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2020

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Full-Text Articles in Mathematics

On Certain Subclasses Of Starlike And Convex Functions Associated With Pascal Distribution Series, Bi̇lal Şeker, Sevtap Sümer Eker Jan 2020

On Certain Subclasses Of Starlike And Convex Functions Associated With Pascal Distribution Series, Bi̇lal Şeker, Sevtap Sümer Eker

Turkish Journal of Mathematics

In this article, we introduced a new power series whose coefficients are probabilities of the Pascal distribution. We investigated new approaches between the Pascal distribution series and some subclasses of normalized analytic functions. Also, we defined some mappings containing these functions the Alexander type integral operator. Moreover, we obtained sufficient conditions such that these mappings belong to some subclass of univalent functions.

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Generalized $\Pi$-Baer Rings, Ali Shahidikia, Hamid Haj Seyyed Javadi, Ahmad Moussavi Jan 2020

Generalized $\Pi$-Baer Rings, Ali Shahidikia, Hamid Haj Seyyed Javadi, Ahmad Moussavi

Turkish Journal of Mathematics

We call a ring $R$ generalized right $\pi$-Baer, if for any projection invariant left ideal $Y$ of $R$, the right annihilator of $Y^n$ is generated, as a right ideal, by an idempotent, for some positive integer $n$, depending on $Y$. In this paper, we investigate connections between the \g $\pi$-Baer rings and related classes of rings (e.g., $\pi$-Baer, generalized Baer, generalized quasi-Baer, etc.) In fact, generalized right $\pi$-Baer rings are special cases of generalized right quasi-Baer rings and also are a generalization of $\pi$-Baer and generalized right Baer rings. The behavior of the generalized right $\pi$-Baer condition is investigated with …

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Some Deformations Of The Fibred Biset Category, Laurence Barker, İsmai̇l Alperen Öğüt Jan 2020

Some Deformations Of The Fibred Biset Category, Laurence Barker, İsmai̇l Alperen Öğüt

Turkish Journal of Mathematics

We prove the well-definedness of some deformations of the fibred biset category in characteristic zero. The method is to realize the fibred biset category and the deformations as the invariant parts of some categories whose compositions are given by simpler formulas. Those larger categories are constructed from a partial category of subcharacters by linearizing and introducing a cocycle.

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The Height Of A Permutation And Applications To Distance Between Real Line Arrangements, Meirav Amram, Moshe Cohen, Hao Max Sun, Mina Teicher Jan 2020

The Height Of A Permutation And Applications To Distance Between Real Line Arrangements, Meirav Amram, Moshe Cohen, Hao Max Sun, Mina Teicher

Turkish Journal of Mathematics

We present a new notion of a distance between two real line arrangements. We define the height of a permutation and use this idea in our main theorem, which gives us a lower bound on the distance between the pair. We apply these techniques to the seven special cases of real arrangements with ten lines found in previous work by the authors.

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The Relation Between The Existence Of Bounded Global Solutions Of The Differential Equations And Equations On Time Scales, Olha Karpenko, Oleksandr Stanzhytskyi, Tetiana Dobrodzii Jan 2020

The Relation Between The Existence Of Bounded Global Solutions Of The Differential Equations And Equations On Time Scales, Olha Karpenko, Oleksandr Stanzhytskyi, Tetiana Dobrodzii

Turkish Journal of Mathematics

This work is devoted to the study of existence of a bounded solution of the differential equation, defined on a family of time scales $\mathbb{T}_\lambda$, provided the graininess function $\mu_\lambda$ converges to zero as $\lambda\to 0$. We obtained the conditions, under which the existence of a bounded solution of differential equation implies the existence of a bounded solution of the corresponding equation, defined on time scales, and vice versa.

