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Mathematics

2011

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Full-Text Articles in Physical Sciences and Mathematics

Review: On The Near Periodicity Of Eigenvalues Of Toeplitz Matrices, Stephan Ramon Garcia Dec 2011

Review: On The Near Periodicity Of Eigenvalues Of Toeplitz Matrices, Stephan Ramon Garcia

Pomona Faculty Publications and Research

No abstract provided.

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Multiple Soliton Solutions Of (2+1)-Dimensional Potential Kadomtsev-Petviashvili Equation, Mohammad Najafi M.Najafi, Ali Jamshidi Dec 2011

Multiple Soliton Solutions Of (2+1)-Dimensional Potential Kadomtsev-Petviashvili Equation, Mohammad Najafi M.Najafi, Ali Jamshidi

mohammad najafi

We employ the idea of Hirota’s bilinear method, to obtain some new exact soliton solutions for high nonlinear form of (2+1)-dimensional potential Kadomtsev-Petviashvili equation. Multiple singular soliton solutions were obtained by this method. Moreover, multiple singular soliton solutions were also derived.

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Nonparametric Copula Density Estimation In Sensor Networks, Leming Qu, Hao Chen, Yicheng Tu Dec 2011

Nonparametric Copula Density Estimation In Sensor Networks, Leming Qu, Hao Chen, Yicheng Tu

Mathematics Faculty Publications and Presentations

Statistical and machine learning is a fundamental task in sensor networks. Real world data almost always exhibit dependence among different features. Copulas are full measures of statistical dependence among random variables. Estimating the underlying copula density function from distributed data is an important aspect of statistical learning in sensor networks. With limited communication capacities or privacy concerns, centralization of the data is often impossible. By only collecting the ranks of the data observed by different sensors, we estimate and evaluate the copula density on an equally spaced grid after binning the standardized ranks at the fusion center. Without assuming any …

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Nonparametric Copula Density Estimation In Sensor Networks, Leming Qu, Hao Chen, Yicheng Tu Dec 2011

Nonparametric Copula Density Estimation In Sensor Networks, Leming Qu, Hao Chen, Yicheng Tu

Leming Qu

Statistical and machine learning is a fundamental task in sensor networks. Real world data almost always exhibit dependence among different features. Copulas are full measures of statistical dependence among random variables. Estimating the underlying copula density function from distributed data is an important aspect of statistical learning in sensor networks. With limited communication capacities or privacy concerns, centralization of the data is often impossible. By only collecting the ranks of the data observed by different sensors, we estimate and evaluate the copula density on an equally spaced grid after binning the standardized ranks at the fusion center. Without assuming any …

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Lagrange's Theory Of Analytical Functions And His Ideal Of Purity Of Method, Giovanni Ferraro, Marco Panza Dec 2011

Lagrange's Theory Of Analytical Functions And His Ideal Of Purity Of Method, Giovanni Ferraro, Marco Panza

MPP Published Research

We reconstruct essential features of Lagrange’s theory of analytical functions by exhibiting its structure and basic assumptions, as well as its main shortcomings. We explain Lagrange’s notions of function and algebraic quantity, and we concentrate on power-series expansions, on the algorithm for derivative functions, and the remainder theorem—especially on the role this theorem has in solving geometric and mechanical problems. We thus aim to provide a better understanding of Enlightenment mathematics and to show that the foundations of mathematics did not, for Lagrange, concern the solidity of its ultimate bases, but rather purity of method—the generality and internal organization of …

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Cardinal Invariants And The Borel Tukey Order, Samuel Coskey Dec 2011

Cardinal Invariants And The Borel Tukey Order, Samuel Coskey

Samuel Coskey

Many proofs of inequalities between cardinal characteristics of the continuum are combinatorial in nature. These arguments can be carried out in any model of set theory, even a model of CH where the inequalities themselves are trivial. Thus, such arguments appear to establish a stronger relationship than a mere inequality. The Borel Tukey order was introduced by Blass in a 1996 article to address just this. Specifically, he observed that the combinatorial information linking two cardinal characteristics is often captured by a pair of Borel maps called a Borel Tukey morphism. The existence of a Borel Tukey morphisms between …

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Elliptic Operators And Maximal Regularity On Periodic Little-Hölder Spaces, Jeremy Lecrone Dec 2011

Elliptic Operators And Maximal Regularity On Periodic Little-Hölder Spaces, Jeremy Lecrone

Department of Math & Statistics Faculty Publications

We consider one-dimensional inhomogeneous parabolic equations with higher-order elliptic differential operators subject to periodic boundary conditions. In our main result we show that the property of continuous maximal regularity is satisfied in the setting of periodic little-Hölder spaces, provided the coefficients of the differential operator satisfy minimal regularity assumptions.We address parameter-dependent elliptic equations, deriving invertibility and resolvent bounds which lead to results on generation of analytic semigroups. We also demonstrate that the techniques and results of the paper hold for elliptic differential operators with operator-valued coefficients, in the setting of vector-valued functions.

