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2019

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Articles 931 - 960 of 1389

Full-Text Articles in Mathematics

When The Intrinsic Algebraic Entropy Is Not Really Intrinsic, Brendan Goldsmith, Luigi Salce Jan 2019

When The Intrinsic Algebraic Entropy Is Not Really Intrinsic, Brendan Goldsmith, Luigi Salce

Articles

The intrinsic algebraic entropy ent(ɸ) of an endomorphism ɸ of an Abelian group G can be computed using fully inert subgroups of ɸ-invariant sections of G, instead of the whole family of ɸ-inert subgroups. For a class of groups containing the groups of finite rank, aswell as those groupswhich are trajectories of finitely generated subgroups, it is proved that only fully inert subgroups of the group itself are needed to comput ent(ɸ). Examples show how the situation may be quite different outside of this class.

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Math Department Newsletter, 2018-2019, Mathematics Department Jan 2019

Math Department Newsletter, 2018-2019, Mathematics Department

Mathematics Newsletter

No abstract provided.

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Student's Self Discovery Of Right Triangle Trigonometry., Elizabeth Dereu Jan 2019

Student's Self Discovery Of Right Triangle Trigonometry., Elizabeth Dereu

Undergraduate Theses, Professional Papers, and Capstone Artifacts

Research has shown that right triangle trigonometry poses a significant learning challenge for high school geometry students. One potential source of this challenge is the tendency for students to experience right triangle trig as an exclusively action-oriented set of strategies (i.e. SOHCAHTOA). This article describes a teaching experiment where students built understanding of right triangle trig using a unique set of manipulatives and direct measurement. Results of the experiment show that the lessons provided opportunities for students to develop their understanding beyond action-oriented strategies.

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Modeling Stochastically Intransitive Relationships In Paired Comparison Data, Ryan Patrick Alexander Mcshane Jan 2019

Modeling Stochastically Intransitive Relationships In Paired Comparison Data, Ryan Patrick Alexander Mcshane

Statistical Science Theses and Dissertations

If the Warriors beat the Rockets and the Rockets beat the Spurs, does that mean that the Warriors are better than the Spurs? Sophisticated fans would argue that the Warriors are better by the transitive property, but could Spurs fans make a legitimate argument that their team is better despite this chain of evidence?

We first explore the nature of intransitive (rock-scissors-paper) relationships with a graph theoretic approach to the method of paired comparisons framework popularized by Kendall and Smith (1940). Then, we focus on the setting where all pairs of items, teams, players, or objects have been compared to …

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The Origins Of Spectra, An Organization For Lgbt Mathematicians, Lily S. Khadjavi Jan 2019

The Origins Of Spectra, An Organization For Lgbt Mathematicians, Lily S. Khadjavi

Mathematics, Statistics and Data Science Faculty Works

No abstract provided.

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An Enumeration Process For Racks, Patrick Shanahan Jan 2019

An Enumeration Process For Racks, Patrick Shanahan

Mathematics, Statistics and Data Science Faculty Works

Given a presentation for a rack , we define a process which systematically enumerates the elements of . The process is modeled on the systematic enumeration of cosets first given by Todd and Coxeter. This generalizes and improves the diagramming method for -quandles introduced by Winker. We provide pseudocode that is similar to that given by Holt, Eick, and O'Brien for the Todd-Coxeter process. We prove that the process terminates if and only if is finite, in which case, the procedure outputs an operation table for the finite rack. We conclude with an application to knot theory

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From Ordered Semigroups To Ordered Hypersemigroups, Niovi Kehayopulu Jan 2019

From Ordered Semigroups To Ordered Hypersemigroups, Niovi Kehayopulu

Turkish Journal of Mathematics

In an attempt to show the way we pass from ordered semigroups to ordered hypersemigroups, we examine some well known results of regular and intraregular ordered semigroups in case of ordered hypersemigroups. The corresponding results on hypersemigroups (without order) can also be obtained as application of the results of the present paper. The sets we use in our investigation shows the pointless character of the results.

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On A Pair Of Ramanujan's Modular Equations And $P$-$Q$ Theta Functions Of Level 35, K. R. Vasuki, Anusha T Jan 2019

On A Pair Of Ramanujan's Modular Equations And $P$-$Q$ Theta Functions Of Level 35, K. R. Vasuki, Anusha T

Turkish Journal of Mathematics

S. Ramanujan recorded several modular equations and $P$-$Q$ theta function identities in his notebooks and lost notebook without recording the proofs. In this paper, we provide an elementary proof of two modular equations and two $P$-$Q$ theta function identities of level 35, which have been proved by B.C. Berndt using the theory of modular forms.

