Mathematics Commons^™

A Constructive Proof Of Fundamental Theory For Fuzzy Variable Linear Programming Problems, A. Ebrahimnejad

Applications and Applied Mathematics: An International Journal (AAM)

Two existing methods for solving fuzzy variable linear programming problems based on ranking functions are the fuzzy primal simplex method proposed by Mahdavi-Amiri et al. (2009) and the fuzzy dual simplex method proposed by Mahdavi-Amiri and Nasseri (2007). In this paper, we prove that in the absence of degeneracy these fuzzy methods stop in a finite number of iterations. Moreover, we generalize the fundamental theorem of linear programming in a crisp environment to a fuzzy one. Finally, we illustrate our proof using a numerical example.

Boolean And Profinite Loops, Benjamin Andrew Phillips

Dissertations

A Quasigroup G consists of a set G together with a binary operation ∗ : G × G → G such that, for any elements a, b ∈ G there are unique solutions to the equations a ∗ x = b and y ∗ a = b within G. A loop is a quasigroup which also contains a 2-sided identity element. More heuristically, loops are essentially non-associative groups. However, without an associative binary operation, some of the familiar properties found in groups, such as 2-sided inverse, need not be present in loops.

The study of quasigroups and loops emerges …

On The Behavior Of The Gamma Function On The Negative Side, Tri Minh Ngo

Senior Honors Theses

In this paper we analyze the behavior of the Gamma function at its critical points and points of discontinuity on the negative side of the x-axis. We will also explain the bluntness of the gamma function on this negative side.

A New Approach For Computing Wz Factorization, Effat Golpar-Raboky

Applications and Applied Mathematics: An International Journal (AAM)

Linear systems arise frequently in scientific and engineering computing. Various serial and parallel algorithms have been introduced for their solution. This paper seeks to compute the WZ and the ZW factorizations of a nonsingular matrix A using the right inverse of nested submatrices of A. We introduce two new matrix factorizations, the QZ and the QW factorizations, and compute the factorizations using our proposed approach.

Generalizations Of Two Statistics On Linear Tilings, Toufik Mansour, Mark Shattuck

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, we study generalizations of two well-known statistics on linear square-and-domino tilings by considering only those dominos whose right half covers a multiple of 􀝇, where 􀝇 is a fixed positive integer. Using the method of generating functions, we derive explicit expressions for the joint distribution polynomials of the two statistics with the statistic that records the number of squares in a tiling. In this way, we obtain two families of q -generalizations of the Fibonacci polynomials. When 􀝇 􀵌 1, our formulas reduce to known results concerning previous statistics. Special attention is payed to the case 􀝇 …

Two Reliable Methods For Solving The Modified Improved Kadomtsev-Petviashvili Equation, N. Taghizadeh, S. R. Moosavi Noori

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, the tanh-coth method and the extended (G'/G)-expansion method are used to construct exact solutions of the nonlinear Modified Improved Kadomtsev-Petviashvili (MIKP) equation. These methods transform nonlinear partial differential equation to ordinary differential equation and can be applied to nonintegrable equation as well as integrable ones. It has been shown that the two methods are direct, effective and can be used for many other nonlinear evolution equations in mathematical physics.

Color Models As Tools In Teaching Mathematics, Ma. Louise Antonette N. De Las Peñas

Mathematics Faculty Publications

In this paper we discuss various situations how color models and patterns can be used to simplify the study of abstract mathematics and serve as tools in understanding mathematical ideas. We illustrate the realization of such models through the development of advanced computer technology. In particular, we present how a computer algebra software such as Mathematica, or a dynamic geometry environment, can be utilized to facilitate the study of transformation geometry and group theory.

Regular Homotopy Of Closed Curves On Surfaces, Katherine Kylee Zebedeo

Boise State University Theses and Dissertations

The use of rotation numbers in the classification of regular closed curves in the plane up to regular homotopy sparked the investigation of winding numbers to classify regular closed curves on other surfaces. Chillingworth [1] defined winding numbers for regular closed curves on particular surfaces and used them to classify orientation preserving regular closed curves that are based at a fixed point and direction. We define geometrically a group structure of the set of equivalence classes of regular closed curves based at a fixed point and direction. We prove this group structure coincides with the one introduced by Smale [9] …

On The Representation Of Inverse Semigroups By Difunctional Relations, Nathan Bloomfield

Graduate Theses and Dissertations

A semigroup S is called inverse if for each s in S, there exists a unique t in S such that sts = s and tst = t. A relation σ contained in X x Y is called full if for all x in X and y in Y there exist x' in X and y' in Y such that (x, y') and (x', y) are in σ, and is called difunctional if σ satisfies the equation σ σ^-1 σ = σ. Inverse semigroups were introduced by Wagner and Preston in 1952 and 1954, respectively, and difunctional relations were …

On The Independent Domination Number Of Regular Graphs, Wayne Goddard, Michael A. Henning, Jeremy Lyle, Justin Southey

Faculty Publications

A set S of vertices in a graph G is an independent dominating set of G if S is an independent set and every vertex not in S is adjacent to a vertex in S. In this paper, we consider questions about independent domination in regular graphs.