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Statistical Inferences For The Youden Index, Haochuan Zhou Dec 2011

Statistical Inferences For The Youden Index, Haochuan Zhou

Mathematics Dissertations

In diagnostic test studies, one crucial task is to evaluate the diagnostic accuracy of a test. Currently, most studies focus on the Receiver Operating Characteristics Curve and the Area Under the Curve. On the other hand, the Youden index, widely applied in practice, is another comprehensive measurement for the performance of a diagnostic test. For a continuous-scale test classifying diseased and non-diseased groups, finding the Youden index of the test is equivalent to maximize the sum of sensitivity and specificity for all the possible values of the cut-point. This dissertation concentrates on statistical inferences for the Youden index. First, an …

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Mixed Discriminants, Eduardo Cattani, Maria Angelica Cueto, Alicia Dickenstein, Sandra Di Rocco, Bernd Strumfels Dec 2011

Mixed Discriminants, Eduardo Cattani, Maria Angelica Cueto, Alicia Dickenstein, Sandra Di Rocco, Bernd Strumfels

Eduardo Cattani

No abstract provided.

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Dynamic Appointment Scheduling In Healthcare, Mckay N. Heasley Dec 2011

Dynamic Appointment Scheduling In Healthcare, Mckay N. Heasley

Theses and Dissertations

In recent years, healthcare management has become fertile ground for the scheduling theory community. In addition to an extensive academic literature on this subject, there has also been a proliferation of healthcare scheduling software companies in the marketplace. Typical scheduling systems use rule-based analytics that give schedulers advisory information from programmable heuristics such as the Bailey-Welch rule cite{B,BW}, which recommends overbooking early in the day to fill-in potential no-shows later on. We propose a dynamic programming problem formulation to the scheduling problem that maximizes revenue. We formulate the problem and discuss the effectiveness of 3 different algorithms that solve the …

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Partial Connectivity In Wireless Sensor Networks, Robert Andre Murphy Dec 2011

Partial Connectivity In Wireless Sensor Networks, Robert Andre Murphy

Dissertations

Given a bounded region of the 2-dimensional plane, a discrete set of nodes is distributed throughout according to a Poisson point process. Given some fixed, finite, real number, two nodes are said to connect and form an edge if their mutual distance is less than this number. Let G be the graph of all such edges over the set of generated nodes and let C be any set of mutually connected nodes. It is shown that there is a critical mutual distance such that at least half of all generated nodes are mutually connected to form a connected cluster. Now, …

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Robust 𝒍𝟏 And 𝒍∞ Solutions Of Linear Inequalities, Maziar Salahi Dec 2011

Robust 𝒍𝟏 And 𝒍∞ Solutions Of Linear Inequalities, Maziar Salahi

Applications and Applied Mathematics: An International Journal (AAM)

Infeasible linear inequalities appear in many disciplines. In this paper we investigate the 𝑙1 and 𝑙∞ solutions of such systems in the presence of uncertainties in the problem data. We give equivalent linear programming formulations for the robust problems. Finally, several illustrative numerical examples using the cvx software package are solved showing the importance of the robust model in the presence of uncertainties in the problem data.

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Density Dependent Utilities With Transaction Costs, Eriyoti Chikodza, Julius N Esunge Dec 2011

Density Dependent Utilities With Transaction Costs, Eriyoti Chikodza, Julius N Esunge

Communications on Stochastic Analysis

No abstract provided.

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Mrm-Applicable Measures For The Power Function Of The Second Order, Izumi Kubo, Hui-Hsiung Kuo, Suat Namli Dec 2011

Mrm-Applicable Measures For The Power Function Of The Second Order, Izumi Kubo, Hui-Hsiung Kuo, Suat Namli

Communications on Stochastic Analysis

No abstract provided.

