A Quasi-Classical Logic For Classical Mathematics,
2014
University of Nevada, Las Vegas
A Quasi-Classical Logic For Classical Mathematics, Henry Nikogosyan
Honors College Theses
Classical mathematics is a form of mathematics that has a large range of application; however, its application has boundaries. In this paper, I show that Sperber and Wilson’s concept of relevance can demarcate classical mathematics’ range of applicability by demarcating classical logic’s range of applicability. Furthermore, I introduce how to systematize Sperber and Wilson’s concept of relevance into a quasi-classical logic that can explain classical logic’s and classical mathematics’ range of applicability.
Limit Distributions Of Random Walks On Stochastic Matrices,
2014
The University of Texas Rio Grande Valley
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 …
A Combinatorial Proof Of A Theorem Of Katsuura,
2014
Trinity University
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.
The Lp Relaxation Orthogonal Array Polytope And Its Permutation Symmetries,
2014
Air Force Institute of Technology
The Lp Relaxation Orthogonal Array Polytope And Its Permutation Symmetries, Andrew J. Geyer, Dursun A. Bulutoglu, Steven J. Rosenberg
Faculty Publications
Symmetry plays a fundamental role in design of experiments. In particular, symmetries of factorial designs that preserve their statistical properties are exploited to find designs with the best statistical properties. By using a result proved by Rosenberg [6], the concept of the LP relaxation orthogonal array polytope is developed and studied. A complete characterization of the permutation symmetry group of this polytope is made. Also, this characterization is verified computationally for many cases. Finally, a proof is provided.
Symplectic Mackey Theory,
2014
Georgia Southern University
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.
Nonsmooth Algorithms And Nesterov's Smoothing Technique For Generalized Fermat-Torricelli Problems,
2014
Portland State University
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.
Online Resource Platform For Mathematics Education,
2014
Technological University Dublin
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 …
Physics: Rethinking The Foundations,
2014
University at Albany, State University of New York
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 …
Casimir Energies In Spherically Symmetric Background Potentials Revisited,
2014
Stephen F. Austin State University
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.
A Case Study Of How Ninth Grade Mathematics Students Construct Knowledge During A Productive Failure Model,
2014
Mercer University
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), …
Semi-Fredholm Solvability In The Framework Of Singular Solutions For The (3+1)-D Protter-Morawetz Problem,
2014
Technical University of Sofia
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 …
The Antisymmetry Betweenness Axiom And Hausdorff Continua,
2014
Marquette University
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.
Fractal Growth On The Surface Of A Planet And In Orbit Around It,
2014
Wilfrid Laurier University
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 …
The Mass Of Graviton And Its Relation To The Number Of Information According To The Holographic Principle,
2014
Wilfrid Laurier University
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 …
Planarity Of Whitney Levels,
2014
Missouri University of Science and Technology
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].
Ua66 Ogden College Of Science & Engineering Newsletter,
2014
Western Kentucky University
Ua66 Ogden College Of Science & Engineering Newsletter, Cheryl Stevens, Dean
Ogden College of Science & Engineering Publications
No abstract provided.
Generalized Theoretical Criteria For Annihilation Of Hiv-1 Virions During Haart,
2014
Fayetteville State University
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 …
Lie Algebroid Modules And Representations Up To Homotopy,
2014
Smith College
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.
Probabilistic Uncertainty Quantification And Experiment Design For Nonlinear Models: Applications In Systems Biology,
2014
Purdue University
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 …
On The Occurrences Of Motifs In Recursive Trees, With Applications To Random Structures,
2014
Purdue University
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 …