Using The Taylor Center To Teach Odes, Alexander Gofen

CODEE Journal

This article introduces a powerful ODE solver called the Taylor Center for PCs (http://taylorcenter.org/Gofen/) as a tool for teaching and performing numeric experiments with ODEs. The Taylor Center is an All-in-One GUI-style application for integrating ODEs by applying the modern Taylor Method (Automatic Differentiation). The Taylor Center also offers dynamic graphics (including 3D stereo vision). After a brief review of the features of the Taylor Center, we consider instructive examples of ODEs in various applications and also several particular examples illustrating intricacies of numeric integration. The article therefore continues the thesis of Borrelli and Coleman (CODEE Journal, http://www.codee.org/ref/CJ09-0157) that awareness …

Enhancing Effective Depth-Of-Field By Multi-Focus Image Fusion Using Morphological Techniques., Ishita De Ghosh Dr.

Doctoral Theses

A scene to be photographed, usually includes objects at varying distances from the camera. Depth-of-field of a digital camera is the range of distance, all objects within which appear to be sharp in the image. Due to the low depth-of-field of the camera, images acquired by them often suffer from degradation called out-of-foc us blur. One way to enhance the effective depth-of-field is to acquire se veral images of a scene with focus on different parts of it and then combine these images into a single image in such a way that all regions of the scene are in focus. …

Dark Solitons Of The Qiao's Hierarchy, Rossen Ivanov, Tony Lyons

Articles

We obtain a class of soliton solutions of the integrable hierarchy which has been put forward in a series of works by Z. Qiao. The soliton solutions are in the class of real functions approaching constant value fast enough at infinity, the so-called 'dark solitons'.

Spectral Clustering: An Empirical Study Of Approximation Algorithms And Its Application To The Attrition Problem, B. Cung, T Jin, J. Ramirez, A. Thompson, C. Boutsidis, Deanna Needell

CMC Faculty Publications and Research

Clustering is the problem of separating a set of objects into groups (called clusters) so that objects within the same cluster are more similar to each other than to those in different clusters. Spectral clustering is a now well-known method for clustering which utilizes the spectrum of the data similarity matrix to perform this separation. Since the method relies on solving an eigenvector problem, it is computationally expensive for large datasets. To overcome this constraint, approximation methods have been developed which aim to reduce running time while maintaining accurate classification. In this article, we summarize and experimentally evaluate several approximation …

Immunoglobulins Against Tyrosine-Nitrated Epitopes In Coronary Artery Disease, Leonor Thomson, Margarita Tenopoulou, Richard Lightfoot, Epida Tsika, Ioannis Parastatidis, Marissa Martinez, Todd M. Greco, Paschalis Thomas Doulias, Yuping Wu, W.H. Wilson Tang, Stanley L. Hazen, Harry Ischiropoulos

Mathematics and Statistics Faculty Publications

Background—Several lines of evidence support a pathophysiological role of immunity in atherosclerosis. Tyrosine-nitrated proteins, a footprint of oxygen- and nitrogen-derived oxidants generated by cells of the immune system, are enriched in atheromatous lesions and in circulation of patients with coronary artery disease (CAD). However, the consequences of possible immune reactions triggered by the presence of nitrated proteins in subjects with clinically documented atherosclerosis have not been explored. Methods and Results—Specific immunoglobulins that recognize 3-nitrotyrosine epitopes were identified in human lesions, as well as in circulation of patients with CAD. The levels of circulating immunoglobulins against 3-nitrotyrosine epitopes were quantified in …

Variational Methods And Critical Point Theory, Victoria Otero-Espinar, Juan J. Nieto, Donal O'Regan, Kanishka Perera

Mathematics and System Engineering Faculty Publications

[No abstract provided]

Numerical Solutions Of Elliptic Inverse Problems Via The Equation Error Method, Mohammad F. Al-Jamal

Dissertations, Master's Theses and Master's Reports - Open

To estimate a parameter in an elliptic boundary value problem, the method of equation error chooses the value that minimizes the error in the PDE and boundary condition (the solution of the BVP having been replaced by a measurement). The estimated parameter converges to the exact value as the measured data converge to the exact value, provided Tikhonov regularization is used to control the instability inherent in the problem. The error in the estimated solution can be bounded in an appropriate quotient norm; estimates can be derived for both the underlying (infinite-dimensional) problem and a finite-element discretization that can be …

Radar Signal Delay In The Dvali-Gabadadze-Porrati Gravity In The Vicinity Of The Sun, Ioannis Haranas, Omiros Ragos, Ioannis Gkigkitzis

Physics and Computer Science Faculty Publications

In this paper we examine the recently introduced Dvali-Gabadadze-Porrati (DGP) gravity model. We use the space time metric in which the local gravitation source dominates the metric over the contributions from the cosmological flow. Anticipating ideal possible solar system effects we derive expressions for the signal time delays in the vicinity of the sun, and for various angles of the signal approach. We use the corresponding numerical value for the parameter r₀ to be equal to 5 Mpc, and from that we calculate that the time contribution due to DGP correction to the metric is proportional to b^{3/2 …}

Zadeh's Vision Of Going From Fuzzy To Computing With Words: From The Idea's Origin To Current Successes To Remaining Challenges, Vladik Kreinovich

Departmental Technical Reports (CS)

No abstract provided.

Forbidden Symmetries, Frank A. Farris

Mathematics and Computer Science

The purpose of this paper is to show that an effort to construct functions known not to exist may on occasion produce interesting frauds. Our method produces a family of Harald Bohr's quasiperiodic functions, which may well remind readers of the quasicrystals that have been much in the news since Daniel Shechtman won the Nobel Prize in Chemistry in 2011.