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The Minimal Martingale Measure For The Price Process With Poisson Shot Noise Jumps, Jun Yan Dec 2011

The Minimal Martingale Measure For The Price Process With Poisson Shot Noise Jumps, Jun Yan

Communications on Stochastic Analysis

No abstract provided.

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Consistent Price Systems For Bounded Processes, Florian Maris, Eric Mbakop, Hasanjan Sayit Dec 2011

Consistent Price Systems For Bounded Processes, Florian Maris, Eric Mbakop, Hasanjan Sayit

Communications on Stochastic Analysis

No abstract provided.

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Changes Of Measure And Representations Of The First Hitting Time Of A Bessel Process, Gerardo Hernandez-Del-Valle Dec 2011

Changes Of Measure And Representations Of The First Hitting Time Of A Bessel Process, Gerardo Hernandez-Del-Valle

Communications on Stochastic Analysis

No abstract provided.

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Intraday Empirical Analysis Of Electricity Price Behaviour, Eckhard Platen, Jason West Dec 2011

Intraday Empirical Analysis Of Electricity Price Behaviour, Eckhard Platen, Jason West

Communications on Stochastic Analysis

No abstract provided.

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A Martingale Representation For The Maximum Of A Lévy Process, Bruno Rémillard, Jean-François Renaud Dec 2011

A Martingale Representation For The Maximum Of A Lévy Process, Bruno Rémillard, Jean-François Renaud

Communications on Stochastic Analysis

No abstract provided.

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A Connection Between The Poissonian Wick Product And The Discrete Convolution, Alberto Lanconelli, Luigi Sportelli Dec 2011

A Connection Between The Poissonian Wick Product And The Discrete Convolution, Alberto Lanconelli, Luigi Sportelli

Communications on Stochastic Analysis

No abstract provided.

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Stochastic Analysis Of Backward Tidal Dynamics Equation, Hong Yin Dec 2011

Stochastic Analysis Of Backward Tidal Dynamics Equation, Hong Yin

Communications on Stochastic Analysis

No abstract provided.

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Finitely Presented Modules Over The Steenrod Algebra In Sage, Michael J. Catanzaro Dec 2011

Finitely Presented Modules Over The Steenrod Algebra In Sage, Michael J. Catanzaro

Wayne State University Theses

No abstract provided.

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Second-Order Subdifferential Calculus With Applications To Tilt Stability In Optimization, Boris S. Mordukhovich, R T. Rockafellar Dec 2011

Second-Order Subdifferential Calculus With Applications To Tilt Stability In Optimization, Boris S. Mordukhovich, R T. Rockafellar

Mathematics Research Reports

The paper concerns the second-order generalized differentiation theory of variational analysis and new applications of this theory to some problems of constrained optimization in finitedimensional spaces. The main attention is paid to the so-called (full and partial) second-order subdifferentials of extended-real-valued functions, which are dual-type constructions generated by coderivatives of first-order sub differential mappings. We develop an extended second-order subdifferential calculus and analyze the basic second-order qualification condition ensuring the fulfillment of the principal secondorder chain rule for strongly and fully amenable compositions. The calculus results obtained in this way and computing the second-order subdifferentials for piecewise linear-quadratic functions and …

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Symmetry-Breaking Bifurcation In The Nonlinear Schrödinger Equation With Symmetric Potentials, E. Kirr, Panos Kevrekidis, D. E. Pelinovsky Dec 2011

Symmetry-Breaking Bifurcation In The Nonlinear Schrödinger Equation With Symmetric Potentials, E. Kirr, Panos Kevrekidis, D. E. Pelinovsky

Panos Kevrekidis

We consider the focusing (attractive) nonlinear Schr\"odinger (NLS) equation with an external, symmetric potential which vanishes at infinity and supports a linear bound state. We prove that the symmetric, nonlinear ground states must undergo a symmetry breaking bifurcation if the potential has a non-degenerate local maxima at zero. Under a generic assumption we show that the bifurcation is either subcritical or supercritical pitchfork. In the particular case of double-well potentials with large separation, the power of nonlinearity determines the subcritical or supercritical character of the bifurcation. The results are obtained from a careful analysis of the spectral properties of the …

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Differential Geometry Based Solvation Model Ii: Lagrangian Formulation, Zhan Chen, Nathan A. Baker, Guo-Wei Wei Dec 2011

