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Solution Of Nonlinear Time-Dependent Pde Through Componentwise Approximation Of Matrix Functions, Alexandru Cibotarica 2015 University of Southern Mississippi

Solution Of Nonlinear Time-Dependent Pde Through Componentwise Approximation Of Matrix Functions, Alexandru Cibotarica

Dissertations

Exponential propagation iterative (EPI) methods provide an efficient approach to the solution of large stiff systems of ODE, compared to standard integrators. However, the bulk of the computational effort in these methods is due to products of matrix functions and vectors, which can become very costly at high resolution due to an increase in the number of Krylov projection steps needed to maintain accuracy. In this dissertation, it is proposed to modify EPI methods by using Krylov subspace spectral (KSS) methods, instead of standard Krylov projection methods, to compute products of matrix functions and vectors. This improvement allowed the benefits ...


Lorentz Invariant Spacelike Surfaces Of Constant Mean Curvature In Anti-De Sitter 3-Space, Jamie Patrick Lambert 2015 University of Southern Mississippi

Lorentz Invariant Spacelike Surfaces Of Constant Mean Curvature In Anti-De Sitter 3-Space, Jamie Patrick Lambert

Master's Theses

In this thesis, I studied Lorentz invariant spacelike surfaces with constant mean curvature H = c in the anti-de Sitter 3-space H31(−c2) of constant curvature −c2. In particular, I construct Lorentz invariant spacelike surfaces of constant mean curvature c and maximal Lorentz invariant spacelike surfaces in H31(−c2). I also studied the limit behavior of those constant mean curvature c surfaces in H31(−c2). It turns out that they approach a maximal catenoid in Minkowski 3-space E31 as c 0. The limit maximal catenoid is Lorentz invariant in ...


Dynamic Approach To K-Forcing, Yair Caro, Ryan Pepper 2015 University of Houston - Downtown

Dynamic Approach To K-Forcing, Yair Caro, Ryan Pepper

Theory and Applications of Graphs

The k-forcing number of a graph is a generalization of the zero forcing number. In this note, we give a greedy algorithm to approximate the k-forcing number of a graph. Using this dynamic approach, we give corollaries which improve upon two theorems from a recent paper of Amos, Caro, Davila and Pepper [2], while also answering an open problem posed by Meyer [9].


Global Optimized Isothermal And Nonlinear Models Of Earth’S Standard Atmosphere, Nihad E. Daidzic, Ph.D., 2015 AAR Aerospace Consulting, LLC

Global Optimized Isothermal And Nonlinear Models Of Earth’S Standard Atmosphere, Nihad E. Daidzic, Ph.D.,

International Journal of Aviation, Aeronautics, and Aerospace

Both, a global isothermal temperature model and a nonlinear quadratic temperature model of the ISA was developed and presented here. Constrained optimization techniques in conjunction with the least-square-root approximations were used to design best-fit isothermal models for ISA pressure and density changes up to 47 geopotential km for NLPAM, and 86 orthometric km for ISOAM respectively. The mass of the dry atmosphere and the relevant fractional-mass scale heights have been computed utilizing the very accurate eight-point Gauss-Legendre numerical quadrature for both ISOAM and NLPAM. Both, the ISOAM and the NLPAM represent viable alternatives to ISA in many practical applications and ...


Graph Centers, Hypergraph Degree Sequences, And Induced-Saturation, Sarah Lynne Behrens 2015 University of Nebraska-Lincoln

Graph Centers, Hypergraph Degree Sequences, And Induced-Saturation, Sarah Lynne Behrens

Dissertations, Theses, and Student Research Papers in Mathematics

The center of a graph is the set of vertices whose distance to other vertices is minimal. The centralizing number of a graph G is the minimum number of additional vertices in any graph H where V(G) is the center of H. Buckley, Miller, and Slater and He and Liu provided infinite families of graphs with each centralizing number. We show the number of graphs with each nonzero centralizing number grows super-exponentially with the number of vertices. We also provide a method of altering graphs without changing the centralizing number and give results about the centralizing number of dense ...


The Topology Of Absence, Nora E. Culik 2015 Claremont Colleges

The Topology Of Absence, Nora E. Culik

Journal of Humanistic Mathematics

“The Topology of Absence” literalizes triangulations, hyperbeloids, and the concept of the limit in the story of “locating” a lost mother. This story, like “The Physicist’s Basement” in the July 2014 issue, is part of a series that worries about competing notions of mathematics, i.e., mathematics as some sort of disembodied configuration or as emergent in the material reality of human life.


