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2022

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Articles 17341 - 17370 of 18300

Full-Text Articles in Physical Sciences and Mathematics

The Complex Error Functions And Various Extensive Results Together With Implications Pertaining To Certain Special Functions, Hüseyi̇n Irmak, Praveen Agarwal, Ravi P. Agarwal Jan 2022

The Complex Error Functions And Various Extensive Results Together With Implications Pertaining To Certain Special Functions, Hüseyi̇n Irmak, Praveen Agarwal, Ravi P. Agarwal

Turkish Journal of Mathematics

The error functions play very important roles in science and technology. In this investigation, the error functions in the complex plane will be introduced, then comprehensive results together with several nonlinear implications in relation to the related complex functions will be indicated, and some possible special results of them will be next presented. Furthermore, various interesting or important suggestions will be also made for the scientific researchers who are interested in this topic.

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On The Blow-Up Of Solutions To A Fourth-Order Pseudoparabolic Equation, Mustafa Polat Jan 2022

On The Blow-Up Of Solutions To A Fourth-Order Pseudoparabolic Equation, Mustafa Polat

Turkish Journal of Mathematics

In this note, we consider a fourth-order semilinear pseudoparabolic differential equation including a strong damping term together with a nonlocal source term. The problem is considered under the periodic boundary conditions and a finite time blow-up result is established. Also a lower bound estimate for the blow-up time is obtained.

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$K$-Fibonacci Numbers And $K$-Lucas Numbers And Associated Bipartite Graphs, Gwangyeon Lee Jan 2022

$K$-Fibonacci Numbers And $K$-Lucas Numbers And Associated Bipartite Graphs, Gwangyeon Lee

Turkish Journal of Mathematics

In [6], [8] and [10], the authors studied the generalized Fibonacci numbers. Also, in [7], the author found a class of bipartite graphs whose number of $1$-factors is the $n$th $k$-Lucas numbers. In this paper, we give a new relationship between $g_n^{(k)}$ and $l_n^{(k)}$ and the number of $1$-factors of a bipartite graph.

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Oscillation Criteria For Third-Order Neutral Differential Equations With Unbounded Neutral Coefficients And Distributed Deviating Arguments, Yibing Sun, Yige Zhao, Qiangqiang Xie Jan 2022

Oscillation Criteria For Third-Order Neutral Differential Equations With Unbounded Neutral Coefficients And Distributed Deviating Arguments, Yibing Sun, Yige Zhao, Qiangqiang Xie

Turkish Journal of Mathematics

This paper focuses on the oscillation criteria for the third-order neutral differential equations with unbounded neutral coefficients and distributed deviating arguments. Using comparison principles, new sufficient conditions improve some known existing results substantially due to less constraints on the considered equation. At last, two examples are established to illustrate the given theorems.

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On The Inclusion Properties For $\Vartheta $-Spirallike Functions Involving Both Mittag-Leffler And Wright Function, Şahsene Altinkaya Jan 2022

On The Inclusion Properties For $\Vartheta $-Spirallike Functions Involving Both Mittag-Leffler And Wright Function, Şahsene Altinkaya

Turkish Journal of Mathematics

By making use of the both Mittag-Leffler and Wright function, we establish a new subfamily of the class $S_{\vartheta }$ of $\vartheta $-spirallike functions. The main object of the paper is to provide sufficient conditions for a function to be in this newly established class and to discuss subordination outcomes.

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Clairaut Semi-Invariant Riemannian Maps From Almost Hermitian Manifolds, Sushil Kumar, Rajendra Prasad, Sumeet Kumar Jan 2022

Clairaut Semi-Invariant Riemannian Maps From Almost Hermitian Manifolds, Sushil Kumar, Rajendra Prasad, Sumeet Kumar

Turkish Journal of Mathematics

In this article, we define Clairaut semi-invariant Riemannian maps (CSIR Maps, In short) from almost Hermitian manifolds onto Riemannian manifolds and investigate fundamental results on such maps. We also obtain conditions for totally geodesicness on distributions defined in the introduced notion. Moreover, we provide an explicit example of CSIR map.

