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Mathematics

2011

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Articles 1 - 30 of 452

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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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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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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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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Both The Journal And Handbook Of Research On Urban Mathematics Teaching And Learning, David W. Stinson Dec 2011

Both The Journal And Handbook Of Research On Urban Mathematics Teaching And Learning, David W. Stinson

Middle-Secondary Education and Instructional Technology Faculty Publications

In this editorial, the author explores the prestige that the edited "Handbook" has gained in the social sciences generally and in mathematical education specifically over the past few decades, and explores how this has established new power relationships and scholarly practices within urban mathematical education.

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Design And Implementation Of An Open Framework For Ubiquitous Carbon Footprint Calculator Applications, Farzana Rahman, Casey O'Brien, Sheikh Iqbal Ahamed, He Zhang, Lin Liu Dec 2011

Design And Implementation Of An Open Framework For Ubiquitous Carbon Footprint Calculator Applications, Farzana Rahman, Casey O'Brien, Sheikh Iqbal Ahamed, He Zhang, Lin Liu

Mathematics, Statistics and Computer Science Faculty Research and Publications

As climate change is becoming an important global issue, more and more people are beginning to pay attention to reducing greenhouse gas emissions. To measure personal or household carbon dioxide emission, there are already plenty of carbon footprint calculators available on the web. Most of these calculators use quantitative models to estimate carbon emission caused by a user's activities. Although these calculators can promote public awareness regarding carbon emission due to an individual's behavior, there are concerns about the consistency and transparency of these existing CO2 calculators. Apart from a small group of smart phone based carbon footprint calculator …

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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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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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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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The Schroedinger Equation With Potential In Random Motion, Marius Beceanu, Soffer Avy Nov 2011

The Schroedinger Equation With Potential In Random Motion, Marius Beceanu, Soffer Avy

Mathematics and Statistics Faculty Scholarship

We study Schroedinger's equation with a potential moving along a Brownian motion path. We prove a RAGE-type theorem and Strichartz estimates for the solution on average.

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Spatial Population Models In Spatiotemporally Structured Environments, David Hiebeler Nov 2011

Spatial Population Models In Spatiotemporally Structured Environments, David Hiebeler

University of Maine Office of Research Administration: Grant Reports

Spatial effects, such as habitat fragmentation and the location and size of disturbance events, play a key role in the dynamics of populations. This is true in natural populations (such as herbs living under a forest canopy) as well as human-dominated systems (for example, crop pests in agricultural landscapes). Focusing on the development of spatial population models, the project seeks to better understand how and why spatially autocorrelated disturbances affect the dynamics of populations with mixtures of short- and long-distance dispersal. A variety of disturbances are considered, including (1) static disturbance, representing habitat heterogeneity across a landscape; (2) short-term disturbance …

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Extreme Math Makeover: Mathematics Assessment And Reporting In The Era Of The Common Core Standards, Glenn W. "Max" Mcgee Nov 2011

Extreme Math Makeover: Mathematics Assessment And Reporting In The Era Of The Common Core Standards, Glenn W. "Max" Mcgee

Publications & Research

This presentation discusses the need to develop high quality performance based assessments of the Common Core Mathematical Standards and Mathematical Practices. Several examples of performance assessments from high achieving countries as well as from the 2009 PISA test are included.

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Biomimetic Broadband Antireflection Gratings On Solar-Grade Multicrystalline Silicon Wafers, Blayne M. Phillips, Peng Jiang, Bin Jiang Nov 2011

Biomimetic Broadband Antireflection Gratings On Solar-Grade Multicrystalline Silicon Wafers, Blayne M. Phillips, Peng Jiang, Bin Jiang

Mathematics and Statistics Faculty Publications and Presentations

The authors report a simple and scalable bottom-up technique for fabricating broadband antireflection gratings on solar-grade multicrystalline silicon (mc-Si) wafers. A Langmuir-Blodgett process is developed to assemble close-packed silica microspheres on rough mc-Si substrates. Subwavelength moth-eye pillars can then be patterned on mc-Si by using the silica microspheres as structural template. Hemispherical reflectance measurements show that the resulting mc-Si gratings exhibit near zero reflection for a wide range of wavelengths. Both experimental results and theoretical prediction using a rigorous coupled-wave analysis model show that close-packed moth-eye arrays exhibit better antireflection performance than non-close-packed arrays due to a smoother refractive index …

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Sensitivity Analysis For Two-Level Value Functions With Applications To Bilevel Programming, S Dempe, Boris S. Mordukhovich, B Zemkoho Nov 2011

