Open Access. Powered by Scholars. Published by Universities.®

Mathematics Commons™

Open Access. Powered by Scholars. Published by Universities.®

2014

Discipline
Institution
Keyword
Publication
Publication Type
File Type

Articles 91 - 120 of 995

Full-Text Articles in Mathematics

A Game-Theoretic Analysis Of The Nuclear Non-Proliferation Treaty, Peter Revesz Nov 2014

A Game-Theoretic Analysis Of The Nuclear Non-Proliferation Treaty, Peter Revesz

School of Computing: Conference and Workshop Papers

Although nuclear non-proliferation is an almost universal human desire, in practice, the negotiated treaties appear unable to prevent the steady growth of the number of states that have nuclear weapons. We propose a computational model for understanding the complex issues behind nuclear arms negotiations, the motivations of various states to enter a nuclear weapons program and the ways to diffuse crisis situations.

Go to article

A Combinatorial Proof Of A Theorem Of Katsuura, Brian K. Miceli Nov 2014

A Combinatorial Proof Of A Theorem Of Katsuura, Brian K. Miceli

Mathematics Faculty Research

We give a combinatorial proof of an algebraic result of Katsuura's. Moreover, we use the proof of this result to shed some light on an interesting property of the result itself.

Go to article

Functions On Adjacent Vertex Degrees Of Trees With Given Degree Sequence, Hua Wang Nov 2014

Functions On Adjacent Vertex Degrees Of Trees With Given Degree Sequence, Hua Wang

Mathematical Sciences: Faculty Publications

In this note we consider a discrete symmetric function f(x, y) where f(x; a) + f(y, b) ≥ f(y, a) + f(x, b) for any x ≥ y and a ≥ b, associated with the degrees of adjacent vertices in a tree. The extremal trees with respect to the corresponding graph invariant, defined as Σ uv∈E(T) f(deg(u), deg(v)), are characterized by the “greedy tree” and “alternating greedy tree”. This is achieved through simple generalizations of previously used ideas on similar questions. As special cases, the already known extremal structures of the Randić index follow as corollaries. The extremal structures for …

Go to article

Limit Distributions Of Random Walks On Stochastic Matrices, Santanu Chakraborty, Arunava Mukherjea Nov 2014

Limit Distributions Of Random Walks On Stochastic Matrices, Santanu Chakraborty, Arunava Mukherjea

School of Mathematical & Statistical Sciences Faculty Publications

Problems similar to Ann. Prob. 22 (1994) 424–430 and J. Appl. Prob. 23 (1986) 1019–1024 are considered here. The limit distribution of the sequence XnXn−1 ··· X1, where (Xn)n≥1 is a sequence of i.i.d. 2 × 2 stochastic matrices with each Xn distributed as μ, is identified here in a number of discrete situations. A general method is presented and it covers the cases when the random components Cn and Dn (not necessarily independent), (Cn, Dn) being the first column of Xn, have the same (or different) Bernoulli distributions. Thus (Cn, Dn) is valued in {0, r}2, where r is …

Go to article

Symplectic Mackey Theory, Francois Ziegler Oct 2014

Symplectic Mackey Theory, Francois Ziegler

Mathematical Sciences: Faculty Publications

Many years ago Kazhdan, Kostant and Sternberg defined the notion of inducing a hamiltonian action from a Lie subgroup. In this paper, we develop the attendant imprimitivity theorem and Mackey analysis in the full generality needed to deal with arbitrary closed normal subgroups.

Go to article

Nonsmooth Algorithms And Nesterov's Smoothing Technique For Generalized Fermat-Torricelli Problems, Nguyen Mau Nam, Nguyen Thai An, R. Blake Rector, Jie Sun Oct 2014

Nonsmooth Algorithms And Nesterov's Smoothing Technique For Generalized Fermat-Torricelli Problems, Nguyen Mau Nam, Nguyen Thai An, R. Blake Rector, Jie Sun

Mathematics and Statistics Faculty Publications and Presentations

We present algorithms for solving a number of new models of facility location which generalize the classical Fermat--Torricelli problem. Our first approach involves using Nesterov's smoothing technique and the minimization majorization principle to build smooth approximations that are convenient for applying smooth optimization schemes. Another approach uses subgradient-type algorithms to cope directly with the nondifferentiability of the cost functions. Convergence results of the algorithms are proved and numerical tests are presented to show the effectiveness of the proposed algorithms.