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Sequences Of Polynomials Satisfying The Pascal Property, Tuangrat Chaichana, Vichian Laohakosol, Rattiya Meesa Jan 2022

Sequences Of Polynomials Satisfying The Pascal Property, Tuangrat Chaichana, Vichian Laohakosol, Rattiya Meesa

Turkish Journal of Mathematics

Since one of the most important properties of binomial coefficients is the Pascal's triangle identity (referred to as the Pascal property) and since the sequence of binomial polynomials forms a regular basis for integer-valued polynomials, it is natural to ask whether the Pascal property holds in some more general setting, and what types of integer-valued polynomials possess the Pascal property. After defining the general Pascal property, a sequence of polynomials which satisfies the Pascal property is characterized with the classical case as an example. In connection with integer-valued polynomials, characterizations are derived for a sequence of polynomials which satisfies the …

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On Hypersemigroups, Niovi Kehayopulu Jan 2022

On Hypersemigroups, Niovi Kehayopulu

Turkish Journal of Mathematics

This is from the paper "Hypergroupes canoniques values et hypervalues" by J. Mittas in Mathematica Balkanica 1971: "The concept of hypergroup introduced by Fr. MARTY in 1934 [Actes du Congres des Math. Scand. Stocholm 1935, p. 45] is as follows: "A hypergroup is a nonempty set $H$ endowed with a multiplication $xy$ such that, for every $x,y,z\in H,$ the following hold: (1) $xy\subseteq H$; (2) $x(yz)=(xy)z$ and (3) $xH=Hx=H$. The first condition expresses that the multiplication is an hyperoperation on $H$, in other words, the composition of two elements $x,y$ of $H$ is a subset of $H$. It is very …

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$Gl_N$-Invariant Functions On $M_N(\Mathcal{G})$, Alan Berele Jan 2022

$Gl_N$-Invariant Functions On $M_N(\Mathcal{G})$, Alan Berele

Turkish Journal of Mathematics

We describe the $GL_n(F)$-invariant functions on $M_n(\mathcal{G})$ (where $\mathcal{G}$ is the infinite dimensional Grassmann algebra) and show that not all of them are trace polynomials, if $n\ge3$

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A Note On The $\Mathcal{A}$-Generators Of The Polynomial Algebra Of Six Variables And Applications, Tin Nguyen Khac Jan 2022

A Note On The $\Mathcal{A}$-Generators Of The Polynomial Algebra Of Six Variables And Applications, Tin Nguyen Khac

Turkish Journal of Mathematics

Let $ \mathcal P_{n}:=H^{*}((\mathbb{R}P^{\infty})^{n}) \cong \mathbb Z_2[x_{1},x_{2},\ldots,x_{n}]$ be the polynomial algebra of $n$ generators $x_1, x_2, \ldots, x_n$ with the degree of each $x_i$ being 1. We investigate the Peterson hit problem for the polynomial algebra $ \mathcal P_{n},$ regarded as a module over the mod-$2$ Steenrod algebra, $ \mathcal{A}.$ For $n>4,$ this problem remains unsolvable, even with the aid of computers in the case of $n=5.$ In this article, we study the hit problem for the case $n=6$ in degree $d_s=6(2^s -1)+3.2^s,$ with $s$ an arbitrary nonnegative integer. By considering $ \mathbb Z_2$ as a trivial $ \mathcal …

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Nilpotent Varieties And Metabelian Varieties, Angela Valenti, Sergey Mishchenko Jan 2022

Nilpotent Varieties And Metabelian Varieties, Angela Valenti, Sergey Mishchenko

Turkish Journal of Mathematics

We deal with varieties of nonassociative algebras having polynomial growth of codimensions. We describe some results obtained in recent years in the class of left nilpotent algebras of index two. Recently the authors established a correspondence between the growth rates for left nilpotent algebras of index two and the growth rates for commutative or anticommutative metabelian algebras that allows to transfer the results concerning varieties of left nilpotent algebras of index two to varieties of commutative or anticommutative metabelian algebras.