Sensitivity Analysis For Two-Level Value Functions With Applications To Bilevel Programming, S Dempe, Boris S. Mordukhovich, B Zemkoho

Mathematics Research Reports

This paper contributes to a deeper understanding of the link between a now conventional framework in hierarchical optimization spread under the name of the optimistic bilevel problem and its initial more difficult formulation that we call here the original optimistic bilevel optimization problem. It follows from this research that, although the process of deriving necessary optimality conditions for the latter problem is more involved, the conditions themselves do not to a large extent differ from those known for the conventional problem. It has been already well recognized in the literature that for optimality conditions of the usual optimistic bilevel program …

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Combinatorics Of Two-Toned Tilings, Arthur T. Benjamin, Phyllis Chinn, Jacob N. Scott '11, Greg Simay Nov 2011

Combinatorics Of Two-Toned Tilings, Arthur T. Benjamin, Phyllis Chinn, Jacob N. Scott '11, Greg Simay

All HMC Faculty Publications and Research

We introduce the function a(r, n) which counts tilings of length n + r that utilize white tiles (whose lengths can vary between 1 and n) and r identical red squares. These tilings are called two-toned tilings. We provide combinatorial proofs of several identities satisfied by a(r, n) and its generalizations, including one that produces kth order Fibonacci numbers. Applications to integer partitions are also provided.

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An Analysis Of The Effect Of Stress Diffusion On The Dynamics Of Creeping Viscoelastic Flow, Becca Thomases Nov 2011

An Analysis Of The Effect Of Stress Diffusion On The Dynamics Of Creeping Viscoelastic Flow, Becca Thomases

Mathematics Sciences: Faculty Publications

The effect of stress diffusivity is examined in both the Oldroyd-B and FENE-P models of a viscoelastic fluid in the low Reynolds (Stokes) limit for a 2D periodic time-dependent flow. A local analytic solution can be obtained when assuming a flow of the form u=Wi-1(x,-y), where Wi is the Weissenberg number. In this case the width of the birefringent strand of the polymer stress scales with the added viscosity as ν1/2, and is independent of the Weissenberg number. Also, the " expected" maximum extension of the polymer coils remains finite with any stress diffusion and scales as Wi·ν-1/2. These predictions …

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Compositions, Partitions, And Fibonacci Numbers, Andrew Sills Nov 2011

Compositions, Partitions, And Fibonacci Numbers, Andrew Sills

Department of Mathematical Sciences Faculty Publications

A bijective proof is given for the following theorem: the number of compositions of n into odd parts equals the number of compositions of n+ 1 into parts greater than one. Some commentary about the history of partitions and compositions is provided.

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Cagan Type Rational Expectations Model On Time Scales With Their Applications To Economics, Funda Ekiz Nov 2011

Cagan Type Rational Expectations Model On Time Scales With Their Applications To Economics, Funda Ekiz

Masters Theses & Specialist Projects

Rational expectations provide people or economic agents making future decision with available information and past experiences. The first approach to the idea of rational expectations was given approximately fifty years ago by John F. Muth. Many models in economics have been studied using the rational expectations idea. The most familiar one among them is the rational expectations version of the Cagans hyperination model where the expectation for tomorrow is formed using all the information available today. This model was reinterpreted by Thomas J. Sargent and Neil Wallace in 1973. After that time, many solution techniques were suggested to solve the …

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Support Varieties And Representation Type Of Self-Injective Algebras, Jorg Feldvoss, Sarah Witherspoon Nov 2011

Support Varieties And Representation Type Of Self-Injective Algebras, Jorg Feldvoss, Sarah Witherspoon

University Faculty and Staff Publications

We use the theory of varieties for modules arising from Hochschild cohomology to give an alternative version of the wildness criterion of Bergh and Solberg [7]: If a finite dimensional self-injective algebra has a module of complexity at least 3 and satisfies some finiteness assumptions on Hochschild cohomology, then the algebra is wild. We show directly how this is related to the analogous theory for Hopf algebras that we developed in [23]. We give applications to many different types of algebras: Hecke algebras, reduced universal enveloping algebras, small half- quantum groups, and Nichols (quantum symmetric) algebras.