Go to article

Online Resource Platform For Mathematics Education, Marisa Llorens, Edmund Nevin, Eileen Mageean Oct 2014

Online Resource Platform For Mathematics Education, Marisa Llorens, Edmund Nevin, Eileen Mageean

Conference papers

Engineering education is facing many challenges: a decline in core mathematical skills; lowering entry requirements; and the diversity of the student cohort. One approach to confronting these challenges is to make subject content appropriate to the communication styles of today’s student. To achieve this, a pedagogical shift from the traditional hierarchical approach to learning to one that embraces the use of technology as a tool to enhance the student learning experience is required. By including the student as co-creator of course content, a greater sense of engagement is achieved and a change to one where students become agents of their …

Go to article

Physics: Rethinking The Foundations, Kevin H. Knuth Oct 2014

Physics: Rethinking The Foundations, Kevin H. Knuth

Physics Faculty Scholarship

Physics is traditionally conceived of as a set of laws that universally governs the behavior of physical systems. These laws, however they are decreed, are believed to govern the behavior of not only everything in the universe, but the form of the universe itself. However, this traditional concept of physics as a universal governance is at odds with our modern theories of quantum mechanics and relativity, which place the observer and information in a central role. In this talk, I aim to rethink the foundations and attempt to build physics from the bottom up based on a very simple foundational …

Go to article

Casimir Energies In Spherically Symmetric Background Potentials Revisited, Matthew Beauregard, Michael Bordag, Klaus Kirsten Oct 2014

Casimir Energies In Spherically Symmetric Background Potentials Revisited, Matthew Beauregard, Michael Bordag, Klaus Kirsten

Faculty Publications

In this paper we reconsider the formulation for the computation of the Casimir energy in spherically symmetric background potentials. Compared to the previous analysis, the technicalities are much easier to handle and final answers are surprisingly simple.

Go to article

A Case Study Of How Ninth Grade Mathematics Students Construct Knowledge During A Productive Failure Model, Amy F. Westbrook Dr. Oct 2014

A Case Study Of How Ninth Grade Mathematics Students Construct Knowledge During A Productive Failure Model, Amy F. Westbrook Dr.

Georgia Educational Research Association Conference

The purpose of this qualitative study was to explain how ninth grade mathematics students at a rural high school in Georgia constructed knowledge through student talk when problem solving using Kapur’s (2012) productive failure design. An embedded case study design was used to understand how a group of students constructed knowledge through their use of talk, persistence during the task, and use of prior knowledge while working on a productive failure modeled task. Triangulation resulted from the collected data from multiple sources, which included videotaping, interviewing, and analyzing student artifacts. Utilization of the constructivist perspectives of Vygotsky (1934/1962), Piaget (1971), …

Go to article

Semi-Fredholm Solvability In The Framework Of Singular Solutions For The (3+1)-D Protter-Morawetz Problem, Nedyu Popivanov, Todor Popov, Allen Tesdall Oct 2014

Semi-Fredholm Solvability In The Framework Of Singular Solutions For The (3+1)-D Protter-Morawetz Problem, Nedyu Popivanov, Todor Popov, Allen Tesdall

Publications and Research

For the four-dimensional nonhomogeneous wave equation boundary value problems that are multidimensional analogues of Darboux problems in the plane are studied. It is known that for smooth right-hand side functions the unique generalized solution may have a strong power-type singularity at only one point. This singularity is isolated at the vertex �� of the boundary light characteristic cone and does not propagate along the bicharacteristics.The present paper describes asymptotic expansions of the generalized solutions in negative powers of the distance to ��. Some necessary and sufficient conditions for existence of bounded solutions are proven and additionally a priori estimates for …

Go to article

The Antisymmetry Betweenness Axiom And Hausdorff Continua, Paul Bankston Oct 2014

The Antisymmetry Betweenness Axiom And Hausdorff Continua, Paul Bankston

Mathematics, Statistics and Computer Science Faculty Research and Publications

An interpretation of betweenness on a set satisfies the antisymmetry axiom at a point a if it is impossible for each of two distinct points to lie between the other and a. In this paper we study the role of antisymmetry as it applies to the K-interpretation of betweenness in a Hausdorff continuum X, where a point c lies between points a and b exactly when every subcontinuum of X containing both a and b contains c as well.

