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2011

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Articles 451 - 480 of 882

Full-Text Articles in Mathematics

Studies On Public Key And Identity-Based Cryptographic Primitives., Mahabir Prasad Jhanwar Dr. Feb 2011

Studies On Public Key And Identity-Based Cryptographic Primitives., Mahabir Prasad Jhanwar Dr.

Doctoral Theses

No abstract provided.

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Sampling 'Survey Populations': Some Problems And Their Solutions., Kajal Dihidar Dr. Feb 2011

Sampling 'Survey Populations': Some Problems And Their Solutions., Kajal Dihidar Dr.

Doctoral Theses

In this thesis we study some problems in survey sampling and propose their solutions. The thesis is divided into seven chapters, the first being an introductory one. Chapters 2-4 relate to surveys with direct responses, while Chapters 5-7 deal with randomized responses. We begin by introducing the motivations behind the principal problems studied in this thesis.The first problem arose while developing a survey where the objective was to estimate the tot al number of workers in different industries in the rural unorganized sector in a district of the state of West Bengal, India. For this, the technique of adaptive sampling …

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Spectral Asymptotics Of Laplacians Associated To One-Dimensional Iterated Function Systems With Overlaps, Sze-Man Ngai Feb 2011

Spectral Asymptotics Of Laplacians Associated To One-Dimensional Iterated Function Systems With Overlaps, Sze-Man Ngai

Mathematical Sciences: Faculty Publications

We set up a framework for computing the spectral dimension of a class of one-dimensional self-similar measures that are defined by iterated function systems with overlaps and satisfy a family of second-order self-similar identities. As applications of our result we obtain the spectral dimension of important measures such as the infinite Bernoulli convolution associated with the golden ratio and convolutions of Cantor-type measures. The main novelty of our result is that the iterated function systems we consider are not post-critically finite and do not satisfy the well-known open set condition.

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Degenerate Anisotropic Differential Operators And Applications, Veli B. Shakhmurov Feb 2011

Degenerate Anisotropic Differential Operators And Applications, Veli B. Shakhmurov

Mathematics and System Engineering Faculty Publications

The boundary value problems for degenerate anisotropic differential operator equations with variable coefficients are studied. Several conditions for the separability and Fredholmness in Banach-valued Lp spaces are given. Sharp estimates for resolvent, discreetness of spectrum, and completeness of root elements of the corresponding differential operators are obtained. In the last section, some applications of the main results are given.

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Selected Aspects Of Performance Of Indian Industries: An Empirical Investigation., Anup Kumar Bhandari Dr. Feb 2011

Selected Aspects Of Performance Of Indian Industries: An Empirical Investigation., Anup Kumar Bhandari Dr.

Doctoral Theses

At the time of India’s independence the need of the hour was to develop the economy at a fast pace so as to achieve a reasonable standard of living for the masses within a short period of time. India’s first Industrial Policy Resolution was adopted in 1948 which put emphasis on the expansion of production of both agricultural and industrial goods to satisfy the basic needs of the masses, a large proportion of whom lived well below a subsistence level of living. Hence, emphasis was given on agricultural expansion in the First Five Year Plan and on building up the …

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Quantum Stochastic Flows: Trotter Product Formula, Dilations And Quantum Brownian Motion., Biswarup Das Dr. Feb 2011

Quantum Stochastic Flows: Trotter Product Formula, Dilations And Quantum Brownian Motion., Biswarup Das Dr.

Doctoral Theses

Motivated by the major role played by probabilistic models in many areas of science, several quantum (i.e. non-commutative) generalizations of classical probability have been attempted by a number of mathematicians. The pioneering works of K.R. Parthasarathy, L. Accardi, R.L. Hudson, P.A. Meyer and others led to the development of one such non-commutative model called ‘quantum probability’ which has a very rich theory of quantum stochastic calculus a la Hudson and Parthasarathy. Within the framework of quantum stochastic calculus, the ‘grand design’ that engages us is the canonical construction and study of ∗-homomorphic flows (jt)t≥0 on a given C ∗ or …

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Bowles, John (Sc 593), Manuscripts & Folklife Archives Feb 2011

Bowles, John (Sc 593), Manuscripts & Folklife Archives

Manuscript Collection Finding Aids

Finding aid and full-text (click on "Additional Files" below) for Manuscripts Small Collection 593. Ciphering book kept by John Bowles of Granville County, North Carolina. Bowles used "Pike's Arithmetic" in making his ciphering book.