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Dual Quaternion Algebra And Its Derivations, Eyüp Kizil, Yasemi̇n Alagöz Jan 2020

Dual Quaternion Algebra And Its Derivations, Eyüp Kizil, Yasemi̇n Alagöz

Turkish Journal of Mathematics

It is well known that the automorphism group $Aut(H)$ of the algebra of real quaternions $H$ consists entirely of inner automorphisms $i_{q}:p\rightarrow q\cdot p\cdot q^{-1}$ for invertible $q\in H$ and is isomorphic to the group of rotations $SO(3)$. Hence, $H$ has only inner derivations $D=ad(x),$ $x\in H$. See [4] for derivations of various types of quaternions over the reals. Unlike real quaternions, the algebra $H_{d}$ of dual quaternions has no nontrivial inner derivation. Inspired from almost inner derivations for Lie algebras, which were first introduced in [3] in their study of spectral geometry, we introduce coset invariant derivations for dual …

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Generating Sets Of An Infinite Semigroup Of Transformations Preserving A Zig-Zag Order, Laddawan Lohapan, Jörg Koppitz, Somnuek Worawiset Jan 2020

Generating Sets Of An Infinite Semigroup Of Transformations Preserving A Zig-Zag Order, Laddawan Lohapan, Jörg Koppitz, Somnuek Worawiset

Turkish Journal of Mathematics

A zig-zag order is like a directed path, only with alternating directions. A generating set of minimal size for the semigroup of all full transformations on a finite set preserving the zig-zag order was determined by Fenandes et al. in 2019. This paper deals with generating sets of the semigroup $F_{\mathbb{N}}$ of all full transformations on the set of all natural numbers preserving the zig-zag order. We prove that $F_{\mathbb{N}}$ has no minimal generating sets and present two particular infinite decreasing chains of generating sets of $F_{\mathbb{N}}.$

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Commutator Subgroups Of Generalized Hecke And Extended Generalized Hecke Groups,Ii, Gülşah Doğrayici, Recep Şahi̇n Jan 2020

Commutator Subgroups Of Generalized Hecke And Extended Generalized Hecke Groups,Ii, Gülşah Doğrayici, Recep Şahi̇n

Turkish Journal of Mathematics

Let $p_{1},\ \cdots,\ p_{n}$ be integers where $n\geq 2$ and each $p_{i} \geq 2$. Let also $H(p_{1},\ \cdots,\ p_{n})$ be the generalized Hecke group associated to all $p_{i}\geq 2.$ In this paper, we study the commutator subgroups $H^{\prime}(p_{1},\ \cdots,\ p_{n})$ and $\overline{H}^{\prime }(p_{1},\ \cdots,\ p_{n})$ of the generalized Hecke group $H(p_{1},\ \cdots,\ p_{n})$ and the extended generalized Hecke group $\overline{H}% (p_{1},\ \cdots,\ p_{n})$. We give the generators and the signatures of $% H^{\prime}(p_{1},\ \cdots,\ p_{n})$ and $\overline{H}^{\prime}(p_{1},\ \cdots,\ p_{n})$.

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Asymptotic Theory For A Critical Class Of Third-Order Differential Equations, Aziz S. A. Alhammadi Jan 2020

Asymptotic Theory For A Critical Class Of Third-Order Differential Equations, Aziz S. A. Alhammadi

Turkish Journal of Mathematics

An asymptotic theory is developed for a class of third-order differential equations. We identify a critical case to obtain the asymptotic form of three linearly independent solutions for large $x$.

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Entire Large Positive Radial Symmetry Solutions For Combined Quasilinear Elliptic System, Seshadev Padhi, Smita Pati Jan 2020

Entire Large Positive Radial Symmetry Solutions For Combined Quasilinear Elliptic System, Seshadev Padhi, Smita Pati

Turkish Journal of Mathematics

We prove the existence of entire large positive solutions to the system \begin{equation*} \begin{cases} (r^{N-1}\phi_{1}(u^{\prime}))^{\prime} = r^{N-1}P_{1}(r)f(u,v),\, \, 0 \leq r < \infty \\ (r^{N-1}\phi_{2}(v^{\prime}))^{\prime} = r^{N-1}P_{2}(r)g(u,v),\, \, 0 \leq r < \infty \\ u(0) = a, \, v(0) = b, \, u^{\prime}(0) = 0, \, v^{\prime}(0) = b, \end{cases} \end{equation*} where the functions $\phi_{i}(s) = \alpha_{i}(s^{2})s, \,\, i= 1, 2$ are odd, increasing homeomorphisms, $P_{1},P_{2}:[0,\infty)\to [0,\infty)$ are continuous, and $f,g:[0,\infty) \times [0,\infty) \to [0,\infty)$ are continuous and increasing functions.