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Eta Quotients Of Level $\Mathbf{12}$ And Weight $\Mathbf{1}$, Ayşe Alaca, Şaban Alaca, Zafer Selcuk Aygin Jan 2019

Eta Quotients Of Level $\Mathbf{12}$ And Weight $\Mathbf{1}$, Ayşe Alaca, Şaban Alaca, Zafer Selcuk Aygin

Turkish Journal of Mathematics

We find all the eta quotients in the spaces $M_1 \Big(\Gamma_0(12), \left(\frac{d}{\cdot}\right) \Big)$ ($d=-3, -4$) of modular forms and determine their Fourier coefficients, where $\left(\frac{d}{\cdot}\right)$ is the Legendre-Jacobi-Kronecker symbol.

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Construction Of The Holonomy Invariantfoliated Cocycles On The Tangent Bundle Via Formal Integrability, Fatemeh Ahangari Jan 2019

Construction Of The Holonomy Invariantfoliated Cocycles On The Tangent Bundle Via Formal Integrability, Fatemeh Ahangari

Turkish Journal of Mathematics

This paper is dedicated to exhaustive structural analysis of the holonomy invariant foliated cocycles on the tangent bundle of an arbitrary $(m+n)$-dimensional manifold. For this purpose, by applying Spencer theory of formal integrability, sufficient conditions for the metric associated with the semispray $S$ are determined to extend to a transverse metric for the lifted foliated cocycle on $TM$. Accordingly, this geometric structure converts to a holonomy invariant foliated cocycle on the tangent space, which is totally adapted to the Helmholtz conditions.

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$C$-Paracompactness And $C_2$-Paracompactness, Maha Mohammed, Lutfi Kalantan, Hala Alzumi Jan 2019

$C$-Paracompactness And $C_2$-Paracompactness, Maha Mohammed, Lutfi Kalantan, Hala Alzumi

Turkish Journal of Mathematics

A topological space $X$ is called $C$-paracompact if there exist a paracompact space $Y$ and a bijective function $f:X\longrightarrow Y$ such that the restriction $f _{A}:A\longrightarrow f(A)$ is a homeomorphism for each compact subspace $A\subseteq X$. A topological space $X$ is called $C_2$-paracompact if there exist a Hausdorff paracompact space $Y$ and a bijective function $f:X\longrightarrow Y$ such that the restriction $f _{A}:A\longrightarrow f(A)$ is a homeomorphism for each compact subspace $A\subseteq X$. We investigate these two properties and produce some examples to illustrate the relationship between them and $C$-normality, minimal Hausdorff, and other properties.

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Multiple-Group Adjustment Method In Indirect Adjustment, Changjun Huang, Hongmei Xia, Xike Zhang Jan 2019

Multiple-Group Adjustment Method In Indirect Adjustment, Changjun Huang, Hongmei Xia, Xike Zhang

Turkish Journal of Mathematics

In view of the low accuracy of traditional adjustment, an improved multiple-group adjustment method in indirect adjustment is proposed in this paper. In the process of improved multiple-group adjustment, the first group is first adjusted, and then the adjustment result of the first group and the observation value of the second group are adjusted together, which makes the results in the first-group adjustment meet the overall adjustment results. Finally, the posteriori unit-weight variance value, the coordinated factor matrix of the adjustment result, and the unknown function weight reciprocal are calculated. The experimental results show that the accuracy of multiple-group adjustment …

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When Do Quasinilpotents Lie In The Jacobson Radical?, Peng Cao, Xin Wang Jan 2019

When Do Quasinilpotents Lie In The Jacobson Radical?, Peng Cao, Xin Wang

Turkish Journal of Mathematics

In this paper, we give some spectral characterizations of the Jacobson radical; that is, we will show that some conditions with $\lambda$-multiplicativity imply that the set of all quasinilpotent elements equals the Jacobson radical. We also give some conditions to make sure the quasinilpotents lie in the Jacobson radical, using the set of elements with singleton spectra.

