Mathematics Commons^™

Application Of The Extended G'/G-Expansion Method To The Improved Eckhaus Equation, Nasir Taghizadeh, Seyyedeh R. Moosavi Noori, Seyyedeh B. Moosavi Noori

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, the extended (G'/G)-expansion method is used to seek more general exact solutions of the improved Eckhaus equation and the (2+1)-dimensional improved Eckhaus equation. As a result, hyperbolic function solutions, trigonometric function solutions and rational function solutions with free parameters are obtained. When the parameters are taken as special values the solitary wave solutions are also derived from the traveling wave solutions. Moreover, it is shown that the proposed method is direct, effective and can be used for many other nonlinear evolution equations in mathematical physics.

A New Adjustment Of Laplace Transform For Fractional Bloch Equation In Nmr Flow, Sunil Kumar, Devendra Kumar, U. S. Mahabaleshwar

Applications and Applied Mathematics: An International Journal (AAM)

This work purpose suggest a new analytical technique called the fractional homotopy analysis transform method (FHATM) for solving time fractional Bloch NMR (nuclear magnetic resonance) flow equations, which are a set of macroscopic equations that are used for modeling nuclear magnetization as a function of time. The true beauty of this article is the coupling of the homotopy analysis method and the Laplace transform method for systems of fractional differential equations. The solutions obtained by the proposed method indicate that the approach is easy to implement and computationally very attractive.

On Some Hadamard-Type Inequalıtıes For (R,M) -Convex Functıons, M. E. Özdemir, Erhan Set, Ahmet O. Akdemir

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, we define a new class of convex functions which is called (r,m) - convex functions. We also prove some Hadamard's type inequalities based on this new definition.

Isotopic Form Of M-Rings, M. R. Molaei, A. Keyhaninejad

Applications and Applied Mathematics: An International Journal (AAM)

The aim of this work is to generalize the notion of isofields by presenting the notion of Misorings. A method for constructing new M-isorings is presented. It is proved that an M-isoring for which its isounit is the fixed point of its identity function is an M-ring. Two methods for constructing new M-rings are presented.

Beta Burr Xii Or Five Parameter Beta Lomax Distribution: Remarks And Characterizations, Z. Javanshiri, Mehdi Maadooliat

Mathematics, Statistics and Computer Science Faculty Research and Publications

The distributions taken up in two recently published papers are compared and certain characterizations of them are presented. These characterizations are based on: (i) a simple relationship between two truncated moments; (ii) truncated moments of certain functions of the nth order statistic; (iii) truncated moments of certain functions of the random variable.

Regularized Multivariate Regression Models With Skew-T Error Distributions, Lianfu Chen, Mohsen Pourahmadi, Mehdi Maadooliat

Mathematics, Statistics and Computer Science Faculty Research and Publications

We consider regularization of the parameters in multivariate linear regression models with the errors having a multivariate skew-t distribution. An iterative penalized likelihood procedure is proposed for constructing sparse estimators of both the regression coefficient and inverse scale matrices simultaneously. The sparsity is introduced through penalizing the negative log-likelihood by adding L₁-penalties on the entries of the two matrices. Taking advantage of the hierarchical representation of skew-t distributions, and using the expectation conditional maximization (ECM) algorithm, we reduce the problem to penalized normal likelihood and develop a procedure to minimize the ensuing objective function. Using a …

Mathematical Methods Of Analysis For Control And Dynamic Optimization Problems On Manifolds, Robert J. Kipka

Dissertations

Mathematical Methods Of Analysis For Control And Dynamic Optimization Problems On Manifolds Driven by applications in fields such as robotics and satellite attitude control, as well as by a need for the theoretical development of appropriate tools for the analysis of geometric systems, problems of control of dynamical systems on manifolds have been studied intensively during the past three decades. In this dissertation we suggest new mathematical techniques for the study of control and dynamic optimization problems on manifolds. This work has several components including: an extension of the classical Chronological Calculus to control and dynamical systems which are merely …

Reliable Study Of Nonhomogeneous Bbm Equation With Time-Dependent Coefficients By The Modified Sine-Cosine Method, Aminah Qawasmeh, Marwan Alquran

Applications and Applied Mathematics: An International Journal (AAM)

The modified sine-cosine method is an efficient and powerful mathematical tool in finding exact traveling wave solutions to nonlinear partial differential equations (NLPDEs) with time-dependent coefficients. In this paper, the proposed approach is applied to study a nonhomogeneous generalized form of Benjamin-Bona-Mahony (BBM) equation with time-dependent coefficients. Explicit traveling wave solutions of the equation are obtained under certain constraints on the coefficient functions.

Numerical Solution For The Systems Of Variable-Coefficient Coupled Burgers’ Equation By Two-Dimensional Legendre Wavelets Method, Hossein Aminikhah, Sakineh Moradian

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, a numerical method for solving the systems of variable-coefficient coupled Burgers’ equation is proposed. The method is based on two-dimensional Legendre wavelets. Two-dimensional operational matrices of integration are introduced and then employed to find a solution to the systems of variable-coefficient coupled Burgers’ equation. Two examples are presented to illustrate the capability of the method. It is shown that the numerical results are in good agreement with the exact solutions for each problem.

Existence Of Solutions For Multi-Points Fractional Evolution Equations, Soumia Belarbi, Zoubir Dahmani

Applications and Applied Mathematics: An International Journal (AAM)

In this paper we study an impulsive fractional evolution equation with nonlinear boundary conditions. Sufficient conditions for the existence and uniqueness of solutions are established. To illustrate our results, an example is presented.