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Pre-Markov Operators, Hülya Duru, Serkan İlter Jan 2020

Pre-Markov Operators, Hülya Duru, Serkan İlter

Turkish Journal of Mathematics

In operator theory characterizing extreme points has been systematically studied in a convex set of linear operators from an algebra to another. This paper presents some new characterizations. We define pre-Markov operators and identify when the second adjoint of a linear positive operator being an extreme point in the collection of all Markov operators between the unital second order duals of two unital f-algebras. Moreover a characterization of extreme points is given in the collection of all contractive operators between unital f-algebras. In addition, we give a condition that makes an order bounded algebra homomorphism is a lattice homomorphism.

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Almost Symmetric Arf Partitions, Ni̇hal Gümüşbaş Öztürk, Nesri̇n Tutaş, Naci̇ Er Jan 2020

Almost Symmetric Arf Partitions, Ni̇hal Gümüşbaş Öztürk, Nesri̇n Tutaş, Naci̇ Er

Turkish Journal of Mathematics

In this paper, we introduce almost symmetric Arf partitions (for short, ASA-partitions) and using properties of partitions of positive integers, we give the number of almost symmetric Arf semigroups of genus $g$.

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A Special Approach To Derive New Formulas For Some Special Numbers And Polynomials, Nesli̇han Kilar, Yilmaz Şi̇mşek Jan 2020

A Special Approach To Derive New Formulas For Some Special Numbers And Polynomials, Nesli̇han Kilar, Yilmaz Şi̇mşek

Turkish Journal of Mathematics

By applying Laplace differential operator to harmonic conjugate components of the analytic functions and using Wirtinger derivatives, some identities and relations including Bernoulli and Euler polynomials and numbers are obtained. Next, using the Legendre identity, trigonometric functions and the Dirichlet kernel, some formulas and relations involving Bernoulli and Euler numbers, cosine-type Bernoulli and Euler polynomials, and sine-type Bernoulli and Euler polynomials are driven. Then, by using the generating functions method and the well-known Euler identity, many new identities, formulas, and combinatorial sums among the Fibonacci numbers and polynomials, the Lucas numbers and polynomials, the Chebyshev polynomials, and Bernoulli and Euler …

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Compactness Of Soft Cone Metric Space And Fixed Point Theorems Related To Diametrically Contractive Mapping, İsmet Altintaş, Kemal Taşköprü Jan 2020

Compactness Of Soft Cone Metric Space And Fixed Point Theorems Related To Diametrically Contractive Mapping, İsmet Altintaş, Kemal Taşköprü

Turkish Journal of Mathematics

In this article, we describe the concepts such as sequentially soft closeness, sequential compactness, totally boundedness and sequentially continuity in any soft cone metric space and prove their some properties. Also, we examine soft closed set, soft closure, compactness and continuity in an elementary soft topological cone metric space. Unlike classical cone metric space, sequential compactness and compactness are not the same here. Because the compactness is an elementary soft topological property and cannot be defined for every soft cone metric space. However, in the restricted soft cone metric spaces, they are the same. Additionally, we prove some fixed point …

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Banach Algebra Structure On Simple Extensions, Sara El Kinani Jan 2020

Banach Algebra Structure On Simple Extensions, Sara El Kinani

Turkish Journal of Mathematics

We study the existence of Banach algebra structures on simple extensions of a unitary commutative Banach algebra. The link with the integrality of these extensions is studied. For any simple extension, a characterization of the existence of the Banach algebra norm making continuous the canonical injection is also given.