Geometry Of Life, Janice Dykacz 2015 retired

Geometry Of Life, Janice Dykacz

Journal of Humanistic Mathematics

Relationships in life can be expressed through geometric curves


Mathematical Double Dactyls, Tristan Miller 2015 Department of Computer Science, Technische Universität Darmstadt

Mathematical Double Dactyls, Tristan Miller

Journal of Humanistic Mathematics

No abstract provided.


On Mathematicians' Eccentricity, Robert Haas 2015 None

On Mathematicians' Eccentricity, Robert Haas

Journal of Humanistic Mathematics

Eccentricity, though not inevitable, happens. Lightheartedly classifying examples, the author traces it back to factors, like creativity and absorption, essential to mathematical success, and recommends an attitude of amused tolerance towards others as well as to ourselves.


A System Of Equations: Mathematics Lessons In Classical Literature, Valery F. Ochkov, Andreas Look 2015 Moscow Power Engineering Institute (National Research University)

A System Of Equations: Mathematics Lessons In Classical Literature, Valery F. Ochkov, Andreas Look

Journal of Humanistic Mathematics

The aim of this paper is to showcase a handful of mathematical challenges found in classical literature and to offer possible ways of integrating classical literature in mathematics lessons. We analyze works from a range of authors such as Jules Verne, Anton Chekhov, and others. We also propose ideas for further tasks. Most of the problems can be restated in terms of simple mathematical equations, and they can often be solved without a computer. Nevertheless, we use the computer program Mathcad to solve the problems and to illustrate the solutions to enhance the reader’s mathematical experience.


Mathematics: What Has It To Do With Me?, Man Keung Siu 2015 Department of Mathematics, University of Hong Kong

Mathematics: What Has It To Do With Me?, Man Keung Siu

Journal of Humanistic Mathematics

Mathematics teachers must have encountered the following question raised by students: “What is the use of mathematics?” Although the value of mathematics is not to be determined solely by its applications, to the general public this is a more important and more convincing facet of the subject. Nevertheless, this also brings up the corresponding query: is this subject being properly used? Does mathematics play a role in moral education?


On Similarities And Differences Between Proving And Problem Solving, Milos Savic 2015 University of Oklahoma

On Similarities And Differences Between Proving And Problem Solving, Milos Savic

Journal of Humanistic Mathematics

A link between proving and problem solving has been established in the literature [5, 21]. In this paper, I discuss similarities and differences between proving and problem solving using the Multidimensional Problem-Solving Framework created by Carlson and Bloom [2] with Livescribepen data from a previous study [13]. I focus on two participants’ proving processes: Dr. G, a topologist, and L, a mathematics graduate student. Many similarities between the framework and the proving processes of Dr. G and L were revealed, but there were also some differences. In addition, there were some distinct differences between the proving actions of the ...


Counting The Angels And Devils In Escher's Circle Limit Iv, John Choi, Nicholas Pippenger 2015 Harvey Mudd College

Counting The Angels And Devils In Escher's Circle Limit Iv, John Choi, Nicholas Pippenger

Journal of Humanistic Mathematics

We derive the rational generating function that enumerates the angels and devils in M. C. Escher's Circle Limit IV according to their combinatorial distance from the six creatures whose feet meet at the center of the disk. This result shows that the base of the exponential rate of growth is 1.582... (the largest root of the polynomial 1 - z^2 - 2z^3 - z^4 + z^6).


On Derivatives And Norms Of Generalized Matrix Functions And Respective Symmetric Powers, Sonia Carvalho, Pedro J. Freitas 2015 Centro de Estruturas Lineares e Combinat ́oria da Universidade de Lisboa

On Derivatives And Norms Of Generalized Matrix Functions And Respective Symmetric Powers, Sonia Carvalho, Pedro J. Freitas

Electronic Journal of Linear Algebra

In recent papers, S. Carvalho and P. J. Freitas obtained formulas for directional derivatives, of all orders, of the immanant and of the m-th $\xi$-symmetric tensor power of an operator and a matrix, when $\xi$ is a character of the full symmetric group. The operator bound norm of these derivatives was also calculated. In this paper similar results are established for generalized matrix functions and for every symmetric tensor power.


