolutionary modules. Using the tools developed in the process, we also demonstrate that in terms of their fitness effects, separation and fusion of genes are associated with the increase and decrease of the …

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Statistical Analysis Of Wastewater Remediation And Bio-Fuels Production Of Algae, Jay D. Jones Jan 2010

Statistical Analysis Of Wastewater Remediation And Bio-Fuels Production Of Algae, Jay D. Jones

All Graduate Plan B and other Reports, Spring 1920 to Spring 2023

The Logan city wastewater treatment system consists of a series of seven large aerated ponds (460 acres) that biologically treats 15 million gallons per day of wastewater from Logan city and six other communities. Tighter regulations of allowed phosphorus levels in the effluent have recently been implemented due to environmental concerns of a downstream reservoir. The Biological Engineering program at Utah State University, the Bio-fuels Center, the Utah Water Research Laboratory (UWRL) and the city of Logan are working together to remediate the wastewater treatment system using microalgae. Algal growth requires the uptake of phosphorus. Thus, phosphorus in the effluent …

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From Energy Gradient And Natural Selection To Biodiversity And Stability Of Ecosystems, Bo Deng Jan 2010

From Energy Gradient And Natural Selection To Biodiversity And Stability Of Ecosystems, Bo Deng

Department of Mathematics: Faculty Publications

The purpose of this paper is to incorporate well-established ecological principles into a foodweb model consisting of four trophic levels --- abiotic resources, plants, herbivores, and carnivores. The underlining principles include Kimura's neutral theory of genetic evolution, Liebig's Law of the Minimum for plant growth, Holling's functionals for herbivore foraging and carnivore predation, the One-Life Rule for all organisms, and Lotka-Volterra's model for intraand interspecific competitions. Numerical simulations of the model led to the following statistical findings: (a) particular foodwebs can give contradicting observations on biodiversity and productivity, in particular, all known functional forms -- - positive, negative, sigmoidal, and …

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Metastability And Plasticity In A Conceptual Model Of Neurons, Bo Deng Jan 2010

Metastability And Plasticity In A Conceptual Model Of Neurons, Bo Deng

Department of Mathematics: Faculty Publications

For a new class of neuron models we demonstrate here that typical membrane action potentials and spike-bursts are only transient states but appear to be asymptotically stable; and yet such metastable states are plastic — being able to dynamically change from one action potential to another with different pulse frequencies and from one spike-burst to another with different spike-per-burst numbers. The pulse and spike-burst frequencies change with individual ions’ pump currents while their corresponding metastable-plastic states maintain the same transmembrane voltage and current profiles in range. It is also demonstrated that the plasticity requires two one-way ion pumps operating in …

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Parity Periodicity: An Eliminative Approach To The Collatz Conjecture, Austin J. Phillips Jan 2010

Parity Periodicity: An Eliminative Approach To The Collatz Conjecture, Austin J. Phillips

Honors Theses

The 3n + l Conjecture states that when the Collatz function is applied repeatedly to an initial value, the sequence of values generated always converges to 1, regardless of the starting value. This paper strengthens the claim that all such sequences are convergent by showing that certain types of nonconvergent sequences cannot exist. Specifically, no sequence with parity-periodic values can exist This eliminates all possible nontrivially periodic sequences and all divergent sequences with periodic parity. Therefore, if a counterexample to the conjecture exists, It must be a divergent sequence whose values display no parity periodicity.

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Optimal Control And Nonlinear Programming, Qingxia Li Jan 2010

Optimal Control And Nonlinear Programming, Qingxia Li

LSU Doctoral Dissertations

In this thesis, we have two distinct but related subjects: optimal control and nonlinear programming. In the first part of this thesis, we prove that the value function, propagated from initial or terminal costs, and constraints, in the form of a differential equation, satisfy a subgradient form of the Hamilton-Jacobi equation in which the Hamiltonian is measurable with respect to time. In the second part of this thesis, we first construct a concrete example to demonstrate conjugate duality theory in vector optimization as developed by Tanino. We also define the normal cones corresponding to Tanino's concept of the subgradient of …

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Copula And Default Correlation, Dongxiang Yan Jan 2010

Copula And Default Correlation, Dongxiang Yan

LSU Master's Theses

This work presents a study of copulas, with special focus on the Gaussian copula model and its behavior under a certain conditioning process. Simulations are carried out to examine the behavior of the moments on conditional copula model, as measured by the behavior of Wick identities which hold for multivariate Gaussians.