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Weighted Composition Operators Between Vector-Valued Bloch-Type Spaces, Kobra Esmaeili, Hakimeh Mahyar Jan 2019

Weighted Composition Operators Between Vector-Valued Bloch-Type Spaces, Kobra Esmaeili, Hakimeh Mahyar

Turkish Journal of Mathematics

Let $X$ and $Y$ be complex Banach spaces and $\mathbb{D}$ be the open unit disc in the complex plane $\mathbb{C}$. Let $\varphi$ be an analytic self-map of $\mathbb{D}$ and $\psi$ be an analytic operator-valued function from $\mathbb{D}$ into the space of all bounded linear operators from $X$ to $Y.$ The weighted composition operator $W_{\psi,\varphi}:\mathcal{H} \rightarrow\mathcal{H}(\mathbb{D}, Y)$ is defined by $$ W_{\psi,\varphi}( f)(z)=\psi(z)(f(\varphi(z))), \quad \quad (z\in\mathbb{D}, f\in \mathcal{H}),$$ where $\mathcal{H}$ is the space of all analytic $X$-valued functions on $\mathbb{D}$. In this paper we provide necessary and sufficient conditions for the boundedness and compactness of weighted composition operators $W_{\psi,\varphi}$ between vector-valued …

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Some Classes Of Harmonic Mappings With Analytic Part Defined By Subordination, Shuhai Li, Ma Li-Na, Ao En, Tang Huo Jan 2019

Some Classes Of Harmonic Mappings With Analytic Part Defined By Subordination, Shuhai Li, Ma Li-Na, Ao En, Tang Huo

Turkish Journal of Mathematics

Let $S_{H}$ be the class of functions $f=h+\bar{g}$ that are harmonic univalent and sense-preserving in the open unit disk $\mathbb{U}=\{z\in \mathbb{C}: z

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On Integrability Conditions, Operators, And The Purityconditions Of The Sasakian Metric With Respect To Lifts Of $F_{\Lambda}(7,1)$-Structure On The Cotangent Bundle, Haşi̇m Çayir Jan 2019

On Integrability Conditions, Operators, And The Purityconditions Of The Sasakian Metric With Respect To Lifts Of $F_{\Lambda}(7,1)$-Structure On The Cotangent Bundle, Haşi̇m Çayir

Turkish Journal of Mathematics

There are many structures in the cotangent bundle. These include the complete and horizontal lifts of the $F_{\lambda }(7,1)$-structure. The $F_{\lambda }(7,1)$-structure was first extended in $M^{n}$ to $T^{\ast }(M^{n})$ by Das, Nivas, and Pathak. Later, the horizontal and complete lift of the $F_{a}(K,1)$-structure in the tangent bundle was given by Prasad and Chauhan. This paper consists of two main sections. In the first part, we find the integrability conditions by calculating Nijenhuis tensors of the complete lifts of the $F_{\lambda }(7,1)$-structure. Later, we get the results of the Tachibana operators applied to vector and covector fields according to the …

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A Note On Polynomial Expressions For Sums Of Power Of Integers Multiplied By Exponential Terms, Altan Erdoğan Jan 2019

A Note On Polynomial Expressions For Sums Of Power Of Integers Multiplied By Exponential Terms, Altan Erdoğan

Turkish Journal of Mathematics

The possible polynomial expressions for sums of powers of integers multiplied by an exponential term are investigated. We explicitly give factorization of these polynomials in terms of the roots of Apostol-Bernoulli polynomials. As a special case, alternating sums of powers of integers are also considered, and some new polynomial expressions are given.

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Quartic Trigonometric B-Spline Algorithm Fornumerical Solution Of The Regularized Long Wave Equation, Dursun Irk, Pinar Keski̇n Yildiz, Meli̇s Zorşahi̇n Görgülü Jan 2019

Quartic Trigonometric B-Spline Algorithm Fornumerical Solution Of The Regularized Long Wave Equation, Dursun Irk, Pinar Keski̇n Yildiz, Meli̇s Zorşahi̇n Görgülü

Turkish Journal of Mathematics

In this paper, an application of the quartic trigonometric B-spline finite element method is used to solve the regularized long wave equation numerically. This approach involves a Galerkin method based on the quartic trigonometric B-spline function in space discretization together with second and fourth order schemes in time discretization. The accuracy of the proposed methods are demonstrated by test problems and numerical results are compared with the exact solution and some previous results.

