Separation Axioms On Neutrosophic Soft Topological Spaces,
2019
TÜBİTAK
Separation Axioms On Neutrosophic Soft Topological Spaces, Çi̇ğdem Gündüz, Taha Yasi̇n Öztürk, Sadi Bayramov
Turkish Journal of Mathematics
A neutrosophic set, proposed by Smarandache, considers a truth membership function, an indeterminacy membership function, and a falsity membership function. Neutrosophic soft sets combined by Maji have been utilized successfully to model uncertainty in several areas of application such as control, reasoning, pattern recognition, and computer vision. In the present paper, some basic notions of neutrosophic soft sets have been redefined and the neutrosophic soft point concept has been introduced. Later we give the neutrosophic soft $T_{i}$-space and the relationships between them are discussed in detail.
Young Tableaux And Arf Partitions,
2019
TÜBİTAK
Young Tableaux And Arf Partitions, Nesri̇n Tutaş, Hali̇l İbrahi̇m Karakaş, Ni̇hal Gümüşbaş
Turkish Journal of Mathematics
The aim of this work is to exhibit some relations between partitions of natural numbers and Arf semigroups. We also give characterizations of Arf semigroups via the hook-sets of Young tableaux of partitions.
A New Class Of Generalized Polynomials Associated With Laguerre And Bernoulli Polynomials,
2019
TÜBİTAK
A New Class Of Generalized Polynomials Associated With Laguerre And Bernoulli Polynomials, Nabiullah Khan, Talha Usman, Junesang Choi
Turkish Journal of Mathematics
Motivated by their importance and potential for applications in certain problems in number theory, combinatorics, classical and numerical analysis, and other fields of applied mathematics, a variety of polynomials and numbers with their variants and extensions have recently been introduced and investigated. In this paper, we aim to introduce generalized Laguerre-Bernoulli polynomials and investigate some of their properties such as explicit summation formulas, addition formulas, implicit formulas, and symmetry identities. Relevant connections of the results presented here with those relatively simple numbers and polynomials are considered.
Slant Helices: A New Approximation,
2019
TÜBİTAK
Slant Helices: A New Approximation, Pascual Lucas, Jose Antonio Ortega-Yagues
Turkish Journal of Mathematics
In this paper, we study a weaker version of classic slant helices in Euclidean space $\mathbb{R}^3$ or Minkowski space $\mathbb{R}^3_1$, which will be called general slant helices. We show that any classic slant helix is a general slant helix but the converse is not true. We also obtain equations involving the curvature and torsion that characterize this family of curves.
Categorical Structures Of Lie-Rinehart Crossed Module,
2019
TÜBİTAK
Categorical Structures Of Lie-Rinehart Crossed Module, Ali̇ Ayteki̇n
Turkish Journal of Mathematics
In this paper we give constructions of pullback, finite product, finite limit, coproduct, colimit, pushout, etc. in a special full subcategory $\mathfrak{XMod}/\mathcal{L}$ of the category of Lie-Rinehart crossed modules.
Some Operator Inequalities Associated With Kantorovich And Hölder-Mccarthyinequalities And Their Applications,
2019
TÜBİTAK
Some Operator Inequalities Associated With Kantorovich And Hölder-Mccarthyinequalities And Their Applications, Hamdullah Başaran, Mehmet Gürdal, Ayşe Nur Güncan
Turkish Journal of Mathematics
We prove analogs of certain operator inequalities, including Hölder-McCarthy inequality, Kantorovich inequality, and Heinz-Kato inequality, for positive operators on the Hilbert space in terms of the Berezin symbols and the Berezin number of operators on the reproducing kernel Hilbert space.
Curves Over Finite Fields And Permutations Of The Form $X^K-\Gamma \Mathrm{Tr}(X)$,
2019
TÜBİTAK
Curves Over Finite Fields And Permutations Of The Form $X^K-\Gamma \Mathrm{Tr}(X)$, Nurdagül Anbar Meidl
Turkish Journal of Mathematics
We consider the polynomials of the form $P(x)=x^k-\gamma \mathrm{Tr}(x)$ over $\mathbb{F}_{q^n}$ for $n\geq 2$. We show that $P(x)$ is not a permutation of $\mathbb{F}_{q^n}$ in the case $\gcd(k, q^n-1)>1$. Our proof uses an absolutely irreducible curve over $\mathbb{F}_{q^n}$ and the number of rational points on it.