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Temporal Scales For Transport Patterns In The Gulf Of Finland, Bert Viikmae, Tarmo Soomere, Mikk Viidebaum, Mihhail Berezovski Jan 2010

Temporal Scales For Transport Patterns In The Gulf Of Finland, Bert Viikmae, Tarmo Soomere, Mikk Viidebaum, Mihhail Berezovski

Publications

The basic time scales for current-induced net transport of surface water and associated time scales of reaching the nearshore in the Gulf of Finland, the Baltic Sea, are analysed based on Lagrangian trajectories of water particles reconstructed from three-dimensional velocity fields by the Rossby Centre circulation model for 1987–1991. The number of particles reaching the nearshore exhibits substantial temporal variability whereas the rate of leaving the gulf is almost steady. It is recommended to use an about 3 grid cells wide nearshore area as a substitute to the coastal zone and about 10–15 day long trajectories for calculations of the …

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Positive Solutions Of The (N-1, 1) Conjugate Boundary Value Problem, Bo Yang Jan 2010

Positive Solutions Of The (N-1, 1) Conjugate Boundary Value Problem, Bo Yang

Faculty Articles

We consider the (n - 1, 1) conjugate boundary value problem. Some upper estimates to positive solutions for the problem are obtained. We also establish some explicit sufficient conditions for the existence and nonexistence of positive solutions of the problem.

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A Class Of Discontinuous Petrov–Galerkin Methods. Ii. Optimal Test Functions, Leszek Demkowicz, Jay Gopalakrishnan Jan 2010

A Class Of Discontinuous Petrov–Galerkin Methods. Ii. Optimal Test Functions, Leszek Demkowicz, Jay Gopalakrishnan

Mathematics and Statistics Faculty Publications and Presentations

We lay out a program for constructing discontinuous Petrov–Galerkin (DPG) schemes having test function spaces that are automatically computable to guarantee stability. Given a trial space, a DPG discretization using its optimal test space counterpart inherits stability from the well posedness of the undiscretized problem. Although the question of stable test space choice had attracted the attention of many previous authors, the novelty in our approach lies in the fact we identify a discontinuous Galerkin (DG) framework wherein test functions, arbitrarily close to the optimal ones, can be locally computed. The idea is presented abstractly and its feasibility illustrated through …

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Strong Orbit Equivalence And Residuality, Brett M. Werner Jan 2010

Strong Orbit Equivalence And Residuality, Brett M. Werner

Electronic Theses and Dissertations

In this dissertation, we consider notions of equivalence between minimal Cantor systems, in particular strong orbit equivalence. By constructing the systems, we show that there exist two nonisomorphic substitution systems that are both Kakutani equivalent and strongly orbit equivalent. We go on to define a metric on a strong orbit equivalence class of minimal Cantor systems and prove several properties about the metric space. If the strong orbit equivalence class contains a finite rank system, we show that the set of finite rank systems is residual in the metric space. The last result shown is that set of systems with …

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Correlation Of Defaults In Complex Portfolios Using Copula Techniques, Adam Lodygowski Jan 2010

Correlation Of Defaults In Complex Portfolios Using Copula Techniques, Adam Lodygowski

LSU Master's Theses

This work, dealing with the correlation between subportfolios in more complex portfolios, begins with a brief survey of the necessary theoretical background. The basic statistical and probabilistic concepts are reviewed. The notion of copulas is introduced along with the fundamental theorem of Sklar. After this background a numerical procedure and code are developed for correlated defaults in multiple correlated portfolio. Further on, interesting results regarding the impact of changes in correlation on the portfolio performance are investigated in the simulations. The most valuable observations regarding the expected default ratios of two subportfolios considered jointly are presented and explained with particular …

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Fraction Competency And Algebra Success, Coretta Thomas Jan 2010

Fraction Competency And Algebra Success, Coretta Thomas

LSU Master's Theses

Abstract In this thesis, I investigated the importance of fraction competence to success in algebra. I studied 107 of the students whom I teach. These students were all enrolled in Algebra I. A fraction pretest and an algebra pretest were given at the beginning of the 2009-2010 school year. A comparison was done to study the connection between the fraction pretest score and the semester grade as well as the algebra pretest score and the semester grade. The strongest correlation was between the fraction pretest and the semester grade. This supported the theory that fraction competence is a strong predictor …

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Subgroups Of The Torelli Group, Leah R. Childers Jan 2010

Subgroups Of The Torelli Group, Leah R. Childers

LSU Doctoral Dissertations

Let Mod(Sg) be the mapping class group of an orientable surface of genus g, Sg. The action of Mod(Sg) on the homology of Sg induces the well-known symplectic representation:

Mod(Sg) ---> Sp(2g, Z).
The kernel of this representation is called the Torelli group, I(Sg).

We will study two subgroups of I(Sg). First we will look at the subgroup generated by all SIP-maps, SIP(Sg). We will show SIP(Sg) is not I(Sg) and is in fact an infinite index subgroup of I(Sg). We will also classify which SIP-maps are in the kernel of the Johnson homomorphism and Birman-Craggs-Johnson homomorphism.