Gait Transition Dynamics Are Modulated By Experimental Protocol, Mohammad Abdolvahab, Jason Gordon 2015 University of Connecticut - Storrs

Gait Transition Dynamics Are Modulated By Experimental Protocol, Mohammad Abdolvahab, Jason Gordon

Mohammad Abdolvahab

No abstract provided.


Mathematician's Apology, Tom Clark 2015 Dordt College

Mathematician's Apology, Tom Clark

Faculty Work: Comprehensive List

"Better standards may help all math teachers to shape our classes to better reflect the creativity and play at the heart of mathematics."

Posting about ways to improve math's negative image­­­­­­­­ from In All Things - an online hub committed to the claim that the life, death, and resurrection of Jesus Christ has implications for the entire world.

http://inallthings.org/a-mathematicians-apology/


Tame Filling Functions And Closure Properties, Anisah Nu'Man 2015 University of Nebraska-Lincoln

Tame Filling Functions And Closure Properties, Anisah Nu'man

Dissertations, Theses, and Student Research Papers in Mathematics

Let G be a group with a finite presentation P = such that A is inverse- closed. Let f : N[1/4] → N[1/4] be a nondecreasing function. Loosely, f is an intrinsic tame filling function for (G;P) if for every word w over A* that represents the identity element in G, there exists a van Kampen diagram Δ for w over P and a continuous choice of paths from the basepoint * of Δ to points on the boundary of Δ such that the paths are steadily moving outward as measured by f. The isodiametric function (or intrinsic diameter ...


Reproducing Kernel Hilbert Space Vs. Frame Estimates, Palle E. T. Jorgensen, Myung-Sin Song 2015 The University of Iowa

Reproducing Kernel Hilbert Space Vs. Frame Estimates, Palle E. T. Jorgensen, Myung-Sin Song

SIUE Faculty Research, Scholarship, and Creative Activity

We consider conditions on a given system F of vectors in Hilbert space H, forming a frame, which turn Hinto a reproducing kernel Hilbert space. It is assumed that the vectors in F are functions on some set Ω . We then identify conditions on these functions which automatically give H the structure of a reproducing kernel Hilbert space of functions on Ω. We further give an explicit formula for the kernel, and for the corresponding isometric isomorphism. Applications are given to Hilbert spaces associated to families of Gaussian processes.


Bounds For The Zero Forcing Number Of Graphs With Large Girth, Randy Davila, Franklin Kenter 2015 Rice University

Bounds For The Zero Forcing Number Of Graphs With Large Girth, Randy Davila, Franklin Kenter

Theory and Applications of Graphs

The zero-forcing number, Z(G) is an upper bound for the maximum nullity of all symmetric matrices with a sparsity pattern described by the graph. A simple lower bound is δ ≤ Z(G) where δ is the minimum degree. An improvement of this bound is provided in the case that G has girth of at least 5. In particular, it is shown that 2δ − 2 ≤ Z(G) for graphs with girth of at least 5; this can be further improved when G has a small cut set. Lastly, a conjecture is made regarding a lower bound for Z(G) as ...


Review Of Developing Quantitative Literacy Skills In History And The Social Sciences: A Web-Based Common Core Approach By Kathleen W. Craver, Victor J. Ricchezza, H L. Vacher 2015 University of South Florida

Review Of Developing Quantitative Literacy Skills In History And The Social Sciences: A Web-Based Common Core Approach By Kathleen W. Craver, Victor J. Ricchezza, H L. Vacher

Numeracy

Kathleen W. Craver. Developing Quantitative Literacy Skills in History and Social Sciences: A Web-Based Common Core Standards Approach (Lantham MD: Rowman & Littlefield Publishing Group, Inc., 2014). 191 pp.
ISBN 978-1-4758-1050-9 (cloth); ISBN …-1051-6 (pbk); ISBN…-1052-3 (electronic).

This book could be a breakthrough for teachers in the trenches who are interested in or need to know about quantitative literacy (QL). It is a resource providing 85 topical pieces, averaging 1.5 pages, in which a featured Web site is presented, described, and accompanied by 2-4 critical-thinking questions purposefully drawing on data from the Web site. The featured Web sites range from primary documents (e.g., All about California and the ...


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