On The Composition And Exterior Products Of Double Forms And $P$-Pure Manifolds,
2019
TÜBİTAK
On The Composition And Exterior Products Of Double Forms And $P$-Pure Manifolds, Abdelhadi Belkhirat, Mohammed Labbi
Turkish Journal of Mathematics
We translate into double forms formalism the basic Greub and Greub-Vanstone identities that were previously obtained in mixed exterior algebras. In particular, we introduce a second product in the space of double forms, namely the composition product, which provides this space with a second associative algebra structure. The composition product interacts with the exterior product of double forms; we show that the resulting relations provide simple alternative proofs to some classical linear algebra identities as well as to recent results in the exterior algebra of double forms. We define and study a refinement of the notion of pure curvature of …
Rt Distance And Weight Distributions Of Type 1 Constacyclic Codes Of Length\\ $4p^S$ Over $\Frac{\Mathbb F_{P^M}[U]}{\Left\Langle U^A \Right\Rangle}$, Hai Dinh, Bac Nguyen, Songsak Sriboonchitta
Turkish Journal of Mathematics
For any odd prime $p$ such that $p^m \equiv 1 \pmod{4}$, the class of $\Lambda$-constacyclic codes of length $4p^s$ over the finite commutative chain ring ${\cal R}_a=\frac{\mathbb F_{p^m}[u]}{\left\langle u^a \right\rangle}=\mathbb F_{p^m} + u \mathbb F_{p^m}+ \dots + u^{a-1}\mathbb F_{p^m}$, for all units $\Lambda$ of $\mathcal R_a$ that have the form $\Lambda=\Lambda_0+u\Lambda_1+\dots+u^{a-1}\Lambda_{a-1}$, where $\Lambda_0, \Lambda_1, \dots, \Lambda_{a-1} \in \mathbb F_{p^m}$, $\Lambda_0 \,{\not=}\, 0, \, \Lambda_1 \,{\not=}\, 0$, is investigated. If the unit $\Lambda$ is a square, each $\Lambda$-constacyclic code of length $4p^s$ is expressed as a direct sum of a $-\lambda$-constacyclic code and a $\lambda$-constacyclic code of length $2p^s$. In the …
Exponential Stabilization Of A Neutrally Delayed Viscoelastic Timoshenko Beam,
2019
TÜBİTAK
Exponential Stabilization Of A Neutrally Delayed Viscoelastic Timoshenko Beam, Sebti Kerbal, Nasser Eddine Tatar
Turkish Journal of Mathematics
A Timoshenko type beam subject to a viscoelastic damping in the rotational displacement component is considered. Taking into account a neutral type delay, we prove a fast stability result despite the previously observed destabilizing effect due to delays in such systems. The proof relies on the introduction of nine different functionals with which we modify the energy of the system. These functionals are carefully selected and adapted to cope with both the viscoelasticity and the neutral delay.
Spectral Properties Of Boundary-Value-Transmission Problems With A Constant Retarded Argument,
2019
TÜBİTAK
Spectral Properties Of Boundary-Value-Transmission Problems With A Constant Retarded Argument, Erdoğan Şen
Turkish Journal of Mathematics
In this work, spectra and asymptotics of eigenfunctions of a generalized class of boundary value problems with constant retarded argument are obtained. Contrary to previous works in the literature, the problem has nonclassical transmission conditions.
Positivity Of Sums And Integrals For $N$-Convex Functions Via The Fink Identity,
2019
TÜBİTAK
Positivity Of Sums And Integrals For $N$-Convex Functions Via The Fink Identity, Asif R. Khan, Josip Pecaric, Marjan Praljak, Sanja Varosanec
Turkish Journal of Mathematics
We consider the positivity of the sum $\sum_{i=1}^n\rho_i\digamma(\xi_i)$, where $\digamma$ is a convex function of higher order, as well as analogous results involving the integral $\int_{a_0}^{b_0}\rho(\xi)\digamma(g(\xi))d\xi$. We use a representation of the function $\digamma$ via the Fink identity and the Green function that leads us to identities from which we obtain conditions for positivity of the above-mentioned sum and integral. We also obtain bounds for the integral remainders which occur in these identities, as well as corresponding mean value results.
Stability Analysis For A Class Of Nabla $(Q,H)$-Fractional Difference Equations,
2019
TÜBİTAK
Stability Analysis For A Class Of Nabla $(Q,H)$-Fractional Difference Equations, Xiang Liu, Baoguo Jia, Lynn Erbe, Allan Peterson
Turkish Journal of Mathematics
This paper investigates stability of the nabla $(q,h)$-fractional difference equations. Asymptotic stability of the special nabla $(q,h)$-fractional difference equations are discussed. Stability theorems for discrete fractional Lyapunov direct method are proved. Furthermore, we give some new lemmas (including important comparison theorems) related to the nabla $(q,h)$-fractional difference operators that allow proving the stability of the nabla $(q,h)$-fractional difference equations, by means of the discrete fractional Lyapunov direct method, using Lyapunov functions. Some examples are given to illustrate these results.
