Mathematics Commons^™

Symmetric Criticality In General Relativity, Charles G. Torre

Research Vignettes

In this worksheet I explore the local Lagrangian version of the Principle of Symmetric Criticality (PSC) due to Anderson, Fels, and Torre], which asserts the commutativity of the processes (i) of symmetry reduction (for finding group-invariant fields) and (ii) forming Euler-Lagrange equations. There are two obstructions to PSC, which I will call the Lie algebra obstruction and the isotropy obstruction. In this worksheet I will illustrate these obstructions in the General Theory of Relativity.

Hardy Space Theory And Endpoint Estimates For Multi-Parameter Singular Radon Transforms, Jiawei Shen

Wayne State University Dissertations

In [12], Christ, Nagel, Stein and Waigner studied the L p theories for the singular Radon Trans-

forms. Furthermore, B. Street in [68], and Stein and Street in [64–67] extended the theories of the

L p boundedness for multi-parameter singular integral operators, such as the Calderón Zygmund

operators and singular Radon transforms. In this dissertation, we will study the Hardy space H p

and its dual space associated with both the one-parameter and multi-parameter singular Radon

transforms, and consider the boundedness of the singular Radon transforms on such Hardy spaces

H p when 0 ≤ p ≤ 1.

Inspired by …

Determining Cloud Cover With Machine Learning, Sarah Sesek

Undergraduate Research Posters 2018

The cloud cover provided by boundary layer cumulus clouds is one of the greatest uncertainties in climate and weather prediction models. It is difficult with current technology to cheaply and accurately collect cloud cover data. The TSI (Total Sky Imager) provides a hemispheric field of view in order to maximize the area it can see. The farther away from the center of the image, the more angled the view of the the cloud is. Therefore, more of the side of the cloud is captured in addition to the cloud base. Machine learning is well suited to seeing through this bias. …

Advances In Processing, Mining, And Learning Complex Data: From Foundations To Real-World Applications, Jia Wu, Shirui Pan, Chuan Zhou, Gang Li, Wu He, Chengqi Zhang

Information Technology & Decision Sciences Faculty Publications

Processing, mining, and learning complex data refer to an advanced study area of data mining and knowledge discovery concerning the development and analysis of approaches for discovering patterns and learning models from data with a complex structure (e.g., multirelational data, XML data, text data, image data, time series, sequences, graphs, streaming data, and trees) [1–5]. These kinds of data are commonly encountered in many social, economic, scientific, and engineering applications. Complex data pose new challenges for current research in data mining and knowledge discovery as they require new methods for processing, mining, and learning them. Traditional …

Existence Of Solution For Some Two-Point Boundary Value Fractional Differential Equations, Kenneth Ifeanyi Isife

Turkish Journal of Mathematics

Using a fixed point theorem, we establish the existence of a solution for a class of boundary value fractional differential equation. Secondly, we will adopt the method of successive approximations to obtain an approximate solution to our problem. Furthermore, using the Laplace transform technique, an explicit solution to a particular case of our problem is obtained. Finally, some examples are given to illustrate our results.

Transversal Lightlikesubmanifolds Of Metallic Semi-Riemannian Manifolds, Feyza Esra Erdoğan

Turkish Journal of Mathematics

The main purpose of the present paper is to study the geometry of transversal lightlike submanifolds and radical transversal lightlike submanifolds of metallic semi-Riemannian manifolds. We investigate the geometry of distributions and obtain necessary and sufficient conditions for the induced connection on these manifolds to be a metric connection. We also obtain characterization of transversal lightlike submanifolds of metallic semi-Riemannian manifolds. Finally, we give two examples.

On Rectifying Curves In Euclidean 3-Space, Sharief Deshmukh, Bang-Yen Chen, Sana Hamoud Alshammari

Turkish Journal of Mathematics

First, we study rectifying curves via the dilation of unit speed curves on the unit sphere $S^{2}$ in the Euclidean space $\mathbb E^3$. Then we obtain a necessary and sufficient condition for which the centrode $d(s)$ of a unit speed curve $\alpha(s)$ in $\mathbb E^3$ is a rectifying curve to improve a main result of \cite{cd05}. Finally, we prove that if a unit speed curve $\alpha(s)$ in $\mathbb E^3$ is neither a planar curve nor a helix, then its dilated centrode $\beta(s)=\rho(s) d(s)$, with dilation factor ${\rho}$, is always a rectifying curve, where $\rho$ is the radius of curvature of …

A New Approach To $H$-Supplemented Modules Via Homomorphisms, Ali Reza Moniri Hamzekolaee, Abdullah Harmanci, Yahya Talebi, Burcu Üngör

