Mathematics Commons^™

The Efficient Use Of Supplementary Information In Finite Population Sampling, Florentin Smarandache, Rajesh Singh

Branch Mathematics and Statistics Faculty and Staff Publications

The purpose of writing this book is to suggest some improved estimators using auxiliary information in sampling schemes like simple random sampling, systematic sampling and stratified random sampling. This volume is a collection of five papers, written by nine co-authors (listed in the order of the papers): Rajesh Singh, Mukesh Kumar, Manoj Kr. Chaudhary, Cem Kadilar, Prayas Sharma, Florentin Smarandache, Anil Prajapati, Hemant Verma, and Viplav Kr. Singh. In first paper dual to ratio-cum-product estimator is suggested and its properties are studied. In second paper an exponential ratio-product type estimator in stratified random sampling is proposed and its properties are …

Collected Papers, Vol. V, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

No abstract provided.

Distance In Matrices And Their Applications To Fuzzy Models And Neutrosophic Models, Florentin Smarandache, W.B. Vasantha Kandasamy, K. Ilanthenral

Branch Mathematics and Statistics Faculty and Staff Publications

In this book authors for the first time introduce the notion of distance between any two m  n matrices. If the distance is 0 or m  n there is nothing interesting. When the distance happens to be a value t; 0 < t < m  n the study is both innovating and interesting. The three cases of study which is carried out in this book are 1. If the difference between two square matrices is large, will it imply the eigen values and eigen vectors of those matrices are distinct? Several open conjectures in this direction are given. 2. The difference between parity check matrix and the generator matrix for the same C(n, k) code is studied. This will help in detecting errors in storage systems as well as in cryptography.

Solving Diophantine Equations, Florentin Smarandache, Octavian Cira

Branch Mathematics and Statistics Faculty and Staff Publications

In recent times, we witnessed an explosion of Number Theory problems that are solved using mathematical software and powerful computers. The observation that the number of transistors packed on integrated circuits doubles every two years made by Gordon E. Moore in 1965 is still accurate to this day. With ever increasing computing power more and more mathematical problems can be tacked using brute force. At the same time the advances in mathematical software made tools like Maple, Mathematica, Matlab or Mathcad widely available and easy to use for the vast majority of the mathematical research community. This tools don’t only …

Independence Polynomials, Gregory Matthew Ferrin

Theses and Dissertations

In this thesis, we investigate the independence polynomial of a simple graph G. In addition to giving several tools for computing these polynomials and giving closed-form representations of these polynomials for common classes of graphs, we prove two results concerning the roots of independence polynomials. The first result gives us the unique root of smallest modulus of the independence polynomial of a graph. The second result tells us that all the roots of the independence polynomial of a claw-free graph fall on the real line.

Interpolation By Polynomials With Symmetries, Daniel Alpay, Izchak Lewkowicz

Mathematics, Physics, and Computer Science Faculty Articles and Research

We here specialize the standard matrix-valued polynomial interpolation to the case where on the imaginary axis the interpolating polynomials admit various symmetries: Positive semidefinite, Skew-Hermitian, J- Hermitian, Hamiltonian and others.

The procedure is comprized of three stages, illustrated through the case where on $i\R$ the interpolating polynomials are to be positive semidefinite. We first, on the expense of doubling the degree, obtain a minimal degree interpolating polynomial P(s) which on $i\R$ is Hermitian. Then we find all polynomials Ψ(s), vanishing at the interpolation points which are positive semidefinite on $i\R$. Finally, using the fact that the set of positive semidefinite …

Relative Equilibria Of Isosceles Triatomic Molecules In Classical Approximation, Damaris Miriam Mckinley

Theses and Dissertations (Comprehensive)

In this thesis we study relative equilibria of di-atomic and isosceles tri-atomic molecules in classical approximations with repulsive-attractive interaction. For di-atomic systems we retrieve well-known results. The main contribution consists of the study of the existence and stability of relative equilibria in a three-atom system formed by two identical atoms of mass $m$ and a third of mass $m_3$, constrained in an isosceles configuration at all times.