$N$-$T$-Torsionfree Modules,
2019
TÜBİTAK
$N$-$T$-Torsionfree Modules, Peiyu Zhang, Jie Geng
Turkish Journal of Mathematics
As a generalization of the Auslander-Reiten transpose, Xi introduced and studied a more general transpose, called the relative transpose (or, $T$-transpose). Based on this notion, the notion of relative $n$-torsionfree modules (or, $n$-$T$-torsionfree modules) is introduced in this paper, which is a generalization of the $n$-torsionfree modules introduced by Auslander and Bridger. We show that relative $n$-torsionfree modules have many similar properties of $n$-torsionfree modules.
Inclusion Properties Of Lucas Polynomials For Bi-Univalent Functionsintroduced Through The $\Mathfrak{Q}$-Analogue Of The Noor Integral Operator, Şahsene Altinkaya
Turkish Journal of Mathematics
In this paper, by using the $(\mathbf{P},\mathbf{Q})$-Lucas polynomials and the $\mathfrak{q}$-analogue of the Noor integral operator, we aim to build a bridge between the theory of geometric functions and that of special functions.
A Generalization Of $\Pi$-Regular Rings,
2019
TÜBİTAK
A Generalization Of $\Pi$-Regular Rings, Peter Danchev
Turkish Journal of Mathematics
We introduce the class of so-called { regularly nil clean rings} and systematically study their fundamental characteristic properties accomplished with relationships among certain classical sorts of rings such as exchange rings, Utumi rings etc. These rings of ours naturally generalize the long-known classes of $\pi$-regular and strongly $\pi$-regular rings. We show that the regular nil cleanness possesses a symmetrization which extends the corresponding one for strong $\pi$-regularity that was visualized by Dischinger \cite{Dis}. Likewise, our achieved results substantially improve on establishments presented in two recent papers by Danchev and \v{S}ter \cite{DS} and Danchev \cite{Da}.
Certain Classes Of Multivalent Functions Defined With Higher-Order Derivatives,
2019
TÜBİTAK
Certain Classes Of Multivalent Functions Defined With Higher-Order Derivatives, Muhamed Kamal Aouf, Abdel Moneim Lashin, Teodor Bulboaca
Turkish Journal of Mathematics
In this paper we derive some properties of multivalent functions belonging to the classes $R_{p,q}(\alpha)$, $B_{p,q}(\alpha)$, and $M_{p,q}(\alpha)$. The results obtained generalize the related works of some authors, and many other new results are obtained.
Mannheim Curves With Modified Orthogonal Frame In Euclidean 3-Space,
2019
TÜBİTAK
Mannheim Curves With Modified Orthogonal Frame In Euclidean 3-Space, Mohammad Saleem Lone, Hasan Es, Murat Kemal Karacan, Bahaddi̇n Bükcü
Turkish Journal of Mathematics
In this paper, we investigate Mannheim pairs, Frenet--Mannheim curves, and weakened Mannheim curves with respect to the modified orthogonal frame in Euclidean 3-space $(E^3)$. We derive some characterization results of these curves.
Compactness Of The Commutators Of Intrinsic Square Functions On Weighted Lebesgue Spaces,
2019
TÜBİTAK
Compactness Of The Commutators Of Intrinsic Square Functions On Weighted Lebesgue Spaces, Xiaomei Wu, Xiao Yu
Turkish Journal of Mathematics
The aim of this paper is to study the compactness for the commutators of intrinsic square functions, including the intrinsic $g_{\lambda}^*$-function and the intrinsic Littlewood-Paley g-function. Using a weighted version of the Frech\'{e}t-Kolmogorov-Riesz theorem, the compactness for their commutators generated with the CMO functions is obtained on the weighted Lebesgue spaces.
Singly Generated Invariant Subspaces In The Hardy Space On The Unit Ball,
2019
TÜBİTAK
Singly Generated Invariant Subspaces In The Hardy Space On The Unit Ball, Beyaz Başak Koca, Nazim Sadik
Turkish Journal of Mathematics
In this paper, we give a complete characterization of singly generated invariant subspaces in the Hardy space on the unit ball. Then we construct a singly generated invariant subspace that cannot be generated by a single inner function, contrary to the one-variable case where every invariant subspace is generated by a single inner function. Some important properties of invariant subspaces are also determined for singly generated invariant subspaces.