Go to article

Fractal Growth On The Surface Of A Planet And In Orbit Around It, Ioannis Haranas, Ioannis Gkigkitzis, Athanasios Alexiou Oct 2014

Fractal Growth On The Surface Of A Planet And In Orbit Around It, Ioannis Haranas, Ioannis Gkigkitzis, Athanasios Alexiou

Physics and Computer Science Faculty Publications

Fractals are defined as geometric shapes that exhibit symmetry of scale. This simply implies that fractal is a shape that it would still look the same even if somebody could zoom in on one of its parts an infinite number of times. This property is also called self-similarity with several applications including nano-pharmacology and drug nanocarriers. We are interested in the study of the properties of fractal aggregates in a microgravity environment above an orbiting spacecraft. To model the effect we use a complete expression for the gravitational acceleration. In particular on the surface of the Earth the acceleration is …

Go to article

The Mass Of Graviton And Its Relation To The Number Of Information According To The Holographic Principle, Ioannis Haranas, Ioannis Gkigkitzis Oct 2014

The Mass Of Graviton And Its Relation To The Number Of Information According To The Holographic Principle, Ioannis Haranas, Ioannis Gkigkitzis

Physics and Computer Science Faculty Publications

We investigate the relation of the mass of the graviton to the number of information 𝑁 in a flat universe. As a result we find that the mass of the graviton scales as 𝑚gr ∝ 1/√𝑁. Furthermore, we find that the number of gravitons contained inside the observable horizon is directly proportional to the number of information 𝑁; that is, 𝑁gr ∝ 𝑁. Similarly, the total mass of gravitons that exist in the universe is proportional to the number of information 𝑁; that is, 𝑀gr ∝ √𝑁. In an effort to establish a relation between the graviton …

Go to article

Planarity Of Whitney Levels, Jorbe Bustamante, W. J. Charatonik, Raul Escobedo Oct 2014

Planarity Of Whitney Levels, Jorbe Bustamante, W. J. Charatonik, Raul Escobedo

Mathematics and Statistics Faculty Research & Creative Works

First, we characterize all locally connected continua whose all Whitney levels are planar. Second, we show by example that planarity is not a (strong) Whitney reversible property. This answers a question from Illanes-Nadler book [2].

Go to article

Ua66 Ogden College Of Science & Engineering Newsletter, Cheryl Stevens, Dean Oct 2014

Ua66 Ogden College Of Science & Engineering Newsletter, Cheryl Stevens, Dean

Ogden College of Science & Engineering Publications

No abstract provided.

Go to article

Generalized Theoretical Criteria For Annihilation Of Hiv-1 Virions During Haart, Frank Nani, Mingxian Jin Oct 2014

Generalized Theoretical Criteria For Annihilation Of Hiv-1 Virions During Haart, Frank Nani, Mingxian Jin

Math and Computer Science Faculty Working Papers

Aims: This paper is an elaborate and quantitative attempt to construct medically applicable mathematical models and derive criteria for efficacious Highly Active Anti-Retroviral Therapy (HAART) protocol for an AIDS patient. The patho-physiological dynamics of Human Immuno-deficiency Virus type 1 (HIV-1) induced AIDS during HAART is modeled by a system of non-linear deterministic differential equations. The physiologically relevant and clinically plausible equations depict the dynamics of uninfected CD4+ T cells (x1), HIV-1 infected CD4+ T cells (x2), HIV-1 virions in the blood plasma (x3), HIV-1 specific CD8+ T cells (x4), and the concentration of HAART drug molecules (x5). The major objective …

Go to article

Probabilistic Uncertainty Quantification And Experiment Design For Nonlinear Models: Applications In Systems Biology, Vu Cao Duy Thien Dinh Oct 2014

Probabilistic Uncertainty Quantification And Experiment Design For Nonlinear Models: Applications In Systems Biology, Vu Cao Duy Thien Dinh

Open Access Dissertations

Despite the ever-increasing interest in understanding biology at the system level, there are several factors that hinder studies and analyses of biological systems. First, unlike systems from other applied fields whose parameters can be effectively identified, biological systems are usually unidentifiable, even in the ideal case when all possible system outputs are known with high accuracy. Second, the presence of multivariate bifurcations often leads the system to behaviors that are completely different in nature. In such cases, system outputs (as function of parameters/inputs) are usually discontinuous or have sharp transitions across domains with different behaviors. Finally, models from systems biology …

Go to article

On The Occurrences Of Motifs In Recursive Trees, With Applications To Random Structures, Mohan Gopaladesikan Oct 2014

On The Occurrences Of Motifs In Recursive Trees, With Applications To Random Structures, Mohan Gopaladesikan