Then we will …

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A Characterization Of Near Outer-Planar Graphs, Tanya Allen Lueder Jan 2010

A Characterization Of Near Outer-Planar Graphs, Tanya Allen Lueder

LSU Master's Theses

This thesis focuses on graphs containing an edge whose removal results in an outer-planar graph. We present partial results towards the larger goal of describing the class of all such graphs in terms of a finite list of excluded graphs. Specifically, we give a complete description of those members of this list that are not 2-connected or do not contain a subdivision of a three-spoke wheel. We also show that no members of the list contain a five-spoke wheel.

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Koszul Duality For Multigraded Algebras, Fareed Hawwa Jan 2010

Koszul Duality For Multigraded Algebras, Fareed Hawwa

LSU Doctoral Dissertations

Classical Koszul duality sets up an adjoint pair of functors establishing an equivalence of categories. The equivalence is between the bounded derived category of complexes of graded modules over a graded algebra and the bounded derived category of complexes of graded modules over the quadratic dual graded algebra. This duality can be extended in many ways. We consider here two extensions: first we wish to allow a multigraded algebra, meaning that the algebra can be graded by any abelian group (not just the integers). Second, we will allow filtered algebras. In fact we are considering filtered quadratic algebras with an …

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Calcium Sparks And Homeostasis In A Minimal Model Of Local And Global Calcium Responses In Quiescent Ventricular Myocytes, Jana M. Hartman, Gregory D. Smith, Eric A. Sobie Jan 2010

Calcium Sparks And Homeostasis In A Minimal Model Of Local And Global Calcium Responses In Quiescent Ventricular Myocytes, Jana M. Hartman, Gregory D. Smith, Eric A. Sobie

Arts & Sciences Articles

"We present a minimal whole cell model that accounts for both local and global aspects of Ca signaling in quiescent ventricular myocytes..."

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Modeling The Effects Of Genetic Manipulations Of Calsequestrin On Local Calcium Release And Depletion In Cardiac Myocytes, Ryan P. Carpenter, Gregory D. Smith, Sandor Gyorke Jan 2010

Modeling The Effects Of Genetic Manipulations Of Calsequestrin On Local Calcium Release And Depletion In Cardiac Myocytes, Ryan P. Carpenter, Gregory D. Smith, Sandor Gyorke

Arts & Sciences Articles

"Cardiac calsequestrin (CASQ2), a Ca buffer localized to the junctional SR (jSR) of cardiac myocytes, is known to bind to the RyR-triadin-junctin complex, participate in the luminal regulation of RyRs, and modulate Ca spark activity..."

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Symmetry And Stability Of Homogeneous Flocks, J. J. P. Veerman Jan 2010

Symmetry And Stability Of Homogeneous Flocks, J. J. P. Veerman

Mathematics and Statistics Faculty Publications and Presentations

The study of the movement of flocks, whether biological or technological, is motivated by the desire to understand the capability of coherent motion of a large number of agents that only receive very limited information. In a biological flock a large group of animals seek their course while moving in a more or less fixed formation. It seems reasonable that the immediate course is determined by leaders at the boundary of the flock. The others follow: what is their algorithm? The most popular technological application consists of cars on a one-lane road. The light turns green and the lead car …

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Fusion Of Sources Of Evidence With Different Importances And Reliabilities, Florentin Smarandache, Jean Dezert, J.M. Tacnet Jan 2010

Fusion Of Sources Of Evidence With Different Importances And Reliabilities, Florentin Smarandache, Jean Dezert, J.M. Tacnet

Branch Mathematics and Statistics Faculty and Staff Publications

This paper presents a new approach for combining sources of evidences with different importances and reliabilities. Usually, the combination of sources of evidences with different reliabilities is done by the classical Shafer’s discounting approach. Therefore, to consider unequal importances of sources, if any, a similar reliability discounting process is generally used, making no difference between the notion of importance and reliability. In fact, in multicriteria decision context, these notions should be clearly distinguished. This paper shows how this can be done and we provide simple examples to show the differences between both solutions for managing importances and reliabilities of sources. …

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Matrix Singular Value Decomposition, Petero Kwizera Jan 2010

Matrix Singular Value Decomposition, Petero Kwizera

UNF Graduate Theses and Dissertations

This thesis starts with the fundamentals of matrix theory and ends with applications of the matrix singular value decomposition (SVD). The background matrix theory coverage includes unitary and Hermitian matrices, and matrix norms and how they relate to matrix SVD. The matrix condition number is discussed in relationship to the solution of linear equations. Some inequalities based on the trace of a matrix, polar matrix decomposition, unitaries and partial isometies are discussed. Among the SVD applications discussed are the method of least squares and image compression. Expansion of a matrix as a linear combination of rank one partial isometries is …

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