Counting Independent Sets Of A Fixed Size In Graphs With Given Minimum Degree, John Engbers, David Galvin

Mathematics, Statistics and Computer Science Faculty Research and Publications

Galvin showed that for all fixed δ and sufficiently large n, the n-vertex graph with minimum degree δ that admits the most independent sets is the complete bipartite graph . He conjectured that except perhaps for some small values of t, the same graph yields the maximum count of independent sets of size t for each possible t. Evidence for this conjecture was recently provided by Alexander, Cutler, and Mink, who showed that for all triples with , no n-vertex bipartite graph with minimum degree δ admits more independent sets of size t than . …

Monoid Rings And Strongly Two-Generated Ideals, Brittney M. Salt

Electronic Theses, Projects, and Dissertations

This paper determines whether monoid rings with the two-generator property have the strong two-generator property. Dedekind domains have both the two-generator and strong two-generator properties. How common is this? Two cases are considered here: the zero-dimensional case and the one-dimensional case for monoid rings. Each case is looked at to determine if monoid rings that are not PIRs but are two-generated have the strong two-generator property. Full results are given in the zero-dimensional case, however only partial results have been found for the one-dimensional case.

Solution Of Fractional Harmonic Oscillator In A Fractional B-Poly Basis, Muhammad I. Bhatti

School of Mathematical & Statistical Sciences Faculty Publications

An algorithm for approximating solutions to fractional-order differential equations in fractional polynomial basis is presented. A finite generalized fractional-order basis set is obtained from the modified Bernstein Polynomials, where α is the fractional-order of the modified Bernstein type polynomials (B-polys). The algorithm determines the desired solution in terms of continuous finite number of generalized fractional polynomials in a closed interval and makes use of Galerkin method to calculate the unknown expansion coefficients for constructing the approximate solution to the fractional differential equations. The Caputo’s definition for a fractional derivative is used to evaluate derivatives of the polynomials. Each term in …

Eigenvalue Estimates Of Laplacians Defined By Fractal Measures, Sze-Man Ngai

Mathematical Sciences: Faculty Presentations (1991-2022)

We study various lower and upper estimates for the first eigenvalue of Dirichlet Laplacians defined by positive Borel measures on bounded open subsets of Euclidean spaces. These Laplacians and the corresponding eigenvalue estimates differ from classical ones in that the defining measures can be singular. By using properties of self-similar measures, such as Strichartz's second-order self-similar identities, we improve some of the eigenvalue estimates.

Evaluation Of Bias-Variance Trade-Off For Commonly Used Post-Summarizing Normalization Procedures In Large-Scale Gene Expression Studies, Zhixin Wu, Rui Hu, Xing Qiu

Mathematics Faculty Publications

Normalization procedures are widely used in high-throughput genomic data analyses to remove various technological noise and variations. They are known to have profound impact to the subsequent gene differential expression analysis. Although there has been some research in evaluating different normalization procedures, few attempts have been made to systematically evaluate the gene detection performances of normalization procedures from the bias-variance trade-off point of view, especially with strong gene differentiation effects and large sample size. In this paper, we conduct a thorough study to evaluate the effects of normalization procedures combined with several commonly used statistical tests and MTPs under different …

A New Public-Key Cryptosystem, Christopher James Hettinger

Theses and Dissertations

Public key cryptosystems offer important advantages over symmetric methods, but the most important such systems rely on the difficulty of integer factorization (or the related discrete logarithm problem). Advances in quantum computing threaten to render such systems useless. In addition, public-key systems tend to be slower than symmetric systems because of their use of number-theoretic algorithms. I propose a new public key system which may be secure against both classical and quantum attacks, while remaining simple and very fast. The system's action is best described in terms of linear algebra, while its security is more naturally explained in the context …

The Linear Cutwidth And Cyclic Cutwidth Of Complete N-Partite Graphs, Stephanie A. Creswell

Electronic Theses, Projects, and Dissertations

The cutwidth of different graphs is a topic that has been extensively studied. The basis of this paper is the cutwidth of complete n-partite graphs. While looking at the cutwidth of complete n-partite graphs, we strictly consider the linear embedding and cyclic embedding. The relationship between the linear cutwidth and the cyclic cutwidth is discussed and used throughout multiple proofs of different cases for the cyclic cutwidth. All the known cases for the linear and cyclic cutwidth of complete bipartite, complete tripartite, and complete n-partite graphs are highlighted.

The main focus of this paper is to expand …

A Kleinian Approach To Fundamental Regions, Joshua L. Hidalgo

Electronic Theses, Projects, and Dissertations

This thesis takes a Kleinian approach to hyperbolic geometry in order to illustrate the importance of discrete subgroups and their fundamental domains (fundamental regions). A brief history of Euclids Parallel Postulate and its relation to the discovery of hyperbolic geometry be given first. We will explore two models of hyperbolic $n$-space: $U^n$ and $B^n$. Points, lines, distances, and spheres of these two models will be defined and examples in $U^2$, $U^3$, and $B^2$ will be given. We will then discuss the isometries of $U^n$ and $B^n$. These isometries, known as M\"obius transformations, have special properties and turn out to be …

Homormophic Images And Their Isomorphism Types, Diana Herrera

Electronic Theses, Projects, and Dissertations

In this thesis we have presented original homomorphic images of permutations and monomial progenitors. In some cases we have used the double coset enumeration tech- nique to construct the images and for all of the homomorphic images that we have discovered, the isomorphism type of each group is given. The homomorphic images discovered include Linear groups, Alternating groups, and two sporadic simple groups J₁ and J₂X2 where J₁ is the smallest Janko group and J₂ is the second Janko sporadic group.

On Eulerian Irregularity And Decompositions In Graphs, Eric Andrews

Dissertations

Abstract attached as separate file.