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2011

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Articles 31 - 60 of 883

Full-Text Articles in Mathematics

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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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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Analyzing Common Algebra-Related Misconceptions And Errors Of Middle School Students., Sarah B. Bush Dec 2011

Analyzing Common Algebra-Related Misconceptions And Errors Of Middle School Students., Sarah B. Bush

Electronic Theses and Dissertations

The purpose of this study was to examine common algebra-related misconceptions and errors of middle school students. In recent years, success in Algebra I is often considered the mathematics gateway to graduation from high school and success beyond. Therefore, preparation for algebra in the middle grades is essential to student success in Algebra I and high school. This study examines the following research question: What common algebra-related misconceptions and errors exist among students in grades six and eight as identified on student responses on an annual statewide standardized assessment? In this study, qualitative document analysis of existing data was used …

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Boundary Element Method (Bem) And Method Of Fundamental Solutions (Mfs) For The Boundary Value Problems Of The 2-D Laplace's Equation, Ermes Anthony Salgado-Ibarra Dec 2011

Boundary Element Method (Bem) And Method Of Fundamental Solutions (Mfs) For The Boundary Value Problems Of The 2-D Laplace's Equation, Ermes Anthony Salgado-Ibarra

UNLV Theses, Dissertations, Professional Papers, and Capstones

In this thesis we study the solution of the two dimensional Laplace equation by the boundary Element method (BEM) and the method of fundamental solutions (MFS). Both the BEM and MFS used to solve boundary value problems involving the Laplace equation 2-D settings. Both methods rely on the use of fundamental solution of the Laplace's equation (the solution of Laplace's equation in the distributional sense). We will contrast and compare the results we get using the BEM with results we get using the MFS.

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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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Geometric Structures On Matrix-Valued Subdivision Schemes, James J. Smith Nov 2011

Geometric Structures On Matrix-Valued Subdivision Schemes, James J. Smith

Dissertations

Surface subdivision schemes are used in computer graphics to generate visually smooth surfaces of arbitrary topology. Applications in computer graphics utilize surface normals and curvature. In this paper, formulas are obtained for the first and second partial derivatives of limit surfaces formed using 1-ring subdivision schemes that have 2 by 2 matrix-valued masks. Consequently, surface normals, and Gaussian and mean curvatures can be derived. Both quadrilateral and triangular schemes are considered and for each scheme both interpolatory and approximating schemes are examined. In each case, we look at both extraordinary and regular vertices. Every 3-D vertex of the refinement polyhedrons …

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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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Topological Properties Of Invariant Sets For Anosov Maps With Holes, Skyler C. Simmons Nov 2011

Topological Properties Of Invariant Sets For Anosov Maps With Holes, Skyler C. Simmons

Theses and Dissertations

We begin by studying various topological properties of invariant sets of hyperbolic toral automorphisms in the linear case. Results related to cardinality, local maximality, entropy, and dimension are presented. Where possible, we extend the results to the case of hyperbolic toral automorphisms in higher dimensions, and further to general Anosov maps.

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

Compositions, Partitions, And Fibonacci Numbers, Andrew Sills

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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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 Modified Stokes-Einstein Equation For Aβ Aggregation, Srisairam Achuthan, Bong Jae Chung, Preetam Ghosh, Vijayaraghavan Rangachari, Ashuwin Vaidya Oct 2011

A Modified Stokes-Einstein Equation For Aβ Aggregation, Srisairam Achuthan, Bong Jae Chung, Preetam Ghosh, Vijayaraghavan Rangachari, Ashuwin Vaidya

Department of Mathematics Faculty Scholarship and Creative Works

Background: In all amyloid diseases, protein aggregates have been implicated fully or partly, in the etiology of the disease. Due to their significance in human pathologies, there have been unprecedented efforts towards physiochemical understanding of aggregation and amyloid formation over the last two decades. An important relation from which hydrodynamic radii of the aggregate is routinely measured is the classic Stokes-Einstein equation. Here, we report a modification in the classical Stokes-Einstein equation using a mixture theory approach, in order to accommodate the changes in viscosity of the solvent due to the changes in solute size and shape, to implement a …

