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2011

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Articles 1 - 30 of 883

Full-Text Articles in 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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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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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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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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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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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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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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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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Dynamic Server Allocation At Parallel Queues, Susan E. Martonosi Dec 2011

Dynamic Server Allocation At Parallel Queues, Susan E. Martonosi

All HMC Faculty Publications and Research

We explore whether dynamically reassigning servers to parallel queues in response to queue imbalances can reduce average waiting time in those queues. We use approximate dynamic programming methods to determine when servers should be switched, and we compare the performance of such dynamic allocations to that of a pre-scheduled deterministic allocation. Testing our method on both synthetic data and data from airport security checkpoints at Boston Logan International Airport, we find that in situations where the uncertainty in customer arrival rates is significant, dynamically reallocating servers can substantially reduce waiting time. Moreover, we find that intuitive switching strategies that are …

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A General Family Of Dual To Ratio-Cum-Product Estimator In Sample Surveys, Florentin Smarandache, Rajesh Singh, Mukesh Kumar, Pankaj Chauhan, Nirmala Sawan Dec 2011

A General Family Of Dual To Ratio-Cum-Product Estimator In Sample Surveys, Florentin Smarandache, Rajesh Singh, Mukesh Kumar, Pankaj Chauhan, Nirmala Sawan

Branch Mathematics and Statistics Faculty and Staff Publications

This paper presents a family of dual to ratio-cum-product estimators for the finite population mean. Under simple random sampling without replacement (SRSWOR) scheme, expressions of the bias and mean-squared error (MSE) up to the first order of approximation are derived. We show that the proposed family is more efficient than usual unbiased estimator, ratio estimator, product estimator, Singh estimator (1967), Srivenkataramana (1980) and Bandyopadhyaya estimator (1980) and Singh et al. (2005) estimator. An empirical study is carried out to illustrate the performance of the constructed estimator over others.

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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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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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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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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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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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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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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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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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From Double Lie Groupoids To Local Lie 2-Groupoids, Rajan Amit Mehta, Xiang Tang Dec 2011

From Double Lie Groupoids To Local Lie 2-Groupoids, Rajan Amit Mehta, Xiang Tang

Mathematics Sciences: Faculty Publications

We apply the bar construction to the nerve of a double Lie groupoid to obtain a local Lie 2-groupoid. As an application, we recover Haefliger's fundamental groupoid from the fundamental double groupoid of a Lie groupoid. In the case of a symplectic double groupoid, we study the induced closed 2-form on the associated local Lie 2-groupoid, which leads us to propose a definition of a symplectic 2-groupoid.

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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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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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Coloring Problems, Thomas Antonio Charles Chartier Dec 2011

Coloring Problems, Thomas Antonio Charles Chartier

Boise State University Theses and Dissertations

This thesis considers several coloring problems all of which have a combinatorial flavor. We review some results on the chromatic number of the plane, and improve a bound on the value of regressive Ramsey numbers. The main work of this thesis considers the problem of whether given any n ≥ 1; one can color Z+ in such a way that for all a ϵ Z+ the numbers a, 2a, 3a, ..., na are assigned different colors. Such colorings are referred to as satisfactory. We provide a sufficient condition for guaranteeing the existence of satisfactory colorings and analyze the …

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Escape Rates For Coupled Particles In A Stochastic Environment, Gregory Slusarczyk Dec 2011

Escape Rates For Coupled Particles In A Stochastic Environment, Gregory Slusarczyk

Theses, Dissertations and Culminating Projects

A particle placed in a deterministic, overdamped potential well will move towards an attractor located at the bottom of the well. Once the particle reaches the attractor, it remains there forever since no other forces are acting on the particle. However, if weak stochasticity is introduced, the particle will fluctuate around the attractor. As a rare event, the noise can organize itself in such a way that a large fluctuation is created that causes the particle to escape from the basin of attraction. The escape rates/escape times can be found both analytically and numerically. Furthermore, it is possible to predict …

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Pattern Avoiding Partitions, Sequence A054391 And The Kernel Method, Toufik Mansour, Mark Shattuck Dec 2011

Pattern Avoiding Partitions, Sequence A054391 And The Kernel Method, Toufik Mansour, Mark Shattuck

Applications and Applied Mathematics: An International Journal (AAM)

Sequence A054391 in OEIS, which we will denote by an , counts a certain two-pattern avoidance class of the permutations of size n . In this paper, we provide additional combinatorial interpretations for these numbers in terms of finite set partitions. In particular, we identify six classes of the partitions of size n , all of which have cardinality an and each avoiding two classical patterns. We use both algebraic and combinatorial methods to establish our results. In one apparently more difficult case, to show the result, we make use of the kernel method in solving a system …

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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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A New Algorithm For Solving Shortest Path Problem On A Network With Imprecise Edge Weight, Amit Kumar, Manjot Kumar Dec 2011

A New Algorithm For Solving Shortest Path Problem On A Network With Imprecise Edge Weight, Amit Kumar, Manjot Kumar

Applications and Applied Mathematics: An International Journal (AAM)

Nayeem and Pal (Shortest path problem on a network with imprecise edge weight, Fuzzy Optimization and Decision Making 4, 293-312, 2005) proposed a new algorithm for solving shortest path problem on a network with imprecise edge weight. In this paper the shortcomings of the existing algorithm, (Nayeem and Pal, 2005) are pointed out and to overcome these shortcomings a new algorithm is proposed. To show the advantages of the proposed algorithm over existing algorithm the numerical examples presented in (Nayeem and Pal, 2005) are solved using the proposed algorithm and obtained results are discussed.

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The Principle Of Linearized Stability For Size-Structured Population Models, M. El-Doma Dec 2011

The Principle Of Linearized Stability For Size-Structured Population Models, M. El-Doma

Applications and Applied Mathematics: An International Journal (AAM)

The principle of linearized stability for size-structured population dynamics models is proved giving validity to previous stability results reported in, for example, El-Doma (2008-1). In particular, we show that if all the roots of the characteristic equation lie to the left of the imaginary axis then the steady state is locally exponentially stable, and on the other hand, if there is at least one root that lies to the right of the imaginary axis then the steady state is unstable. We also point out cases when there is resonance

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