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On The Starlikeness Of P-Valent Functions, Mamoru Nunokawa, Nak Eun Cho, Oh Sang Kwon, Janusz Sokol Jan 2019

On The Starlikeness Of P-Valent Functions, Mamoru Nunokawa, Nak Eun Cho, Oh Sang Kwon, Janusz Sokol

Turkish Journal of Mathematics

For an analytic function in open unit disk $\mathbb{D}$, we consider the $p$-valent analogue of the Noshiro-Warschawski univalence condition. We apply the Fejér-Riesz inequality to establish some sufficient conditions for functions to be $p$-valent or to be a Bazilevič function or to be in some other classes.

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A Novel 3-Pass Identification Scheme And Signature Scheme Based On Multivariate Quadratic Polynomials, Sedat Akleylek, Meryem Soysaldi Jan 2019

A Novel 3-Pass Identification Scheme And Signature Scheme Based On Multivariate Quadratic Polynomials, Sedat Akleylek, Meryem Soysaldi

Turkish Journal of Mathematics

Identification schemes are used to verify identities of parties and signatures. Recently, systems based on multivariate polynomials have been preferred in identification schemes due to their resistance against quantum attacks. In this paper, we propose a quantum secure $3$-pass identification scheme based on multivariate quadratic polynomials. We compare the proposed scheme with the previous ones in view of memory requirements, communication length, and computation time. We define an efficiency metric by using impersonation probability and computation time. According to the comparison results, the proposed one has the same computation time as that of Monteiro et al. and reduces impersonation probability …

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Notes On Certain Analytic Functions, Emel Yavuz Duman, Shigeyoshi Owa Jan 2019

Notes On Certain Analytic Functions, Emel Yavuz Duman, Shigeyoshi Owa

Turkish Journal of Mathematics

Let $\mathcal{A}(n)$ be the class of functions $$f(z)=a_nz^n + a_{n+1}z^{n+1}+\cdots (n\in \mathbb{N}),$$ which are analytic in the open unit disk $\mathbb{U}$, where $a_n \neq 0$. For $f(z)\in \mathcal{A}(n)$, Miller and Mocanu in 1978 showed a very interesting result for $f(z)$. Applying the result due to Miller and Mocanu, we would like to consider some new results for such functions. Our results in this paper are generalizations for results by Nunokawa in 1992.

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Inequalities On Coefficients For Certain Classes Of M-Fold Symmetric And Bi-Univalent Functions Equipped With Faber Polynomial, Fethi̇ye Müge Sakar, Adnan Canbulat Jan 2019

Inequalities On Coefficients For Certain Classes Of M-Fold Symmetric And Bi-Univalent Functions Equipped With Faber Polynomial, Fethi̇ye Müge Sakar, Adnan Canbulat

Turkish Journal of Mathematics

In this work, considering a new subclass of bi-univalent functions which are m-fold symmetric and analytic functions in the open unit disk, we determine estimates for the general Taylor-Maclaurin coefficient of the functions in this class. Furthermore, initial upper bounds of coefficients for m-fold symmetric, analytic and bi-univalent functions were found in this study. For this purpose, we used the Faber polynomial expansions. In certain cases, the coefficient bounds presented in this paper would generalize and improve some recent works in the literature. We hope that this paper will inspire future researchers in applying our approach to other related problems.

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Sectional Curvatures On Weyl Manifolds With A Special Metric Connection, Fatma Özdemi̇r, Mustafa Deni̇z Türkoğlu Jan 2019

Sectional Curvatures On Weyl Manifolds With A Special Metric Connection, Fatma Özdemi̇r, Mustafa Deni̇z Türkoğlu

Turkish Journal of Mathematics

In this paper, Weyl manifolds, denoted by $WS(g,w,\pi,\mu)$, having a special a semisymmetric recurrent-metric connection are introduced and the uniqueness of this connection is proved. We give an example of $WS(g,w,\pi,\mu)$ with a constant scalar curvature. Furthermore, we define sectional curvatures of $WS(g,w,\pi,\mu)$ and prove that any isotropic Weyl manifold $WS(g,w,\pi,\mu)$ is locally conformal to an Einstein manifold with a semisymmetric recurrent-metric connection, $EWS(g,w,\pi,\mu)$.

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Kernel Operators And Their Boundedness From Weighted Sobolev Space To Weighted Lebesgue Space, Aigerim Kalybay, Ryskul Oinarov Jan 2019

Kernel Operators And Their Boundedness From Weighted Sobolev Space To Weighted Lebesgue Space, Aigerim Kalybay, Ryskul Oinarov

Turkish Journal of Mathematics

In this paper, for a wide class of integral operators, we consider the problem of their boundedness from a weighted Sobolev space to a weighted Lebesgue space. The crucial step in the proof of the main result is to use the equivalence of the basic inequality and certain Hardy-type inequality, so we first state and prove this equivalence.