Open Access Dissertations

In this dissertation we study three problems related to motifs and recursive trees. In the first problem we consider a collection of uncorrelated motifs and their occurrences on the fringe of random recursive trees. We compute the exact mean and variance of the multivariate random vector of the counts of occurrences of the motifs. We further use the Cramér-Wold device and the contraction method to show an asymptotic convergence in distribution to a multivariate normal random variable with this mean and variance. ^ The second problem we study is that of the probability that a collection of motifs (of the …

Go to article

Nonparametric Variable Selection And Dimension Reduction Methods And Their Applications In Pharmacogenomics, Jingyi Zhu Oct 2014

Nonparametric Variable Selection And Dimension Reduction Methods And Their Applications In Pharmacogenomics, Jingyi Zhu

Open Access Dissertations

Nowadays it is common to collect large volumes of data in many fields with an extensive amount of variables, but often a small or moderate number of samples. For example, in the analysis of genomic data, the number of genes can be very large, varying from tens of thousands to several millions, whereas the number of samples is several hundreds to thousands. Pharmacogenomics is an example of genomics data analysis that we are considering here. Pharmacogenomics research uses whole-genome genetic information to predict individuals' drug response. Because whole-genome data are high dimensional and their relationships to drug response are complicated, …

Go to article

Exploring The Relationship Between K-8 Prospective Teachers’ Algebraic Thinking Proficiency And The Questions They Pose During Diagnostic Algebraic Thinking Interviews, Leigh A. Van Den Kieboom, Marta T. Magiera, John C. Moyer Oct 2014

Exploring The Relationship Between K-8 Prospective Teachers’ Algebraic Thinking Proficiency And The Questions They Pose During Diagnostic Algebraic Thinking Interviews, Leigh A. Van Den Kieboom, Marta T. Magiera, John C. Moyer

Mathematics, Statistics and Computer Science Faculty Research and Publications

In this study, we explored the relationship between prospective teachers’ algebraic thinking and the questions they posed during one-on-one diagnostic interviews that focused on investigating the algebraic thinking of middle school students. To do so, we evaluated prospective teachers’ algebraic thinking proficiency across 125 algebra-based tasks and we analyzed the characteristics of questions they posed during the interviews. We found that prospective teachers with lower algebraic thinking proficiency did not ask any probing questions. Instead, they either posed questions that simply accepted and affirmed student responses or posed questions that guided the students toward an answer without probing student thinking. …

Go to article

Relatively Congruence-Free Regular Semigroups, Peter R. Jones Oct 2014

Relatively Congruence-Free Regular Semigroups, Peter R. Jones

Mathematics, Statistics and Computer Science Faculty Research and Publications

Yu, Wang, Wu and Ye call a semigroup S τ -congruence-free, where τ is an equivalence relation on S, if any congruence ρ on S is either disjoint from τ or contains τ . A congruence-free semigroup is then just an ω-congruence-free semigroup, where ω is the universal relation. They determined the completely regular semigroups that are τ -congruence-free with respect to each of the Green’s relations. The goal of this paper is to extend their results to all regular semigroups. Such a semigroup is J –congruence-free if and only if it is either a semilattice or has …

Go to article

Generalized Exponentiated Moment Exponential Distribution, Zafar Iqbal, Syed Anwer Hasnain, Muhammad Salman, Munir Ahmad, Gholamhossein Hamedani Oct 2014

Generalized Exponentiated Moment Exponential Distribution, Zafar Iqbal, Syed Anwer Hasnain, Muhammad Salman, Munir Ahmad, Gholamhossein Hamedani

Mathematics, Statistics and Computer Science Faculty Research and Publications

Moment distributions have a vital role in mathematics and statistics, in particular in probability theory, in the perspective research related to ecology, reliability, biomedical field, econometrics, survey sampling and in life-testing. Hasnain (2013) developed an exponentiated moment exponential (EME) distribution and discussed some of its important properties. In the present work, we propose a generalization of EME distribution which we call it generalized EME (GEME) distribution and develop various properties of the distribution. We also present characterizations of the distribution in terms of conditional expectation as well as based on hazard function of the GEME random variable.

Go to article

Some Remarks On Recent Characterizations Of Continuous Distributions, Gholamhossein Hamedani Oct 2014

Some Remarks On Recent Characterizations Of Continuous Distributions, Gholamhossein Hamedani

Mathematics, Statistics and Computer Science Faculty Research and Publications

We would closely look at two recent published papers dealing with characterizations of certain univariate continuous distributions. We shall explain that the main results reported lack important assumptions. These results nevertheless are based on the conditional expectations of monotone functions of the generalized order statistics. We will also mention that similar results have recently been reported without the assumption of monotonicity of the functions of the generalized order statistics.

