The Height Of A Permutation And Applications To Distance Between Real Line Arrangements,
2020
TÜBİTAK
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.
The Relation Between The Existence Of Bounded Global Solutions Of The Differential Equations And Equations On Time Scales,
2020
TÜBİTAK
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.
Dual Quaternion Algebra And Its Derivations,
2020
TÜBİTAK
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 …
Generating Sets Of An Infinite Semigroup Of Transformations Preserving A Zig-Zag Order,
2020
TÜBİTAK
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 $F_{\mathbb{N}}.$
Commutator Subgroups Of Generalized Hecke And Extended Generalized Hecke Groups,Ii,
2020
TÜBİTAK
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 $\overline{H}^{\prime}(p_{1},\ \cdots,\ p_{n})$.
Asymptotic Theory For A Critical Class Of Third-Order Differential Equations,
2020
TÜBİTAK
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 $x$.
Entire Large Positive Radial Symmetry Solutions For Combined Quasilinear Elliptic System,
2020
TÜBİTAK
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.
Pre-Markov Operators,
2020
TÜBİTAK
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.
Almost Symmetric Arf Partitions,
2020
TÜBİTAK
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 $g$.
A Special Approach To Derive New Formulas For Some Special Numbers And Polynomials,
2020
TÜBİTAK
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 …
Compactness Of Soft Cone Metric Space And Fixed Point Theorems Related To Diametrically Contractive Mapping,
2020
TÜBİTAK
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 …
Banach Algebra Structure On Simple Extensions,
2020
TÜBİTAK
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.
Symmetric Polynomials In Leibniz Algebras And Their Inner Automorphisms,
2020
TÜBİTAK
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 $L_n'$ …
Isotropic Riemannian Submersions,
2020
TÜBİTAK
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.
Games Relating To Weak Covering Properties In Bitopological Spaces,
2020
TÜBİTAK
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.
Neutral Multivalued Integro-Differential Evolution Equations With Infinite State-Dependent Delay,
2020
TÜBİTAK
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.
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 …
Existence Results For $\Psi $-Caputo Fractional Neutral Functional Integro-Differential Equations With Finite Delay,
2020
TÜBİTAK
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.
Ascending Chains Of Ideals In The Polynomial Ring,
2020
TÜBİTAK
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.
$Q-$Hamiltonian Systems,
2020
TÜBİTAK
$Q-$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.