Turkish Journal of Mathematics

The class of $H$-supplemented modules, which is a nice generalization of that of lifting modules, has been studied extensively in the last decade. As the concept of homomorphisms plays an important role in module theory, we are interested in $H$-supplemented modules relative to homomorphisms. Let $R$ be a ring, $M$ a right $R$-module, and $S=$ End$_{R}(M)$. We say that $M$ is endomorphism $H$-supplemented (briefly, $E$-$H$-supplemented) provided that for every $f\in S$ there exists a direct summand $D$ of $M$ such that $Imf+X=M$ if and only if $D+X=M$ for every submodule $X$ of $M$. In this paper, we deal with the …

Parametric Nondifferentiable Multiobjective Fractional Programmingunder $(B,\Psi ,\Phi ,\Rho )$-Univexity, Tadeusz Antczak, Ram Verma

Turkish Journal of Mathematics

In this paper, we are concerned with optimality conditions and duality results for nondifferentiable multiobjective fractional programming problems. Parametric necessary optimality conditions are established for such vector optimization problems in which each component of the involved functions is locally Lipschitz. Further, under the introduced concept of nondifferentiable $(b,\Psi ,\Phi ,\rho )$-univexity, the parametric sufficient optimality conditions are established for a new class of nonconvex multiobjective fractional programming problems. Furthermore, for the considered multiobjective fractional programming problem, its parametric vector dual problem in the sense of Schaible is defined. Then several duality theorems are also established under $(b,\Psi ,\Phi ,\rho )$% …

On $H$-Antimagicness Of Cartesian Product Of Graphs, Martin Baca, Andrea Semanicova-Fenovcikova, Muhammad Awais Umar, Des Welyyanti

Turkish Journal of Mathematics

A graph $G=(V(G),E(G))$ admits an $H$-covering if every edge in $E$ belongs to a~subgraph of $G$ isomorphic to $H$. A graph $G$ admitting an $H$-covering is called {\it $(a,d)$-$H$-antimagic} if there is a bijection $f:V(G)\cup E(G) \to \{1,2,\dots, V(G) + E(G) \}$ such that, for all subgraphs $H'$ of $G$ isomorphic to $H$, the $H$-weights, $wt_f(H')= \sum_{v\in V(H')} f(v) + \sum_{e\in E(H')} f(e),$ constitute an arithmetic progression with the initial term $a$ and the common difference $d$. In this paper we provide some sufficient conditions for the Cartesian product of graphs to be $H$-antimagic. We use partitions subsets of integers …

Worst-Case Large Deviations Upper Bounds For I.I.D. Sequencesunder Ambiguity, Mustafa Ç. Pinar

Turkish Journal of Mathematics

An introductory study of large deviations upper bounds from a worst-case perspective under parameter uncertainty (referred to as ambiguity) of the underlying distributions is given. Borrowing ideas from robust optimization, suitable sets of ambiguity are defined for imprecise parameters of underlying distributions. Both univariate and multivariate i.i.d. sequences of random variables are considered. The resulting optimization problems are challenging min‒max (or max‒min) problems that admit some simplifications and some explicit results, mostly in the case of the normal probability law.

A Comparative Study Of Gauss‒Laguerre Quadrature And An Open Type Mixed Quadrature By Evaluating Some Improper Integrals, Pritikanta Patra, Debasish Das, Rajani Ballav Dash

Turkish Journal of Mathematics

An open type mixed quadrature rule is constructed blending the anti-Gauss 3-point rule with Steffensen's 4-point rule. The analytical convergence of the mixed rule is studied. An adaptive integration scheme is designed based on the mixed quadrature rule. A comparative study of the mixed quadrature rule and the Gauss‒Laguerre quadrature rule is given by evaluating several improper integrals of the form $\int\limits_{0}^{\infty}e^{-x}f(x)dx$. The advantage of implementing mixed quadrature rule in developing an efficient adaptive integration scheme is shown by evaluating some improper integrals.

Various Centroids And Some Characterizations Of Catenary Rotation Hypersurfaces, Dong-Soo Kim, Young Ho Kim, Dae Won Yoon

Turkish Journal of Mathematics

We study positive $C^1$ functions $z=f(x), x=(x_1,\cdots, x_n)$ defined on the $n$-dimensional Euclidean space $ \mathbb R^{n}$. For $x=(x_1,\cdots, x_n)$ with nonzero numbers $x_1, \cdots, x_n$, we consider the rectangular domain $I(x)=I(x_1)\times \cdots \times I(x_n)\subset \mathbb R^{n}$, where $I(x_i)= [0, x_i]$ if $x_i>0$ and $I(x_i)= [x_i,0]$ if $x_i

On The Dimension Of Vertex Labeling Of $K$-Uniform Dcsl Of An Even Cycle, Nageswara Rao Karrey, Germina Kizhekekunnel Augustine

Turkish Journal of Mathematics

In this paper, we discuss the lower bound for the dcsl index $ \delta_k $ of a $k$-uniform dcsl of even cycle $ C_{2n},\ n\geq 2 $, in terms of the dimension of a poset and prove that $dim({\mathscr{F}})\leq \delta_k(C_{2n}) $, where ${\mathscr{F}}$ is the range of any $k$-uniform dcsl $ f $ of $ C_{2n},\ n\geq 2 $.