Go to article

Transients In The Synchronization Of Oscillator Arrays, Carlos E. Cantos, J. J. P. Veerman Oct 2014

Transients In The Synchronization Of Oscillator Arrays, Carlos E. Cantos, J. J. P. Veerman

Mathematics and Statistics Faculty Publications and Presentations

The purpose of this note is threefold. First we state a few conjectures that allow us to rigorously derive a theory which is asymptotic in N (the number of agents) that describes transients in large arrays of (identical) linear damped harmonic oscillators in R with completely decentralized nearest neighbor interaction. We then use the theory to establish that in a certain range of the parameters transients grow linearly in the number of agents (and faster outside that range). Finally, in the regime where this linear growth occurs we give the constant of proportionality as a function of the signal velocities …

Go to article

2014 (Fall), University Of Dayton. Department Of Mathematics Oct 2014

2014 (Fall), University Of Dayton. Department Of Mathematics

Colloquia

Abstracts of the talks given at the 2014 Fall Colloquium.

Go to article

The Unimodality Of Pure O-Sequences Of Type Three In Three Variables, Bernadette Boyle Oct 2014

The Unimodality Of Pure O-Sequences Of Type Three In Three Variables, Bernadette Boyle

Mathematics Faculty Publications

Since the 1970’s, great interest has been taken in the study of pure O-sequences, which are in bijective correspondence to the Hilbert functions of Artinian level monomial algebras. Much progress has been made in classifying these by their shape. It has been shown that all monomial complete intersections, Artinian algebras in two variables and Artinian level monomial algebras with type two in both three and four variables have unimodal Hilbert functions. This paper proves that Artinian level monomial algebras of type three in three variables have unimodal Hilbert functions. We will also discuss the licciness of these algebras.

Go to article

Configuration Spaces Of Convex And Embedded Polygons In The Plane, Don H. Shimamoto, Mary K. Wootters , '08 Oct 2014

Configuration Spaces Of Convex And Embedded Polygons In The Plane, Don H. Shimamoto, Mary K. Wootters , '08

Mathematics & Statistics Faculty Works

This paper concerns the topology of configuration spaces of linkages whose underlying graph is a single cycle. Assume that the edge lengths are such that there are no configurations in which all the edges lie along a line. The main results are that, modulo translations and rotations, each component of the space of convex configurations is homeomorphic to a closed Euclidean ball and each component of the space of embedded configurations is homeomorphic to a Euclidean space. This represents an elaboration on the topological information that follows from the convexification theorem of Connelly, Demaine, and Rote.

Go to article

Prognostic Value Of Estimated Functional Capacity Incremental To Cardiac Biomarkers In Stable Cardiac Patients, W.H. Wilson Tang, Eric J. Topol, Yiying Fan, Yuping Wu, Leslie Cho, Cindy Stevenson, Stephen G. Ellis, Stanley L. Hazen Oct 2014

Prognostic Value Of Estimated Functional Capacity Incremental To Cardiac Biomarkers In Stable Cardiac Patients, W.H. Wilson Tang, Eric J. Topol, Yiying Fan, Yuping Wu, Leslie Cho, Cindy Stevenson, Stephen G. Ellis, Stanley L. Hazen

Mathematics and Statistics Faculty Publications

Background: Few studies have investigated functional capacity self-assessment tools in either prediction of future major adverse cardiac outcomes beyond all-cause mortality or direct comparisons with clinically available biomarkers. Methods and Results: We estimated functional capacity using the Duke Activity Status Index (DASI) questionnaire in 8987 sequential stable patients without acute coronary syndrome who were undergoing elective diagnostic coronary angiography with 3-year follow-up of major adverse cardiac events (death, nonfatal myocardial infarction, or stroke). A low DASI score provided independent prediction of a 4.8-fold increase in future risk of incident major adverse cardiac events at 3 years (quartiles 1 versus 4 …

Go to article

Lie Algebroid Modules And Representations Up To Homotopy, Rajan Amit Mehta Oct 2014

Lie Algebroid Modules And Representations Up To Homotopy, Rajan Amit Mehta

Mathematics Sciences: Faculty Publications

We establish a relationship between two different generalizations of Lie algebroid representations: representation up to homotopy and Vaĭntrob’s Lie algebroid modules. Specifically, we show that there is a noncanonical way to obtain a representation up to homotopy from a given Lie algebroid module, and that any two representations up to homotopy obtained in this way are equivalent in a natural sense. We therefore obtain a one-to-one correspondence, up to equivalence.

Go to article

First Prev Next Last