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On $S$-Comultiplication Modules, Eda Yildiz, Ünsal Teki̇r, Suat Koç Jan 2022

On $S$-Comultiplication Modules, Eda Yildiz, Ünsal Teki̇r, Suat Koç

Turkish Journal of Mathematics

Let $R\ $be a commutative ring with $1\neq0$ and $M$ be an $R$-module. Suppose that $S\subseteq R\ $is a multiplicatively closed set of $R.\ $Recently Sevim et al. in \cite{SenArTeKo} introduced the notion of an $S$-prime submodule which is a generalization of a prime submodule and used them to characterize certain classes of rings/modules such as prime submodules, simple modules, torsion free modules,\ $S$-Noetherian modules and etc. Afterwards, in \cite{AnArTeKo}, Anderson et al. defined the concepts of $S$-multiplication modules and $S$-cyclic modules which are $S$-versions of multiplication and cyclic modules and extended many results on multiplication and cyclic modules to …

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Analyzing Bifurcation, Stability, And Chaos Control For A Discrete-Time Prey-Predator Model With Allee Effect, Fi̇gen Kangalgi̇l, Ni̇lüfer Topsakal, Ni̇hal Öztürk Jan 2022

Analyzing Bifurcation, Stability, And Chaos Control For A Discrete-Time Prey-Predator Model With Allee Effect, Fi̇gen Kangalgi̇l, Ni̇lüfer Topsakal, Ni̇hal Öztürk

Turkish Journal of Mathematics

In this paper, the qualitative behavior of a discrete-time prey-predator model with Allee effect in prey population is discussed. Firstly, the existence of the fixed points and their topological classification are analyzed algebraically. Then, the conditions of existence for both period-doubling and Neimark--Sacker bifurcations arising from coexistence fixed point with the help of the center manifold theorem and bifurcation theory are investigated. OGY feedback control method is implemented to control chaos in the proposed model due to the emergence of bifurcations. Finally, numerical simulations are performed to support the theoretical findings.

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Introducing Selective D-Separability In Bitopological Spaces, Selma Özçağ Jan 2022

Introducing Selective D-Separability In Bitopological Spaces, Selma Özçağ

Turkish Journal of Mathematics

We introduce $\sf D$-separability and its game-theoretic version, $\sf D^+$-separability in bitopological spaces, and investigate their relationships with $d$-separability and a weaker form of $\sf H$-separability which will be called ${\sf DH}$-separability. Further we give the connection of these notions with the selective versions of separability-types properties under the bitopological context. We also obtain some results about the $d$-separability properties of bitopological spaces which are slightly different from those one expects for the classical case

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A Multidimensional Diffusion Coefficient Determination Problem For The Time-Fractional Equation, Durdimurod Durdiev, Askar Rahmonov Jan 2022

A Multidimensional Diffusion Coefficient Determination Problem For The Time-Fractional Equation, Durdimurod Durdiev, Askar Rahmonov

Turkish Journal of Mathematics

In this paper, we consider a multidimensional inverse problem for a fractional diffusion equation. The inverse problem is reduced to the equivalent integral equation. For solving this equation the Schauder principle is applied. The local existence and uniqueness results are obtained.

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Semisymmetric Hypersurfaces In Complex Hyperbolic Two-Plane Grassmannians, Doo Hyun Hwang, Changhwa Woo Jan 2022

Semisymmetric Hypersurfaces In Complex Hyperbolic Two-Plane Grassmannians, Doo Hyun Hwang, Changhwa Woo

Turkish Journal of Mathematics

In this paper, we introduce new notions of symmetric operators such as semisymmetric shape operator and structure Jacobi operator in complex hyperbolic two-plane Grassmannians. Next we prove that there does not exist a Hopf real hypersurface in complex hyperbolic two-plane Grassmannians $S U_{2, m} / S\left(U_{2} \cdot U_{m}\right)$ with such notions.