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King, John (Sc 594), Manuscripts & Folklife Archives Feb 2011

King, John (Sc 594), Manuscripts & Folklife Archives

Manuscript Collection Finding Aids

Finding aid and full-text (click on "Additional Files" below) for Manuscripts Small Collection 594. Ciphering book of John King including mathematical exercises, numeration of money, simple and compound reduction, weights and measures, and word problems.

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Curd, Spencer, 1788-1832 (Sc 966), Manuscripts & Folklife Archives Feb 2011

Curd, Spencer, 1788-1832 (Sc 966), Manuscripts & Folklife Archives

Manuscript Collection Finding Aids

Finding aid and full text (click on "Additional Files" below) for Manuscripts Small Collection 966. Ciphering book (94 p.), focusing chiefly on surveying and navigating rules for solving problems as well as giving specific problems, of Spencer Curd, Logan County, Kentucky, with accompanying genealogical data.

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Acceleration Of Randomized Kaczmarz Method Via The Johnson-Lindenstrauss Lemma, Yonina C. Eldar, Deanna Needell Feb 2011

Acceleration Of Randomized Kaczmarz Method Via The Johnson-Lindenstrauss Lemma, Yonina C. Eldar, Deanna Needell

CMC Faculty Publications and Research

The Kaczmarz method is an algorithm for finding the solution to an overdetermined consistent system of linear equations Ax=b by iteratively projecting onto the solution spaces. The randomized version put forth by Strohmer and Vershynin yields provably exponential convergence in expectation, which for highly overdetermined systems even outperforms the conjugate gradient method. In this article we present a modified version of the randomized Kaczmarz method which at each iteration selects the optimal projection from a randomly chosen set, which in most cases significantly improves the convergence rate. We utilize a Johnson-Lindenstrauss dimension reduction technique to keep the runtime on the …

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Refinement Of Operator-Valued Reproducing Kernels, Yuesheng Xu, Haizhang Zhang, Qinghui Zhang Feb 2011

Refinement Of Operator-Valued Reproducing Kernels, Yuesheng Xu, Haizhang Zhang, Qinghui Zhang

Mathematics - All Scholarship

This paper studies the construction of a refinement kernel for a given operator-valued reproducing kernel such that the vector-valued reproducing kernel Hilbert space of the refinement kernel contains that of the given one as a subspace. The study is motivated from the need of updating the current operator-valued reproducing kernel in multi-task learning when underfitting or overfitting occurs. Numerical simulations confirm that the established refinement kernel method is able to meet this need. Various characterizations are provided based on feature maps and vector-valued integral representations of operator-valued reproducing kernels. Concrete examples of refining translation invariant and finite Hilbert-Schmidt operator-valued reproducing …

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An Entropy Proof Of The Kahn-Lovász Theorem, Jonathan Cutler, A. J. Radcliffe Feb 2011

An Entropy Proof Of The Kahn-Lovász Theorem, Jonathan Cutler, A. J. Radcliffe

Department of Mathematics Faculty Scholarship and Creative Works

Brègman [2], gave a best possible upper bound for the number of perfect matchings in a balanced bipartite graph in terms of its degree sequence. Recently Kahn and Lovász [8] extended Brègman's theorem to general graphs. In this paper, we use entropy methods to give a new proof of the Kahn-Lovász theorem. Our methods build on Radhakrishnan's [9] use of entropy to prove Brègman's theorem.