A Study Of The Tubular Surfaces Constructed By Thespherical Indicatrices In Euclidean $3-$Space, Fatma Ateş, Erdem Kocakuşakli, İsmai̇l Gök, Yusuf Yayli

Turkish Journal of Mathematics

A basic goal of this paper is to investigate the tubular surface constructed by the spherical indicatrices of any spatial curve in the Euclidean $3-$ space. This kind of tubular surface is designed for the alternative moving frame $\{N,C,W\}$ in conjunction with finding a relationship between the tubular surfaces and their special curves, such as geodesic curves, asymptotic curves, and minimal curves. The minimal curve $\gamma $ on a surface is defined by the property that its fundamental coefficients satisfy Eq. (3.7) along the curve $\gamma $. At the end of this article, we exemplify these curves on the tubular …

Second Hankel Determinant For Certain Subclasses Of Bi-Univalent Functions Involving Chebyshev Polynomials, Hali̇t Orhan, Evri̇m Toklu, Ekrem Kadioğlu

Turkish Journal of Mathematics

In this paper our purpose is to find the upper bound estimate for the second Hankel determinant $ a_{2}a_{4}-a_{3}^{2} $ for functions defined by convolution belonging to the class $\mathcal{N}_{\sigma}^{\mu,\delta}(\lambda,t)$ by using Chebyshev polynomials.

Existence Of Maximal Ideals In Leavitt Path Algebras, Songül Esi̇n, Müge Kanuni̇ Er

Turkish Journal of Mathematics

Let $E$ be an arbitrary directed graph and let $L$ be the Leavitt path algebra of the graph $E$ over a field $K$. The necessary and sufficient conditions are given to assure the existence of a maximal ideal in $L$ and also the necessary and sufficient conditions on the graph that assure that every ideal is contained in a maximal ideal are given. It is shown that if a maximal ideal $M$ of $L$ is nongraded, then the largest graded ideal in $M$, namely $gr(M)$, is also maximal among the graded ideals of $L$. Moreover, if $L$ has a unique …

Fuzzy Analogues Of Sets And Functions Can Be Uniquely Determined From The Corresponding Ordered Category: A Theorem, Christian Servin, Gerardo Muela, Vladik Kreinovich

Departmental Technical Reports (CS)

In modern mathematics, many concepts and ideas are described in terms of category theory. From this viewpoint, it is desirable to analyze what can be determined if, instead of the basic category of sets, we consider a similar category of fuzzy sets. In this paper, we describe a natural fuzzy analog of the category of sets and functions, and we show that, in this category, fuzzy relations (a natural fuzzy analogue of functions) can be determined in category terms -- of course, modulo 1-1 mapping of the corresponding universe of discourse and 1-1 re-scaling of fuzzy degrees.

Geometric Serendipity, Dakota Becker

AUCTUS: The Journal of Undergraduate Research and Creative Scholarship

The central focus of my practice is the serendipitous exploration into geometry, symmetry, design, and color. I have found more and more that the affinity I have for hard-edge geometric abstraction is a deeper reflection of the way in which I process my thoughts and surroundings. In the past year, I have sought to challenge myself by questioning the core of my practice and pushing it to go beyond its individual elements. In this way, I seek to create work that is more than its parts. As a result, I have become more purposeful with my designs and push both …

Cluster-Based Network Proximities For Arbitrary Nodal Subsets, Kenneth S. Berenhaut, Peter S. Barr, Alyssa M. Kogel, Ryan L. Melvin

Faculty & Staff Scholarship

The concept of a cluster or community in a network context has been of considerable interest in a variety of settings in recent years. In this paper, employing random walks and geodesic distance, we introduce a unified measure of cluster-based proximity between nodes, relative to a given subset of interest. The inherent simplicity and informativeness of the approach could make it of value to researchers in a variety of scientific fields. Applicability is demonstrated via application to clustering for a number of existent data sets (including multipartite networks). We view community detection (i.e. when the full set of network nodes …

Dimensional Analysis: Physical Insight Gained Through Algebra, John A. Adam

Mathematics & Statistics Faculty Publications

No abstract provided.