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Symmetric Polynomials In Leibniz Algebras And Their Inner Automorphisms, Şehmus Findik, Zeynep Özkurt Jan 2020

Symmetric Polynomials In Leibniz Algebras And Their Inner Automorphisms, Şehmus Findik, Zeynep Özkurt

Turkish Journal of Mathematics

Let $L_n$ be the free metabelian Leibniz algebra generated by the set $X_n=\{x_1,\ldots,x_n\}$ over a field $K$ of characteristic zero. This is the free algebra of rank $n$ in the variety of solvable of class $2$ Leibniz algebras. We call an element $s(X_n)\in L_n$ symmetric if $s(x_{\sigma(1)},\ldots,x_{\sigma(n)})=s(x_1,\ldots,x_n)$ for each permutation $\sigma$ of $\{1,\ldots,n\}$. The set $L_n^{S_n}$ of symmetric polynomials of $L_n$ is the algebra of invariants of the symmetric group $S_n$. Let $K[X_n]$ be the usual polynomial algebra with indeterminates from $X_n$. The description of the algebra $K[X_n]^{S_n}$ is well known, and the algebra $(L_n')^{S_n}$ in the commutator ideal $L_n'$ …

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Isotropic Riemannian Submersions, Feyza Esra Erdoğan, Bayram Şahi̇n Jan 2020

Isotropic Riemannian Submersions, Feyza Esra Erdoğan, Bayram Şahi̇n

Turkish Journal of Mathematics

In this paper, we present the notion of isotropic submersions between Riemannian manifolds. We first give examples to illustrate this new notion. Then we express a characterization in terms of O'Neill's tensor field T and examine certain relations between sectional curvatures of the total manifold and the base manifold. We also study $\lambda$-isotropic submersions with pointwise planar horizontal sections.

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Games Relating To Weak Covering Properties In Bitopological Spaces, Ali̇ Emre Eysen, Selma Özçağ Jan 2020

Games Relating To Weak Covering Properties In Bitopological Spaces, Ali̇ Emre Eysen, Selma Özçağ

Turkish Journal of Mathematics

We study topological games related to weak forms of the Menger property in bitopological spaces. In particular we investigate almost Menger game and its connections to games which are associated with the covering properties consisting of covers containing $G_\delta$ subsets.

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Neutral Multivalued Integro-Differential Evolution Equations With Infinite State-Dependent Delay, Abdelaziz Mebarki, Selma Baghli Bendimerad Jan 2020

Neutral Multivalued Integro-Differential Evolution Equations With Infinite State-Dependent Delay, Abdelaziz Mebarki, Selma Baghli Bendimerad

Turkish Journal of Mathematics

Our problem through this work is to give the existence of mild solutions for the first order class of neutral functional multivalued integro-differential evolution equations with infinite state-dependent delay using the nonlinear alternative of Frigon for multivalued contraction maps in Fréchet spaces combined with the semi-group theory.

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New Classes Of Catalan-Type Numbers And Polynomials With Their Applications Related To $P$-Adic Integrals And Computational Algorithms, İrem Küçükoğlu, Burçi̇n Şi̇mşek, Yilmaz Şi̇mşek Jan 2020

New Classes Of Catalan-Type Numbers And Polynomials With Their Applications Related To $P$-Adic Integrals And Computational Algorithms, İrem Küçükoğlu, Burçi̇n Şi̇mşek, Yilmaz Şi̇mşek

Turkish Journal of Mathematics

The aim of this paper is to construct generating functions for new classes of Catalan-type numbers and polynomials. Using these functions and their functional equations, we give various new identities and relations involving these numbers and polynomials, the Bernoulli numbers and polynomials, the Stirling numbers of the second kind, the Catalan numbers and other classes of special numbers, polynomials and functions. Some infinite series representations, including the Catalan-type numbers and combinatorial numbers, are investigated. Moreover, some recurrence relations and computational algorithms for these numbers and polynomials are provided. By implementing these algorithms in the Python programming language, we illustrate the …

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Existence Results For $\Psi $-Caputo Fractional Neutral Functional Integro-Differential Equations With Finite Delay, Abdellatif Boutiara, Mohamed S. Abdo, Maamar Benbachir Jan 2020