Differential Geometry Based Solvation Model Ii: Lagrangian Formulation, Zhan Chen, Nathan A. Baker, Guo-Wei Wei

Zhan Chen

Solvation is an elementary process in nature and is of paramount importance to more sophisticated chemical, biological and biomolecular processes. The understanding of solvation is an essential prerequisite for the quantitative description and analysis of biomolecular systems. This work presents a Lagrangian formulation of our differential geometry based solvation models. The Lagrangian representation of biomolecular surfaces has a few utilities/advantages. First, it provides an essential basis for biomolecular visualization, surface electrostatic potential map and visual perception of biomolecules. Additionally, it is consistent with the conventional setting of implicit solvent theories and thus, many existing theoretical algorithms and computational software packages …

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Bifurcation And Invariant Manifolds Of The Logistic Competition Model, M. Guzowska, Rafael Luís, Saber Elaydi Dec 2011

Bifurcation And Invariant Manifolds Of The Logistic Competition Model, M. Guzowska, Rafael Luís, Saber Elaydi

Mathematics Faculty Research

In this paper we study a new logistic competition model. We will investigate stability and bifurcation of the model. In particular, we compute the invariant manifolds, including the important center manifolds, and study their bifurcation. Saddle-node and period doubling bifurcation route to chaos is exhibited via numerical simulations.

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A Review On Convolutions Of Gamma Random Variables, Baha-Eldin Khaledi, Subhash C. Kochar Dec 2011

A Review On Convolutions Of Gamma Random Variables, Baha-Eldin Khaledi, Subhash C. Kochar

Mathematics and Statistics Faculty Publications and Presentations

Due to its wide range of applications, the topic of the distribution theory of convolutions of Gamma random variables has attracted the attention of many researchers. In this paper we review some of the latest developments on this problem.

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Reliable A-Posteriori Error Estimators For Hp-Adaptive Finite Element Approximations Of Eigenvalue/Leigenvector Problems, Stefano Giani, Luka Grubisic, Jeffrey S. Ovall Dec 2011

Reliable A-Posteriori Error Estimators For Hp-Adaptive Finite Element Approximations Of Eigenvalue/Leigenvector Problems, Stefano Giani, Luka Grubisic, Jeffrey S. Ovall

Mathematics and Statistics Faculty Publications and Presentations

We present reliable a-posteriori error estimates for hp-adaptive finite element approxima- tions of eigenvalue/eigenvector problems. Starting from our earlier work on h adaptive finite element approximations we show a way to obtain reliable and efficient a-posteriori estimates in the hp-setting. At the core of our analysis is the reduction of the problem on the analysis of the associated boundary value problem. We start from the analysis of Wohlmuth and Melenk and combine this with our a-posteriori estimation framework to obtain eigenvalue/eigenvector approximation bounds.

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Approximation By Bernstein Polynomials At The Point Of Discontinuity, Jie Ling Liang Dec 2011

Approximation By Bernstein Polynomials At The Point Of Discontinuity, Jie Ling Liang

HIM 1990-2015

Chlodovsky showed that if x0 is a point of discontinuity of the first kind of the function f, then the Bernstein polynomials Bn(f, x0) converge to the average of the one-sided limits on the right and on the left of the function f at the point x0. In 2009, Telyakovskii in (5) extended the asymptotic formulas for the deviations of the Bernstein polynomials from the differentiable functions at the first-kind discontinuity points of the highest derivatives of even order and demonstrated the same result fails for the odd order case. Then in 2010, Tonkov in (6) found the right formulation …

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Algebraic Properties Of Killing Vectors For Lorentz Metrics In Four Dimensions, Jesse W. Hicks Dec 2011

Algebraic Properties Of Killing Vectors For Lorentz Metrics In Four Dimensions, Jesse W. Hicks

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

Four-dimensional space-times with symmetry play a central role in the theory of general relativity. In 1961, in the book Einstein Spaces, A.Z. Petrov gave a complete local classification of four-dimensional space-times based upon their local isometry group, that is, their Lie algebra of Killing vector fields. In this report we discuss algebraic and geometric properties of these Lie algebras. A database of these properties has been computed for the five-dimensional Lie algebras of Killing vectors found in Petrov. As an application of our work, we present dieomorphisms between a few pairs of these Lie algebras of Killing vectors.

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