Switching Diffusion Systems With Past-Dependent Switching Having A Countable State Space, Hai Dang Nguyen

Wayne State University Dissertations

Emerging and existing applications in wireless communications, queueing networks, biological models, financial engineering, and social networks demand the

mathematical modeling and analysis of hybrid models in which continuous dynamics and discrete events coexist.

Assuming that the systems are in continuous times,

stemming from stochastic-differential-equation-based models and random discrete events,

switching diffusions come into being. In such systems, continuous states and discrete events

(discrete states)

coexist and interact.

A switching diffusion is a two-component process $(X(t),\alpha(t))$, a continuous component and a discrete component taking values in a discrete set (a set consisting of isolated points).

When the discrete component takes a …

Magic Cubes, Jeremiah Farrell, Karen Farrell

Scholarship and Professional Work - LAS

Jeremiah's puzzle "Magic Cubes", which was exchanged at the 2018 San Diego International Puzzle Party. 100 puzzle designers create 100 copies of their puzzle and pass it out at the party and exchange them. This puzzle is also mass produced by Kadon Enterprises, Inc. as "Magic Cubes".

How To Calculate Π: Machin's Inverse Tangents, A Mini-Primary Source Project For Calculus Ii Students, Dominic Klyve

Mathematics Faculty Scholarship

Almost every mathematical culture through history seems to have proved, trusted, or suspected that the area of a circle is a fixed constant times the square of its radius. It is maybe not surprising, then, that the last two millennia have seen a seemingly endless array of attempts to calculate this constant (today usually called π" role="presentation">π) with increasing precision.

Second Hankel Determinant For A Subclass Of Analytic Bi-Univalent Functions Defined By Subordination, Ahmad Motamednezhad, Teodor Bulboaca, Ebrahim Analouei Adegani, Nesa Dibagar

Turkish Journal of Mathematics

In this work with a different technique we obtain upper bounds of the functional $\left a_2a_4-a_3^2\right $ for functions belonging to a comprehensive subclass of analytic bi-univalent functions, which is defined by subordinations in the open unit disk. Moreover, our results extend and improve some of the previously known ones.

Onthe Global $L^{P}$ Boundedness Of A General Classof $H$-Fourier Integral Operators, Chafika Amel Aitemrar, Abderrahmane Senoussaoui

Turkish Journal of Mathematics

In this paper, we study the $L^{p}$-boundedness of a class of semiclassical Fourier integral operators.

Two Asymptotic Results Of Solutions For Nabla Fractional $(Q,H)$-Difference Equations, Feifei Du, Lynn Erbe, Baoguo Jia, Allan Peterson

Turkish Journal of Mathematics

In this paper we study the Caputo and Riemann--Liouville nabla $(q,h)$-fractional difference equation and obtain the following two main results: Assume $0

Spectral Expansion For The Singular Dirac System With Impulsive Conditions, Bi̇lender Paşaoğlu, Hüseyi̇n Tuna

Turkish Journal of Mathematics

In this work, we study the one-dimensional Dirac system on a whole line with impulsive conditions. We construct a spectral function of this system. Using the spectral function, we establish a Parseval equality and spectral expansion formula for such a system.

Evaluations Of Some Terminating Hypergeometric $_2f_1(2)$ Series With Applications, Yong Sup Kim, Arjunkumar Rathie, Richard B. Paris

Turkish Journal of Mathematics

Explicit expressions for the hypergeometric series $_2F_1(-n, a; 2a\pm j;2)$ and $_2F_1(-n, a; -2n \pm j;2)$ for positive integer $n$ and arbitrary integer $j$ are obtained with the help of generalizations of Kummer's second and third summation theorems obtained earlier by Rakha and Rathie. Results for $ j \leq 5$ derived previously using different methods are also obtained as special cases. Two applications are considered, where the first summation formula is applied to a terminating $_3F_2(2)$ series and the confluent hypergeometric function $_1F_1(x)$.

Mathematically Predicting The Aleut Tribe Population Using Archaeological Data, Jack Conrad Kiefer Ii, Paden Allen Thompson

Research on Capitol Hill

Sanak Island, located off the southern Alaska Peninsula, was home to the native Aleut peoples for thousands of years. Their hunter-gatherer society depended heavily on the arctic and marine ecosystem for food resources.

In 2015, a team of archaeologists from Idaho State and Utah State universities went to the island and collected data about the Aleut population size and their diet.

This study constructed a dynamical model to mathematically predict the Aleut population over time in order to gain insights into how food resources affected the Aleut people’s ability to survive.