Given the shape of the binary potential only, we discuss the existence of equilibria and relative equilibria. We represent the results in the form of energy-momentum diagrams. We find that fixing the masses …

Lessons Learned In Establishing Stem Student Cohorts At A Border University And The Effect On Student Retention And Success, Mikhail M. Bouniaev, Immanuel Edinbarough, Bill W. Elliott

School of Mathematical & Statistical Sciences Faculty Publications

The University of Texas at Brownsville (UTB) serves more than 8,000 students in the Lower Rio Grande Valley area and broader Mexico region. UTB is a Hispanic-serving institution that attracts students from the surrounding areas, including the Mexico border region. The College of Science, Mathematics and Technology (CSMT) established a Science, Technology, Engineering, and Mathematics (STEM) cohort program to help the majority of students to earn a degree in a STEM field in the shortest possible time. The challenges and obstacles encountered during the planning and implementation phase of the STEM cohort program are discussed in this paper, as are …

Counting Pseudo-Anosov Mapping Classes On The 3-Punctured Projective Plane, Blazej Szepietowski

Turkish Journal of Mathematics

We prove that in the pure mapping class group of the 3-punctured projective plane equipped with the word metric induced by certain generating set, the ratio of the number of pseudo-Anosov elements to the number of all elements in a ball centered at the identity tends to one, as the radius of the ball tends to infinity. We also compute growth functions of the sets of reducible and pseudo-Anosov elements.

A Note On Closed G_2-Structures And 3-Manifolds, Hyunjoo Cho, Sema Salur, Albert Todd

Turkish Journal of Mathematics

This article shows that given any orientable 3-manifold X, the 7-manifold T^*X \times R admits a closed G_2-structure \varphi = Re \Omega-\omega \wedge dt where \Omega is a certain complex-valued 3-form on T^*X; next, given any 2-dimensional submanifold S of X, the conormal bundle N^*S of S is a 3-dimensional submanifold of T^*X \times R such that \varphi _{N^*S}\equiv 0. A corollary of the proof of this result is that N^*S \times R is a 4-dimensional submanifold of T^*X \times R such that \varphi _{N^*S \times R}\equiv 0.

Hausdorff Dimension Of The Graph Of The Error-Sum Function Of \Alpha-Lüroth Series, Haibo Chen, Wenbo Wang, Min Yu

Turkish Journal of Mathematics

Let \alpha be a countable partition of the unit interval [0,1]. In this paper, we will introduce the error-sum function of \alpha-Lüroth series and determine the Hausdorff dimension of its graph when the partition \alpha is eventually decreasing. Some other properties of the error-sum function are also investigated.

Coverings And Crossed Modules Of Topological Groups With Operations, Osman Mucuk, Tunçar Şahan

Turkish Journal of Mathematics

It is a well-known result of the covering groups that a subgroup G of the fundamental group at the identity of a semilocally simply connected topological group determines a covering morphism of topological groups with characteristic group G. In this paper we generalize this result to a large class of algebraic objects called topological groups with operations, including topological groups. We also prove that the crossed modules and internal categories within topological groups with operations are equivalent. This equivalence enables us to introduce the cover of crossed modules within topological groups with operations. Finally, we draw relations between the coverings …

A Characterization Of The Projective Transformation In Minkowski 3-Space, Yasemi̇n Alagöz

Turkish Journal of Mathematics

We consider transformations preserving asymptotic directions of surfaces in Minkowski 3-space and show that a transformation preserves the asymptotic directions of a surface if only if it is the projective one. Therefore, we obtain a characterization of the projective transformation.