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Universality Of An Absolutely Convergent Dirichlet Series With Modified Shifts, Antanas Laurincikas, Renata Macaitiene, Darius Siauciunas Jan 2022

Universality Of An Absolutely Convergent Dirichlet Series With Modified Shifts, Antanas Laurincikas, Renata Macaitiene, Darius Siauciunas

Turkish Journal of Mathematics

In the paper, a theorem on approximation of a wide class of analytic functions by generalized shifts $\zeta_{u_T}(s+i\varphi(\tau))$ of an absolutely convergent Dirichlet series $\zeta_{u_T}(s)$ which in the mean is close to the Riemann zeta-function is obtained. Here $\varphi(\tau)$ is a monotonically increasing differentiable function having a monotonic continuous derivative such that $\varphi(2\tau)\max\limits_{\tau\leqslant t\leqslant 2\tau} \frac{1}{\varphi'(t)} \ll \tau$ as $\tau\to\infty$, and $u_T\to\infty$ and $u_T\ll T^2$ as $T\to\infty$.

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On A Certain Type Of Warped-Twisted Product Submanifolds, Si̇bel Gerdan Aydin, Hakan Mete Taştan Jan 2022

On A Certain Type Of Warped-Twisted Product Submanifolds, Si̇bel Gerdan Aydin, Hakan Mete Taştan

Turkish Journal of Mathematics

We introduce a certain type of warped-twisted product submanifolds which is called warped-twisted product hemislant submanifolds of the form $_{f_2}M^{\bot}\times_{f_1}M^{\theta}$ with warping function $f_2$ on $M^\theta$ and twisting function $f_1$, where $M^\bot$ is a totally real and $M^\theta$ is a slant submanifold of a globally conformal Kaehler manifold. We prove that a warped-twisted product hemislant submanifold of a globally conformal Kaehler manifold is a locally doubly warped product. Then we establish a general inequality for doubly warped product mixed geodesic hemislant submanifolds and get some results for such submanifolds by using the equality sign of the general inequality.

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Dissipative Mechanism And Global Attractor For Modified Swift-Hohenberg Equation In $R^{N}$, Radoslaw Czaja, Maria Kania Jan 2022

Dissipative Mechanism And Global Attractor For Modified Swift-Hohenberg Equation In $R^{N}$, Radoslaw Czaja, Maria Kania

Turkish Journal of Mathematics

A Cauchy problem for a modification of the Swift-Hohenberg equation in $R^{N}$ with a mildly integrable potential is considered. Applying the dissipative mechanism of fourth order parabolic equations in unbounded domains, it is shown that the equation generates a semigroup of global solutions possessing a global attractor in the scale of Bessel potential spaces and in $H^2(R^{N})$ in particular.

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A Note On The Transfinite Diameter Of Bernstein Sets, Özcan Yazici Jan 2022

A Note On The Transfinite Diameter Of Bernstein Sets, Özcan Yazici

Turkish Journal of Mathematics

A compact set $K\subset \mathbb C^n$ is called Bernstein set if, for some constant $M>0$, the following inequality $$ D^{\alpha}P _K\leq M^{ \alpha }(\deg P)^{ \alpha } P _K $$ is satisfied for every multiindex $\alpha\in \mathbb N^n$ and for every polynomial $P$. We provide here a lower bound for the transfinite diameter of Bernstein sets by using generalized extremal Leja points.

