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Articles 37801 - 37830 of 302522

Full-Text Articles in Physical Sciences and Mathematics

Continuation Value Computation Using Malliavin Calculus Under General Volatility Stochastic Process For American Option Pricing, Mohamed Kharrat, Fabian Bastin Jan 2022

Continuation Value Computation Using Malliavin Calculus Under General Volatility Stochastic Process For American Option Pricing, Mohamed Kharrat, Fabian Bastin

Turkish Journal of Mathematics

American options represent an important financial instrument but are notoriously difficult to price, especially when the volatility is not constant. We explore the conditions required to apply Malliavin calculus to price American options when the volatility follows a general stochastic differential process, and develop the expressions to compute the continuation value at any time before the expiration date, given the current asset price and volatility. The developed methodology can then be applied to price American options.

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Upper And Lower Bounds Of The $A$-Berezin Number Of Operators, Mualla Bi̇rgül Huban Jan 2022

Upper And Lower Bounds Of The $A$-Berezin Number Of Operators, Mualla Bi̇rgül Huban

Turkish Journal of Mathematics

Let $A$ be a positive bounded linear operator acting on a complex Hilbert space $\mathcal{H}$. Any positive operator $A$ induces a semiinner product on $\mathcal{H}$ defined by $\left\langle x,y\right\rangle _{A}:=\left\langle Ax,y\right\rangle _{\mathcal{H}},$ $\forall x,y\in\mathcal{H}.$ For any $T\in\mathcal{B}\left( \mathcal{H}\left( \Omega\right) \right) $, its $A$-Berezin symbol $\widetilde{T}^{_{A}}$ is defined on $\Omega$ by $\widetilde{T}^{_{A}% }:=\left\langle T\widehat{K}_{\lambda},\widehat{K}_{\lambda}\right\rangle _{A},$ $\lambda\in\Omega,$where $\widehat{K}_{\lambda}$ is the normalized reproducing kernel of $\mathcal{H}$. In this paper, we introduce the notions $\left( A,r\right) $-adjoint of operators and $A$-Berezin number of operators on the reproducing kernel Hilbert space and prove some upper and lower bounds of the $A$-Berezin numbers of operators. In …

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New Extension Of Alexander And Libera Integral Operators, Hatun Özlem Güney, Shigeyoshi Owa Jan 2022

New Extension Of Alexander And Libera Integral Operators, Hatun Özlem Güney, Shigeyoshi Owa

Turkish Journal of Mathematics

Let $T$ be the class of analytic functions in the open unit disc $\mathbb{U}$ with $f(0)=0$ and $f'(0)=1.$ For $f(z)\in T,$ the Alexander integral operator $A_{-1}f(z),$ the Libera integral operator $L_{-1}f(z)$ and the Bernardi integral operator $B_{-1}f(z)$ were considered before. Using $A_{-1}f(z)$ and $L_{-1}f(z),$ a new integral operator $F_{\lambda}f(z)$ is considered. After discuss some properties of dominant for $F_{\lambda}f(z),$ another new integral operator $O_{-1}f(z)$ of $f(z)\in T$ is discussed. The object of the present paper is to discuss the dominant of new integral operators $F_{\lambda}f(z)$ and $O_{-1}f(z)$ concerning with some starlike functions and convex functions in $\mathbb{U}.$

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Multivariate Approximation In $\Varphi$-Variation For Nonlinear Integral Operators Via Summability Methods, İsmai̇l Aslan Jan 2022

Multivariate Approximation In $\Varphi$-Variation For Nonlinear Integral Operators Via Summability Methods, İsmai̇l Aslan

Turkish Journal of Mathematics

We consider convolution-type nonlinear integral operators endowed with Musielak-Orlicz $\varphi$-variation. Our aim is to get more powerful approximation results with the help of summability methods. In this study, we use $\varphi$-absolutely continuous functions for our convergence results. Moreover, we study the order of approximation using suitable Lipschitz class of continuous functions. A general characterization theorem for $\varphi $-absolutely continuous functions is also obtained. We also give some examples of kernels in order to verify our approximations. At the end, we indicate our approximations in figures together with some numerical computations.

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Commutativity Degree Of Crossed Modules, Zekeri̇ya Arvasi̇, Eli̇f Ilgaz Çağlayan, Alper Odabaş Jan 2022

Commutativity Degree Of Crossed Modules, Zekeri̇ya Arvasi̇, Eli̇f Ilgaz Çağlayan, Alper Odabaş

Turkish Journal of Mathematics

In this work, we define the notion of commutativity degree of crossed modules and find some bounds on commutativity degree for special types of crossed modules. Also, we give a function for finding commutativity degree of crossed modules in GAP and classify crossed modules by using this function.