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N-Harmonic Mappings Between Annuli, Tadeusz Iwaniec, Jani Onninen Feb 2011

N-Harmonic Mappings Between Annuli, Tadeusz Iwaniec, Jani Onninen

Mathematics - All Scholarship

The central theme of this paper is the variational analysis of homeomorphisms h: X onto −→ Y between two given domains X,Y ⊂ Rn. We look for the extremal mappings in the Sobolev space W1,n(X,Y) which minimize the energy integral Eh =ZX ||Dh(x) ||n dx Because of the natural connections with quasiconformal mappings this n harmonic alternative to the classical Dirichlet integral (for planar domains) has drawn the attention of researchers in Geometric Function Theory. Explicit analysis is made here for a pair of concentric spherical annuli where many unexpected phenomena about minimal n -harmonic …

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Conical Existence Of Closed Curves On Convex Polyhedra, Joseph O'Rourke, Costin Vîlcu Feb 2011

Conical Existence Of Closed Curves On Convex Polyhedra, Joseph O'Rourke, Costin Vîlcu

Computer Science: Faculty Publications

Let C be a simple, closed, directed curve on the surface of a convex polyhedron P. We identify several classes of curves C that "live on a cone," in the sense that C and a neighborhood to one side may be isometrically embedded on the surface of a cone Lambda, with the apex a of Lambda enclosed inside (the image of) C; we also prove that each point of C is "visible to" a. In particular, we obtain that these curves have non-self-intersecting developments in the plane. Moreover, the curves we identify that live on cones to both sides support …

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Tangential Extremal Principles For Finite And Infinite Systems Of Sets, Ii: Applications To Semi-Infinite And Multiobjective Optimization, Boris S. Mordukhovich, Hung M. Phan Feb 2011

Tangential Extremal Principles For Finite And Infinite Systems Of Sets, Ii: Applications To Semi-Infinite And Multiobjective Optimization, Boris S. Mordukhovich, Hung M. Phan

Mathematics Research Reports

This paper contains selected applications of the new tangential extremal principles and related results developed in [20] to calculus rules for infinite intersections of sets and optimality conditions for problems of semi-infinite programming and multiobjective optimization with countable constraints.

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Bounds For Solid Angles Of Lattices Of Rank Three, Lenny Fukshansky, Sinai Robins Feb 2011

Bounds For Solid Angles Of Lattices Of Rank Three, Lenny Fukshansky, Sinai Robins

CMC Faculty Publications and Research

We find sharp absolute constants C1 and C2 with the following property: every well-rounded lattice of rank 3 in a Euclidean space has a minimal basis so that the solid angle spanned by these basis vectors lies in the interval [C1,C2]. In fact, we show that these absolute bounds hold for a larger class of lattices than just well-rounded, and the upper bound holds for all. We state a technical condition on the lattice that may prevent it from satisfying the absolute lower bound on the solid angle, in which case we …

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Finite Basis Problem For 2-Testable Monoids, Edmond W. H. Lee Feb 2011

Finite Basis Problem For 2-Testable Monoids, Edmond W. H. Lee

Mathematics Faculty Articles

A monoid S 1 obtained by adjoining a unit element to a 2-testable semigroup S is said to be 2-testable. It is shown that a 2-testable monoid S 1 is either inherently non-finitely based or hereditarily finitely based, depending on whether or not the variety generated by the semigroup S contains the Brandt semigroup of order five. Consequently, it is decidable in quadratic time if a finite 2-testable monoid is finitely based.

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Location And Scale Estimation With Correlation Coefficients, Rudy Gideon, Adele Marie Rothan Feb 2011

Location And Scale Estimation With Correlation Coefficients, Rudy Gideon, Adele Marie Rothan

Mathematical Sciences Faculty Publications

This article shows how to use any correlation coefficient to produce an estimate of location and scale. It is part of a broader system, called a correlation estimation system (CES), that uses correlation coefficients as the starting point for estimations. The method is illustrated using the well-known normal distribution. This article shows that any correlation coefficient can be used to fit a simple linear regression line to bivariate data and then the slope and intercept are estimates of standard deviation and location. Because a robust correlation will produce robust estimates, this CES can be recommended as a tool for everyday …

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Hayward And Henson Secure Nsf Grant For $350,000, Keri Suarez Feb 2011

Hayward And Henson Secure Nsf Grant For $350,000, Keri Suarez

Lake Union Herald

No abstract provided.