Exponentiated Kumaraswamy-Dagum Distribution With Applications To Income And Lifetime Data, Shujiao Huang, Broderick O. Oluyede

Mathematical Sciences: Faculty Publications

A new family of distributions called exponentiated Kumaraswamy-Dagum (EKD) distribution is proposed and studied. This family includes several well known sub-models, such as Dagum (D), Burr III (BIII), Fisk or Log-logistic (F or LLog), and new sub-models, namely, Kumaraswamy-Dagum (KD), Kumaraswamy-Burr III (KBIII), Kumaraswamy-Fisk or Kumaraswamy-Log-logistic (KF or KLLog), exponentiated Kumaraswamy-Burr III (EKBIII), and exponentiated Kumaraswamy-Fisk or exponentiated Kumaraswamy-Log-logistic (EKF or EKLLog) distributions. Statistical properties including series representation of the probability density function, hazard and reverse hazard functions, moments, mean and median deviations, reliability, Bonferroni and Lorenz curves, as well as entropy measures for this class of distributions and the …

Local Rings Of Embedding Codepth At Most 3 Have Only Trivial Semidualizing Complexes, Saeed Nasseh, Sean Sather-Wagstaff

Mathematical Sciences: Faculty Publications

We prove that a local ring R of embedding codepth at most 3 has at most two semidualizing complexes up to shift-isomorphism, namely, R itself and a dualizing R-complex if one exists.

Frameworks With Crystallographic Symmetry, Ciprian Borcea, Ileana Streinu

Computer Science: Faculty Publications

Periodic frameworks with crystallographic symmetry are investigated from the perspective of a general deformation theory of periodic bar-and-joint structures in R^d. It is shown that natural parametrizations provide affine section descriptions for families of frameworks with a specified graph and symmetry. A simple geometric setting for diaplacive phase transitions is obtained. Upper bounds are derived for the number of realizations of minimally rigid periodic graphs.

Efficient And Long-Time Accurate Second-Order Methods For The Stokes-Darcy System, Wenbin Chen, Max Gunzburger, Dong Sun, Xiaoming Wan

Mathematics and Statistics Faculty Research & Creative Works

We propose and study two second order in time implicit-explicit methods for the coupled Stokes-Darcy system that governs flows in karst aquifers and other subsurface flow systems. the first method is a combination of a second-order backward differentiation formula and the second order Gear's extrapolation approach. the second is a combination of the second-order Adams-Moulton and second-order Adams-Bashforth methods. Both algorithms only require the solution of decoupled Stokes and Darcy problems at each time-step. Hence, these schemes are very efficient and can be easily implemented using legacy codes. We establish the unconditional and uniform in time stability for both schemes. …

Students' Perceived Utility Of Precision Taught Calculus, Rebecca-Anne Dibbs, David Glassmeyer, Wafa Yacoub

Faculty Articles

The last decade of calculus research has showed students learn best when lecture is supplemented with thoughtful use of technology and group work; however, educators are given little direction of how they are to balance the already full first semester calculus class. Precision teaching is an instructional model that employs formative assessment to provide information on what topics are understood by students as well as indicate troublesome concepts. With this information, the instructor can adjust class time accordingly by incorporating supplemental activities most beneficial to students. The purpose of this interview study was to explore the perceived utility of precision …

The Apostles And Brothers Of Jesus, Andrew Sills

Mathematical Sciences: Faculty Publications

Excerpt: The Talpiot tomb, a tomb excavated outside Jerusalem in 1980 and brought to worldwide public attention in 2007, contained ten ossuaries, six of which were inscribed with names. The English equivalents of the names are Jesus son of Joseph, two Marys, a rare diminutive form of Joseph, a diminutive of Matthew, and a Judah son of Jesus. Because of the similarities between this collection of names and certain names appearing in the Christian New Testament, some are curious as to whether the Talpiot tomb may have once interred the remains of Jesus of Nazareth and some of his relatives. …

Model Spaces: A Survey, William T. Ross, Stephan Ramon Garcia

Department of Math & Statistics Faculty Publications

This is a brief and gentle introduction, aimed at graduate students, to the subject of model subspaces of the Hardy space.