Existence Results For $\Psi $-Caputo Fractional Neutral Functional Integro-Differential Equations With Finite Delay, Abdellatif Boutiara, Mohamed S. Abdo, Maamar Benbachir

Turkish Journal of Mathematics

This research article deals with novel two species of initial value problems, one of them, the fractional neutral functional integrodifferential equations, and the other one, the coupled system of fractional neutral functional integrodifferential equations, with finite delay and involving a $\psi$-Caputo fractional operator. The existence and uniqueness results are studied through Banach's contraction principle and Krasnoselskii's fixed point theorem. We also establish two various kinds of Ulam stability results for the proposed problems. Further, two pertinent examples are presented to demonstrate the reported results.

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Ascending Chains Of Ideals In The Polynomial Ring, Grzegorz Pastuszak Jan 2020

Ascending Chains Of Ideals In The Polynomial Ring, Grzegorz Pastuszak

Turkish Journal of Mathematics

Assume that $K$ is a field and $I_{1}\subsetneq ...\subsetneq I_{t}$ is an ascending chain (of length $t$) of ideals in the polynomial ring $K[x_{1},...,x_{m}]$, for some $m\geq 1$. Suppose that $I_{j}$ is generated by polynomials of degrees less or equal to some natural number $f(j)\geq 1$, for any $j=1,...,t$. In the paper we construct, in an elementary way, a natural number B (m,f) (depending on $m$ and the function $f$) such that ≤ (m,f)$. We also discuss some applications of this result.

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$Q-$Hamiltonian Systems, Bi̇lender Paşaoğlu, Hüseyi̇n Tuna Jan 2020

$Q-$Hamiltonian Systems, Bi̇lender Paşaoğlu, Hüseyi̇n Tuna

Turkish Journal of Mathematics

In this paper, we develop the basic theory of linear $q-$ Hamiltonian systems. In this context, we establish an existence and uniqueness result. Regular spectral problems are studied. Later, we introduce the corresponding maximal and minimal operators for this system. Finally, we give a spectral resolution.

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A Robust Hyperviscosity Formulation For Stable Rbf-Fd Discretizations Of Advection-Diffusion-Reaction Equations On Manifolds, Varun Shankar, Grady B. Wright, Akil Narayan Jan 2020

A Robust Hyperviscosity Formulation For Stable Rbf-Fd Discretizations Of Advection-Diffusion-Reaction Equations On Manifolds, Varun Shankar, Grady B. Wright, Akil Narayan

Mathematics Faculty Publications and Presentations

We present a new hyperviscosity formulation for stabilizing radial basis function-finite difference (RBF-FD) discretizations of advection-diffusion-reaction equations on manifolds �� ⊂ ℝ3 of codimension 1. Our technique involves automatic addition of artificial hyperviscosity to damp out spurious modes in the differentiation matrices corresponding to surface gradients, in the process overcoming a technical limitation of a recently developed Euclidean formulation. Like the Euclidean formulation, the manifold formulation relies on von Neumann stability analysis performed on auxiliary differential operators that mimic the spurious solution growth induced by RBF-FD differentiation matrices. We demonstrate high-order convergence rates on problems involving surface advection and …

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Middle-School Mathematics Teachers' Use Of Formative Assessment Data, Shawana T. Green Jan 2020

Middle-School Mathematics Teachers' Use Of Formative Assessment Data, Shawana T. Green

Walden Dissertations and Doctoral Studies

A school district located in the southeastern United States uses benchmark tests as formative assessment to provide teachers with data to differentiate their instruction to meet the individual needs of students in their classrooms. Despite this effort, student achievement in mathematics in this school district has not improved. The purpose of this study was to gain an understanding of how middle-grade mathematics teachers used the benchmark results as formative data to guide instruction and meet student needs. The conceptual framework that grounded this study was the model of formative assessment developed by Black and Wiliam. For this basic qualitative study, …