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A Stability Study Of A New Explicit Numerical Scheme For A System Of Differential Equations With A Large Skew-Symmetric Component, Katharine Gurski, Stephen O'Sullivan Feb 2011

A Stability Study Of A New Explicit Numerical Scheme For A System Of Differential Equations With A Large Skew-Symmetric Component, Katharine Gurski, Stephen O'Sullivan

Articles

Abstract. Explicit numerical methods for the solution of a system of stiff differential equations suffer from a time step size that approaches zero in order to satisfy stability conditions. Implicit schemes allow a larger time-step, but require more computations. When the differential equations are dominated by a skew-symmetric component, the problem is not stiffness in the sense that the size of the eigenvalues are unequal, rather the that the real eigenvalues are dominated by imaginary eigenvalues. We present and compare analytical results for stable time step limits for several explicit methods including the super-time-stepping method of Alexiades, Amiez, and Gremaud …

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An Essay On The Interpolation Theorem Of Józef Marcinkiewicz - Polish Patriot, Tadeusz Iwaniec Feb 2011

An Essay On The Interpolation Theorem Of Józef Marcinkiewicz - Polish Patriot, Tadeusz Iwaniec

Mathematics - All Scholarship

In memory of Polish mathematicians murdured by the Soviets and the Nazis. The total record of accomplishments of Marcinkiewicz in his short life, his talent, perceptions rich in concepts, and technical novelties, go far beyond my ability to give full play within the confines of one article. The importance of Marcinkiewicz's short paper is reflected in the myriad applications and generalizations which earns the right to be called Marcinkiewicz Interpolation Theory Marcinkiewicz interpolation theorem came after the celebrated convexity theorem of M. Riesz and his student G.O. Thorin. These fundamental works by M. Riesz, G.O. Thorin and J. Marcinkiewicz deal …

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Lorentzian Sasaki-Einstein Metrics On Connected Sums Of S² X S³, Ralph R. Gomez Feb 2011

Lorentzian Sasaki-Einstein Metrics On Connected Sums Of S² X S³, Ralph R. Gomez

Mathematics & Statistics Faculty Works

We settle completely an open problem formulated by Boyer and Galicki in [5] which asks whether or not # kS² x S³ are negative Sasakian manifolds for all k. As a consequence of the affirmative answer to this problem, there exists so-called Sasaki eta-Einstein and Lorentzian Sasaki-Einsteinmetrics on these five-manifolds for all k and moreover all of these can be realized as links of isolated hypersurface singularities defined by weighted homogenous polynomials. The key step is to construct infinitely many hypersurfaces in weighted projective space that contain branch divisors Delta = Sigma(i) (1 - 1/m(i)) D-i such that the D-i …

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Polynomial Generalizations Of Two-Variable Ramanujan Type Identities, James Mclaughlin, Andrew Sills Feb 2011

Polynomial Generalizations Of Two-Variable Ramanujan Type Identities, James Mclaughlin, Andrew Sills

Mathematical Sciences: Faculty Publications

We provide finite analogs of a pair of two-variable q-series identities from Ramanujan's lost notebook and a companion identity.