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On A Theorem Of Terzioğlu, Asuman Güven Aksoy Jan 2019

On A Theorem Of Terzioğlu, Asuman Güven Aksoy

Turkish Journal of Mathematics

The theory of compact linear operators acting on a Banach space has a classical core and is familiar to many. Perhaps less known is the characterization theorem of Terzioğlu for compact maps. This theorem has a number of important connections that deserves illumination. In this paper we survey Terzioğlu's characterization theorem for compact maps and some of its consequences. We also prove a similar characterization theorem for $Q$-compact maps.

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Univalent Harmonic Mappings And Hardy Spaces, Ali Ebadian, Saman Azizi, Si̇bel Yalçin Tokgöz Jan 2019

Univalent Harmonic Mappings And Hardy Spaces, Ali Ebadian, Saman Azizi, Si̇bel Yalçin Tokgöz

Turkish Journal of Mathematics

The main purpose of this paper is to establish a relationship between univalent harmonic mappings and Hardy spaces. The main result obtained in this paper improves previously published results. Moreover, we generalize some nice results in the analytic case to the harmonic case.

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A Broken Cycle Theorem For The Restrained Chromatic Function, Aysel Erey Jan 2019

A Broken Cycle Theorem For The Restrained Chromatic Function, Aysel Erey

Turkish Journal of Mathematics

A restraint $r$ on a graph $G$ is a function that assigns each vertex of the graph a finite subset of $\mathbb{N}$. For each vertex $v$ of the graph, $r(v)$ is called the set of colors forbidden at $v$. A proper coloring of $G$ is said to be permitted by a given restraint $r$ if each vertex $v$ of the graph receives a color that is not from its set of forbidden colors $r(v)$. The restrained chromatic function, denoted by $\pi_r(G,x)$, is a function whose evaluations at integer $x$ values count the number of proper $x$-colorings of the graph $G$ …

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A Novel Graph-Operational Matrix Method For Solving Multidelay Fractional Differential Equations With Variable Coefficients And A Numerical Comparative Survey Of Fractional Derivative Types, Ömür Kivanç Kürkçü, Ersi̇n Aslan, Mehmet Sezer Jan 2019

A Novel Graph-Operational Matrix Method For Solving Multidelay Fractional Differential Equations With Variable Coefficients And A Numerical Comparative Survey Of Fractional Derivative Types, Ömür Kivanç Kürkçü, Ersi̇n Aslan, Mehmet Sezer

Turkish Journal of Mathematics

In this study, we introduce multidelay fractional differential equations with variable coefficients in a unique formula. A novel graph-operational matrix method based on the fractional Caputo, Riemann-Liouville, Caputo-Fabrizio, and Jumarie derivative types is developed to efficiently solve them. We also make use of the collocation points and matrix relations of the matching polynomial of the complete graph in the method. We determine which of the fractional derivative types is more appropriate for the method. The solutions of model problems are improved via a new residual error analysis technique. We design a general computer program module. Thus, we can explicitly monitor …

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Harmonic Numbers Associated With Inversion Numbers In Terms Of Determinants, Takao Komatsu, Amalia Pizarro-Madariaga Jan 2019

Harmonic Numbers Associated With Inversion Numbers In Terms Of Determinants, Takao Komatsu, Amalia Pizarro-Madariaga

Turkish Journal of Mathematics

It has been known that some numbers, including Bernoulli, Cauchy, and Euler numbers, have such corresponding numbers in terms of determinants of Hessenberg matrices. There exist inversion relations between the original numbers and the corresponding numbers. In this paper, we introduce the numbers related to harmonic numbers in determinants. We also give several of their arithmetical and/or combinatorial properties and applications. These concepts can be generalized in the case of hyperharmonic numbers.

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Hirzebruch-Kummer Covers Of Algebraic Surfaces, Piotr Pokora Jan 2019

Hirzebruch-Kummer Covers Of Algebraic Surfaces, Piotr Pokora

Turkish Journal of Mathematics

The aim of this paper is to show that using some natural curve arrangements in algebraic surfaces and Hirzebruch-Kummer covers, one cannot construct new examples of ball-quotients, i.e. minimal smooth complex projective surfaces of general type satisfying equality in the Bogomolov-Miyaoka-Yau inequality.

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