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Why Probability Appears In Quantum Mechaincs, Jerome Blackman, Wu Teh Hsiang Oct 2011

Why Probability Appears In Quantum Mechaincs, Jerome Blackman, Wu Teh Hsiang

Mathematics - All Scholarship

Early in the development of quantum theory Bohr introduced what came to be called the Copenhagen interpretation. Specifically, the square of the absolute value of the wave function was to be used as a probability density. There followed lengthy arguments about this ranging from alternative universes to Schrodinger's cat. Einstein famously remarked "I am convinced that He (God) does not play dice." The purpose of this paper is to present a mathematical model of the measuring process that shows that the Copenhagen interpretation can actually follow from the fact that the time development of quantum systems is governed by the …

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Constructing Large Numbers With Cheap Computers, Andrew Shallue, Steven Hayman Oct 2011

Constructing Large Numbers With Cheap Computers, Andrew Shallue, Steven Hayman

Scholarship

No abstract provided.

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A Generalization Of The Fujisawa–Kuh Global Inversion Theorem, M. Radulescu, S. Radulescu, Eduardo C. Balreira Oct 2011

A Generalization Of The Fujisawa–Kuh Global Inversion Theorem, M. Radulescu, S. Radulescu, Eduardo C. Balreira

Mathematics Faculty Research

We discuss the problem of global invertibility of nonlinear maps defined on the finitedimensional Euclidean space via differential tests. We provide a generalization of theFujisawa-Kuh global inversion theorem and introduce a generalized ratio conditionwhich detects when the pre-image of a certain class of linear manifolds is non-emptyand connected. In particular, we provide conditions that also detect global injectivity.

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On The N-Wave Equations And Soliton Interactions In Two And Three Dimensions, Vladimir S. Gerdjikov, Rossen Ivanov, Assen V. Kyuldjiev Oct 2011

On The N-Wave Equations And Soliton Interactions In Two And Three Dimensions, Vladimir S. Gerdjikov, Rossen Ivanov, Assen V. Kyuldjiev

Articles

Several important examples of the N-wave equations are studied. These integrable equations can be linearized by formulation of the inverse scattering as a local Riemann–Hilbert problem (RHP). Several nontrivial reductions are presented. Such reductions can be applied to the generic N-wave equations but mainly the 3- and 4-wave interactions are presented as examples. Their one and two-soliton solutions are derived and their soliton interactions are analyzed. It is shown that additional reductions may lead to new types of soliton solutions. In particular the 4-wave equations with Z2xZ2 reduction group allow breather-like solitons. Finally it is demonstrated that …

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Small And Large Time Stability Of The Time Taken For A Lévy Process To Cross Curved Boundaries, Philip S. Griffin, Ross A. Maller Oct 2011

Small And Large Time Stability Of The Time Taken For A Lévy Process To Cross Curved Boundaries, Philip S. Griffin, Ross A. Maller

Mathematics - All Scholarship

This paper is concerned with the small time behaviour of a Levy process X. In particular, we investigate the stabilities of the times, Tb(r) and Tb*(r), at which X, started with X0 = 0, first leaves the space-time regions {(t, y) ∈ R2 : y ≤ rtb, t ≥ 0} (one-sided exit), or {(t, y) in R2 :|y| ≤ rtb, t ≥ 0} (two-sided exit), 0 ≤ b < 1, as r -> 0. Thus essentially we determine whether or not these passage times behave like deterministic functions in the sense of different modes of convergence; specifically convergence …

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Small And Large Time Stability Of The Time Taken For A Lévy Process To Cross Curved Boundaries, Philip S. Griffin, Ross A. Maller Oct 2011

Small And Large Time Stability Of The Time Taken For A Lévy Process To Cross Curved Boundaries, Philip S. Griffin, Ross A. Maller

Mathematics - All Scholarship

This paper is concerned with the small time behaviour of a Levy process X. In particular, we investigate the stabilities of the times, Tb(r) and T*b (r), at which X, started with X0 = 0, first leaves the space-time regions {(t, y) in R2 : y ≤ rtb, t ≥ 0} (one-sided exit), or {(t, y) in R2 :|y| ≤ rtb, t ≥ 0} (two-sided exit), 0 ≤ b < 1, as r ↓ 0. Thus essentially we determine whether or not these passage times behave like deterministic functions in the sense of different modes of convergence; specifically convergence in probability, almost surely and in Lp. In many instances these are seen to be equivalent to relative stability of the process X itself. The …

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Warped Product Rigidity, Chenxu He, Peter Petersen, William Wylie Oct 2011

Warped Product Rigidity, Chenxu He, Peter Petersen, William Wylie

Mathematics - All Scholarship

In this paper we study the space of solutions to an overdetermined linear system involving the Hessian of functions. We show that if the solution space has dimension greater than one, then the underlying manifold has a very rigid warped product structure. This warped product structure will be used to study warped product Einstein structures in our paper "The space of virtual solutions to the warped product Einstein equation".

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