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Infinitely Many Positive Solutions For An Iterative System Of Conformable Fractional Order Dynamic Boundary Value Problems On Time Scales, Mahammad Khuddush, Kapula Rajendra Prasad Jan 2022

Infinitely Many Positive Solutions For An Iterative System Of Conformable Fractional Order Dynamic Boundary Value Problems On Time Scales, Mahammad Khuddush, Kapula Rajendra Prasad

Turkish Journal of Mathematics

In this paper, we establish infinitely many positive solutions for the iterative system of conformable fractional order dynamic equations on time scales $$ \begin{aligned} &\mathcal{T}_α^{\Delta}\big[\mathcal{T}_β^{\Delta}\big(\vartheta_\mathtt{n}(t)\big)\big]=\varphi(t)\mathtt{f}_\mathtt{n}\left(\vartheta_{\mathtt{n}+1}(t)\right),~t\in(0,1)_\mathbb{T},~1

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Limited Frequency Band Diffusive Representation For Nabla Fractional Order Transfer Functions, Yiheng Wei, Yingdong Wei, Yuqing Hou, Xuan Zhao Jan 2022

Limited Frequency Band Diffusive Representation For Nabla Fractional Order Transfer Functions, Yiheng Wei, Yingdong Wei, Yuqing Hou, Xuan Zhao

Turkish Journal of Mathematics

Though infinite-dimensional characteristic is the natural property of nabla fractional order systems and it is the foundation of stability analysis, controller synthesis and numerical realization, there are few research focusing on this topic. Under this background, this paper concerns the diffusive representation of nabla fractional order systems. Firstly, several variants are developed for the elementary equality in frequency domain, i.e. $\frac{1}{s^\alpha} = \int_0^{ + \infty } {\frac{{{\mu _\alpha }( \omega )}}{{s + \omega }}{\rm{d}}\omega }$. Afterwards, the limited frequency band diffusive representation and the unit impulse response are derived for a series of nabla fractional order transfer functions. Finally, an …

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Mathematical Analysis Of Local And Global Dynamics Of A New Epidemic Model, Sümeyye Çakan Jan 2022

Mathematical Analysis Of Local And Global Dynamics Of A New Epidemic Model, Sümeyye Çakan

Turkish Journal of Mathematics

In this paper, we construct a new $SEIR$ epidemic model reflecting the spread of infectious diseases. After calculating basic reproduction number $% \mathcal{R}_{0}$ by the next generation matrix method, we examine the stability of the model. The model exhibits threshold behavior according to whether the basic reproduction number $\mathcal{R}_{0}$ is greater than unity or not. By using well-known Routh-Hurwitz criteria, we deal with local asymptotic stability of equilibrium points of the model according to $% \mathcal{R}_{0}.$ Also, we present a mathematical analysis for the global dynamics in the equilibrium points of this model using LaSalle's Invariance Principle associated with Lyapunov …

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A Sequential Fractional Differential Problem Of Pantograph Type:Existence Uniqueness And Illustrations, Soumia Belarbi, Zoubir Dahmani, Mehmet Zeki̇ Sarikaya Jan 2022

A Sequential Fractional Differential Problem Of Pantograph Type:Existence Uniqueness And Illustrations, Soumia Belarbi, Zoubir Dahmani, Mehmet Zeki̇ Sarikaya

Turkish Journal of Mathematics

In this study, a new class of sequential fractional differential problems of pantograph type is introduced. New existence and uniqueness criteria for the existence and uniqueness of solutions are discussed. Some existence results using Darbo's fixed point and measure of noncompactness are also studied. At the end, two illustrative examples are discussed.

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On Stability And Oscillation Of Fractional Differential Equations With A Distributed Delay, Limei Feng, Shurong Sun Jan 2022

On Stability And Oscillation Of Fractional Differential Equations With A Distributed Delay, Limei Feng, Shurong Sun

Turkish Journal of Mathematics

In this paper, we study the stability and oscillation of fractional differential equations \begin{equation*} ^cD^\alpha x(t)+ax(t)+\int_0^1x(s+[t-1])dR(s)=0. \end{equation*} We discretize the fractional differential equation by variation of constant formula and semigroup property of Mittag-Leffler function, and get the difference equation corresponding to the integer points. From the equivalence analogy of qualitative properties between the difference equations and the original fractional differential equations, the necessary and sufficient conditions of oscillation, stability and exponential stability of the equations are obtained.

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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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