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Teacher-Student Networks With Multiple Decoders For Solving Math Word Problem, Jipeng Zhang, Roy Ka-Wei Lee, Ee-Peng Lim, Wei Qin, Lei Wang, Jie Shao, Qianru Sun Jan 2020

Teacher-Student Networks With Multiple Decoders For Solving Math Word Problem, Jipeng Zhang, Roy Ka-Wei Lee, Ee-Peng Lim, Wei Qin, Lei Wang, Jie Shao, Qianru Sun

Research Collection School Of Computing and Information Systems

Math word problem (MWP) is challenging due to the limitation in training data where only one “standard” solution is available. MWP models often simply fit this solution rather than truly understand or solve the problem. The generalization of models (to diverse word scenarios) is thus limited. To address this problem, this paper proposes a novel approach, TSN-MD, by leveraging the teacher network to integrate the knowledge of equivalent solution expressions and then to regularize the learning behavior of the student network. In addition, we introduce the multiple-decoder student network to generate multiple candidate solution expressions by which the final answer …

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Making Real-World Connections In High School Mathematics: The Effectiveness Of A Professional Development Program In Changing Teachers’ Knowledge, Beliefs, And Practices, Thad Ludlam Wilhelm Jan 2020

Making Real-World Connections In High School Mathematics: The Effectiveness Of A Professional Development Program In Changing Teachers’ Knowledge, Beliefs, And Practices, Thad Ludlam Wilhelm

Wayne State University Dissertations

The study aimed to assess the impact of a professional development workshop at changing secondary mathematics teachers’ knowledge, beliefs, and practices related to real-world applications of algebra. It also addressed gaps in the research literature related to teacher knowledge of how algebra is used by professionals in non-academic settings and their beliefs about the relevance of algebra to their students’ lives. The observational study employed mixed methods. Principal components analysis was conducted on responses to an online questionnaire. Pre-test vs. post-test comparisons were made for workshop participants. Treatment vs. control comparisons were also made using a nationally representative random sample …

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Estimation And Clustering In Block Models, Majid Noroozi Jan 2020

Estimation And Clustering In Block Models, Majid Noroozi

Electronic Theses and Dissertations, 2020-2023

Networks with community structure arise in many fields such as social science, biological science, and computer science. Stochastic block models are popular tools to describe such networks. For this reason, in this dissertation which is composed of two parts we explore some stochastic block models and the relationship between them. In the first part of the dissertation, we study the Popularity Adjusted Block Model (PABM) and introduce its sparse case, the Sparse Popularity Adjusted Block Model (SPABM). The SPABM is the only existing block model which allows to set some probabilities of connections to zero. For both the PABM and …

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Distributed Algorithms And Inverse Graph Filtering, Nazar Emirov Jan 2020

Distributed Algorithms And Inverse Graph Filtering, Nazar Emirov

Electronic Theses and Dissertations, 2020-2023

Graph signal processing provides an innovative framework to handle data residing on distributed networks, smart grids, neural networks, social networks and many other irregular domains. By leveraging applied harmonic analysis and graph spectral theory, graph signal processing has been extensively exploited, and many important concepts in classical signal processing have been extended to the graph setting such as graph Fourier transform, graph wavelets and graph filter banks. Similarly, many optimization problems in machine learning, sensor networks, power systems, control theory and signal processing can be modeled using underlying network structure. In modern applications, the size of a network is large, …

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Discrete Geometry And Covering Problems, Alexander Hsu Jan 2020

Discrete Geometry And Covering Problems, Alexander Hsu

CMC Senior Theses

This thesis explores several problems in discrete geometry, focusing on covering problems. We first go over some well known results, explaining Keith Ball's solution to the symmetric Tarski plank problem, as well as results of Alon and F\"uredi on covering all but vertices of a cube with hyperplanes. The former extensively utilizes techniques from matrix analysis, and the latter applies polynomial method. We state and explore the related problem, asking for the number of parallel hyperplanes required to cover a given discrete set of points in $\mathbb{Z}^{d}$ whose entries are bounded, and prove that there exist sets which are ``difficult'' …

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