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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 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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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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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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The Space Of Virtual Solutions To The Warped Product Einstein Equation, Chenxu He, Peter Petersen, William Wylie Oct 2011

The Space Of Virtual Solutions To The Warped Product Einstein Equation, Chenxu He, Peter Petersen, William Wylie

Mathematics - All Scholarship

In this paper we introduce a vector space of virtual warping functions that yield Einstein metrics over a fixed base. There is a natural quadratic form on this space and we study how this form interacts with the geometry. We use this structure along with the results in our earlier paper "Warped product rigidity" to show that essentially every warped product Einstein manifold admits a particularly nice warped product structure that we call basic. As applications we give a sharp characterization of when a homogeneous Einstein metric can be a warped product and also generalize a construction of Lauret showing …

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Characteristics Of Optimal Solutions To The Sensor Location Problem, David R. Morrison '08, Susan E. Martonosi Oct 2011

Characteristics Of Optimal Solutions To The Sensor Location Problem, David R. Morrison '08, Susan E. Martonosi

All HMC Faculty Publications and Research

In Bianco et al. (2001), the authors present the Sensor Location Problem: that of locating the minimum number of traffic sensors at intersections of a road network such that the traffic ow on the entire network can be determined. They offer a necessary and sufficient condition on the set of monitored nodes in order for the ow everywhere to be determined. In this paper, we present a counterexample that demonstrates that the condition is not actually sufficient (though it is still necessary). We present a stronger necessary condition for ow calculability, and show that it is a sufficient condition in …

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Interactive Real-Time Embedded Systems Education Infused With Applied Internet Telephony, Kyle Persohn, Dennis Brylow Oct 2011

Interactive Real-Time Embedded Systems Education Infused With Applied Internet Telephony, Kyle Persohn, Dennis Brylow

Mathematics, Statistics and Computer Science Faculty Research and Publications

The transition from traditional circuit-switched phone systems to modern packet-based Internet telephony networks demands tools to support Voice over Internet Protocol (VoIP) development. In this paper, we introduce the XinuPhone, an integrated hardware/software approach for educating users about VoIP technology on a real-time embedded platform. We propose modular course topics for design-oriented, hands-on laboratory exercises: filter design, timing, serial communications, interrupts and resource budgeting, network transmission, and system benchmarking. Our open-source software platform encourages development and testing of new CODECs alongside existing standards, unlike similar commercial solutions. Furthermore, the supporting hardware features inexpensive, readily available components designed specifically for educational …

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Variational Analysis Of Marginal Functions With Applications To Bilevel Programming, Boris S. Mordukhovich, Nguyen Mau Nam, Hung M. Phan Oct 2011

Variational Analysis Of Marginal Functions With Applications To Bilevel Programming, Boris S. Mordukhovich, Nguyen Mau Nam, Hung M. Phan

Mathematics Research Reports

This paper pursues a twofold goal. First to derive new results on generalized differentiation in variational analysis focusing mainly on a broad class of intrinsically nondifferentiable marginal/value functions. Then the results established in this direction apply to deriving necessary optimality conditions for the optimistic version of bilevel programs that occupy a remarkable place in optimization theory and its various applications. We obtain new sets of optimality conditions in both smooth and smooth settings of finite-dimensional and infinite-dimensional spaces.

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2011 (Fall), University Of Dayton. Department Of Mathematics Oct 2011

2011 (Fall), University Of Dayton. Department Of Mathematics

Colloquia

Abstracts of the talks given at the 2011 Fall Colloquium.

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Bytes Of Π, Fall 2011, Department Of Mathematics And Computer Science, Bridgewater State University Oct 2011

Bytes Of Π, Fall 2011, Department Of Mathematics And Computer Science, Bridgewater State University

Department of Mathematics Newsletter

No abstract provided.

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The Editor's Song, Frank A. Farris Oct 2011

The Editor's Song, Frank A. Farris

Mathematics and Computer Science

The program of the 2011 Mathfest's opening banquet was "MAA-The Musical!' Produced by Annalisa Crannell and starring the "MAA Players"(active MAA members all), it highlighted activities of the Association and of Mathfest itself. This song represents the journals. It was sung by past editor Frank Farris to the tune of "A Wand'ring Minstrel I,"from Gilbert and Sullivan's the Mikado.

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