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What Do We Mean By Mathematical Proof?, Todd Cadwalladerolsker Jan 2011

What Do We Mean By Mathematical Proof?, Todd Cadwalladerolsker

Journal of Humanistic Mathematics

Mathematical proof lies at the foundations of mathematics, but there are several notions of what mathematical proof is, or might be. In fact, the idea of mathematical proof continues to evolve. In this article, I review the body of literature that argues that there are at least two widely held meanings of proof, and that the standards of proof are negotiated and agreed upon by the members of mathematical communities. The formal view of proof is contrasted with the view of proofs as arguments intended to convince a reader. These views are examined in the context of the various roles …

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Aesthetic Considerations In Mathematics, Nathalie Sinclair Jan 2011

Aesthetic Considerations In Mathematics, Nathalie Sinclair

Journal of Humanistic Mathematics

Drawing on some of the principles of humanistic mathematics first outlined by Alvin White, this paper seeks to examine the way in which value judgments are implicated in the growth of the mathematics discipline. After a short overview of some of the roles ascribed to the mathematical aesthetic historically, I turn to more contemporary positioning of the aesthetic in order to develop a framework that offers insight into the particular values, assumptions and desires that constrain what is done in mathematics, how it is done and why. My goal, at least in part, is to bring together under one umbrella …

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Welcome To The Journal Of Humanistic Mathematics, Mark Huber, Gizem Karaali Jan 2011

Welcome To The Journal Of Humanistic Mathematics, Mark Huber, Gizem Karaali

Journal of Humanistic Mathematics

No abstract provided.

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Pattern Formation In Oscillatory Systems, Hui Wu Jan 2011

Pattern Formation In Oscillatory Systems, Hui Wu

Dissertations

Synchronization is a kind of ordinary phenomenon in nature, the study of it includes many mathematical branches. Phase space is one of the most powerful inventions of modern mathematical science. There are two variables, the position and velocity, that can describe the 2-dimensional phase space system. For example, the state of pendulum may be specified by its position and its velocity, so its phase space is 2-dimensional. The state of the system at a given time has a unique corresponding point in the phase space. In order to describe the motion of an oscillator, we can talk about its motion …

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The (1,2)-Step Competition Graph Of A Tournament, Kim A. S. Factor, Sarah Merz Jan 2011

The (1,2)-Step Competition Graph Of A Tournament, Kim A. S. Factor, Sarah Merz

Mathematics, Statistics and Computer Science Faculty Research and Publications

The competition graph of a digraph, introduced by Cohen in 1968, has been extensively studied. More recently, in 2000, Cho, Kim, and Nam defined the m-step competition graph. In this paper, we offer another generalization of the competition graph. We define the (1,2)-step competition graph of a digraph D, denoted C1,2(D), as the graph on V(D) where {x,y}∈E(C1,2(D)) if and only if there exists a vertex z≠x,y, such that either dD−y( …

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Mathematical Modeling And Computation Of Channel Flow Over Discrete Structures, Rolando J. Olivares, Daniel N. Riahi Jan 2011

Mathematical Modeling And Computation Of Channel Flow Over Discrete Structures, Rolando J. Olivares, Daniel N. Riahi

School of Mathematical & Statistical Sciences Faculty Publications

In this paper mathematical modeling and computation of channel flow over small discrete structures are carried out under some reasonable conditions. A mathematical model for such a flow problem, which is based on a relevant system of partial differential equations and Fourier analysis, is studied using perturbation and nonlinear stability methods, and the resulting flow solutions over two types of discrete structures are computed under both stable and unstable conditions. It was found, in particular, that for a subcritical domain with the Reynolds number R slightly less than its critical value Rc, which is defined as the value below which …

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Fundamental Transversals On The Complexes Of Polyhedra, Joy D'Andrea Jan 2011

Fundamental Transversals On The Complexes Of Polyhedra, Joy D'Andrea

USF Tampa Graduate Theses and Dissertations

We present a formal description of `Face Fundamental Transversals' on the faces of the Complexes of polyhedra (meaning threedimensional polytopes). A Complex of a polyhedron is the collection of the vertex points of the polyhedron, line segment edges and polygonal faces of the polyhedron. We will prove that for the faces of any 3-dimensional complex of a polyhedron under face adjacency relations, that a `Face Fundamental Transversal' exists, and it is a union of the connected orbits of faces that are intersected exactly once. While exploring the problem of finding a face fundamental transversal, we have found a partial result …

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