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On The Convergence And Stability Analysis Of Finite-Difference Methods For The Fractional Newell-Whitehead-Segel Equations, İnci̇ Çi̇li̇ngi̇r Süngü, Emre Aydin Jan 2022

On The Convergence And Stability Analysis Of Finite-Difference Methods For The Fractional Newell-Whitehead-Segel Equations, İnci̇ Çi̇li̇ngi̇r Süngü, Emre Aydin

Turkish Journal of Mathematics

In this study, standard and non-standard finite-difference methods are proposed for numerical solutions of the time-spatial fractional generalized Newell-Whitehead-Segel equations describing the dynamical behavior near the bifurcation point of the Rayleigh-Benard convection of binary fluid mixtures. The numerical solutions have been found for high values of $p$ which shows the degree of nonlinear terms in the equations. The stability and convergence conditions of the obtained difference schemes are determined for each value of $p$. Errors of methods for various values of $p$ are given in tables. The compatibility of exact solutions and numerical solutions and the effectiveness of the methods …

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On The Bmo Spaces Associated With The Laplace-Bessel Differential Operator, Si̇nem Sezer, Si̇mten Bayrakçi, Güldane Yildiz, Recep Kahraman Jan 2022

On The Bmo Spaces Associated With The Laplace-Bessel Differential Operator, Si̇nem Sezer, Si̇mten Bayrakçi, Güldane Yildiz, Recep Kahraman

Turkish Journal of Mathematics

In this paper, the characteristic properties of the space of functions of bounded mean oscillation called the $B$-$BMO$ associated with the Laplace-Bessel differential operator are obtained. The John-Nirenberg type inequality on the $B$-$BMO$ space and a relation between the $B$-Poisson integral and the $B$-$BMO$ functions are proved.

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Nonunique Best Proximity Point Results With An Application To Nonlinear Fractional Differential Equations, Mustafa Aslantaş Jan 2022

Nonunique Best Proximity Point Results With An Application To Nonlinear Fractional Differential Equations, Mustafa Aslantaş

Turkish Journal of Mathematics

In this paper, we point out an error in proving famous Achari type nonunique fixed point results. Also, we prove some best proximity point results in $b$ -metric spaces by introducing new concepts. Hence, we develop some results existing in the literature. Finally, we give a result for the existence of the solution of nonlinear fractional differential equations.

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Existence And Uniqueness Of Mild Solutions For Mixed Caputo And Riemann-Liouville Semilinear Fractional Integrodifferential Equations With Nonlocal Conditions, Ashraf H. A. Radwan Jan 2022

Existence And Uniqueness Of Mild Solutions For Mixed Caputo And Riemann-Liouville Semilinear Fractional Integrodifferential Equations With Nonlocal Conditions, Ashraf H. A. Radwan

Turkish Journal of Mathematics

The purpose of this paper is to investigate the existence and uniqueness of the mild solution to a class of semilinear fractional integrodifferential equations with state-dependent nonlocal fractional conditions. Our problem includes both Caputo and Riemann-Liouville fractional derivatives. Continuous dependence of solutions on initial conditions and $\epsilon$-approximate mild solutions of the considered problem will be discussed.

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Classical Solutions For 1-Dimensional And 2-Dimensional Boussinesq Equations, Svetlin Georgiev, Aissa Boukarou, Khaled Zennir Jan 2022

Classical Solutions For 1-Dimensional And 2-Dimensional Boussinesq Equations, Svetlin Georgiev, Aissa Boukarou, Khaled Zennir

Turkish Journal of Mathematics

In this article we investigate the IVPs for 1-dimensional and 2-dimensional Boussinesq equations. A new topological approach is applied to prove the existence of at least one classical solution and at least two nonnegative classical solutions for the considered IVPs. The arguments are based upon recent theoretical results.

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New Form Of Laguerre Fractional Differential Equation And Applications, Zahra Kavooci, Kazem Ghanbari, Hanif Mirzaei Jan 2022

New Form Of Laguerre Fractional Differential Equation And Applications, Zahra Kavooci, Kazem Ghanbari, Hanif Mirzaei

Turkish Journal of Mathematics

Laguerre differential equation is a well known equation that appears in the quantum mechanical description of the hydrogen atom. In this paper, we aim to develop a new form of Laguerre Fractional Differential Equation (LFDE) of order $2\alpha$ and we investigate the solutions and their properties. For a positive real number $\alpha$, we prove that the equation has solutions of the form $L_{n,\alpha}(x)=\sum_{k=0}^na_kx^k$, where the coefficients of the polynomials are computed explicitly. For integer case $\alpha=1$ we show that these polynomials are identical to classical Laguerre polynomials. Finally, we solve some fractional differential equations by defining a suitable integral transform.

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On A Subclass Of The Analytic And Bi-Univalent Functions Satisfying Subordinate Condition Defined By $Q$-Derivativ, Ni̇zami̇ Mustafa, Semra Korkmaz Jan 2022

On A Subclass Of The Analytic And Bi-Univalent Functions Satisfying Subordinate Condition Defined By $Q$-Derivativ, Ni̇zami̇ Mustafa, Semra Korkmaz

Turkish Journal of Mathematics

In this paper, we introduce and examine certain subclass $\ M_{q,\Sigma }\left( \varphi ,\beta \right) $ of analytic and bi-univalent functions on the open unit disk in the complex plane. Here, we give coefficient bound estimates, upper bound estimate for the second Hankel determinant and Fekete-Szegö inequality for the function belonging to this class. Some interesting special cases of the results obtained here are also discussed.

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A Galerkin-Type Approach To Solve Systems Of Linear Volterra-Fredholm Integro-Differential Equations, Murat Karaçayir, Şuayi̇p Yüzbaşi Jan 2022

A Galerkin-Type Approach To Solve Systems Of Linear Volterra-Fredholm Integro-Differential Equations, Murat Karaçayir, Şuayi̇p Yüzbaşi

Turkish Journal of Mathematics

The main interest of this paper is to propose a numerical scheme in order to solve linear systems of Volterra-Fredholm integro-differential equations given with mixed conditions. The proposed method is a weighted residual scheme which uses monomials up to a prescribed degree $N$ as the basis functions. By taking inner product of the equation system with the elements of this basis set in a Galerkin-like fashion, the original problem is transformed into a linear algebraic equation system. After a suitable incorporation of the mixed conditions, a final algebraic system is obtained, from which the approximate solutions of the problem are …

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Maximising The Number Of Connected Induced Subgraphs Of Unicyclic Graphs, Audace A V Dossou Olory Jan 2022

Maximising The Number Of Connected Induced Subgraphs Of Unicyclic Graphs, Audace A V Dossou Olory

Turkish Journal of Mathematics

Denote by $\mathcal{G}(n,c,g,k)$ the set of all connected graphs of order $n$, having $c$ cycles, girth $g$, and $k$ pendant vertices. In this paper, we give a partial characterisation of the structure of those graphs in $\mathcal{G}(n,c,g,k)$ maximising the number of connected induced subgraphs. For the special case where $c=1$, we find a complete characterisation of all maximal unicyclic graphs. We also derive a precise formula for the corresponding maximum number given the following parameters: (1) order, girth, and number of pendant vertices; (2) order and girth; (3) order.

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On Unbounded Order Continuous Operators, Bahri̇ Turan, Bi̇rol Altin, Hüma Gürkök Jan 2022

On Unbounded Order Continuous Operators, Bahri̇ Turan, Bi̇rol Altin, Hüma Gürkök

Turkish Journal of Mathematics

Let $U$ and $V$ be two Archimedean Riesz spaces. An operator $S:U\rightarrow V$ is said to be unbounded order continuous ($uo$-continuous), if $r_{\alpha }\overset{uo}{\rightarrow }0$ in $U$ implies $Sr_{\alpha }\overset{uo}{% \rightarrow }0$ in $V$. In this paper, we give some properties of the $uo$% -continuous dual $U_{uo}^{\sim }$ of $U$. We show that a nonzero linear functional $f$ on $U$ is $uo$-continuous if and only if $f$ is a linear combination of finitely many order continuous lattice homomorphisms. The result allows us to characterize the $uo$-continuous dual $U_{uo}^{\sim }.$ In general, by giving an example that the $uo$-continuous dual $U_{uo}^{\sim …

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