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Articles 1111 - 1140 of 10317
Full-Text Articles in Physical Sciences and Mathematics
Quasilinear Systems With Unpredictable Relay Perturbations, Mehmet Onur Fen, Fatma Fen
Quasilinear Systems With Unpredictable Relay Perturbations, Mehmet Onur Fen, Fatma Fen
Turkish Journal of Mathematics
It is rigorously proven under certain assumptions that a quasilinear system with discontinuous right-hand side possesses a unique unpredictable solution. The discontinuous perturbation function on the right-hand side is defined by means of an unpredictable sequence. A Gronwall-Coppel type inequality is utilized to achieve the main result, and the stability of the unpredictable solution is discussed. Examples with exponentially asymptotically stable and unstable unpredictable solutions are provided.
Representation Variety Of Free Or Surface Groups And Reidemeister Torsion, Fati̇h Hezenci̇, Yaşar Sözen
Representation Variety Of Free Or Surface Groups And Reidemeister Torsion, Fati̇h Hezenci̇, Yaşar Sözen
Turkish Journal of Mathematics
For $G \in \left\{ \mathrm{GL}(n,\mathbb{C}) , \mathrm{SL}(n,\mathbb{C})\right\} ,$ we consider $G-$valued representations of free or surface group with genus $ >1.$ We establish a formula for computing Reidemeister torsion of such representations in terms of Atiyah-Bott-Goldman symplectic form for $G.$ Furthermore, we apply the obtained results to hyperbolic 3-manifolds.
On Sharpening And Generalization Of Rivlin's Inequality, Prasanna Kumar, Gradimir Milovanovic
On Sharpening And Generalization Of Rivlin's Inequality, Prasanna Kumar, Gradimir Milovanovic
Turkish Journal of Mathematics
n inequality due to T. J. Rivlin from 1960 states that if $P(z)$ is a polynomial of degree $n$ having no zeros in $ z
Arf Numerical Semigroups With Multiplicity $11$ And $13$, Hali̇l İbrahi̇m Karakaş, Sedat İlhan, Meral Süer
Arf Numerical Semigroups With Multiplicity $11$ And $13$, Hali̇l İbrahi̇m Karakaş, Sedat İlhan, Meral Süer
Turkish Journal of Mathematics
Parametrizations are given for Arf numerical semigroups with multiplicity up to 10. In this work, we give parametrizations of Arf numerical semigroups with multiplicity $11$ and $13$, and combining these results with previous results about the number of Arf numerical semigroups with multiplicity $2, 3, 5, 7$, we share some observations about the set of Arf numerical semigroups with prime multiplicity.
On Slack $2$-Geodesic Convex Set And Geodesic $E$-Pseudoconvex Function With Application, Akhlad Iqbal, Praveen Kumar, Izhar Ahmad
On Slack $2$-Geodesic Convex Set And Geodesic $E$-Pseudoconvex Function With Application, Akhlad Iqbal, Praveen Kumar, Izhar Ahmad
Turkish Journal of Mathematics
We introduce a new class of sets named, slack $2$-geodesic convex set on Riemannian manifolds and verify by a nontrivial example. We define a geodesic $E$-pseudoconvex function with a suitable example. Some properties of geodesic $E$-quasiconvex function are discussed. We establish some relationships between slack $2$-geodesic convex set, geodesic $E$-pseudoconvex function and geodesic $E$-quasiconvex function. Moreover, an application of geodesic $E$-quasiconvex function to a nonlinear programming problem is also presented.
Tensor Products Of Graded-Simple $\Mathfrak{Sl}_2(\Mathbb{C})$-Modules, Yuri Bahturin, Abdallah Shihadeh
Tensor Products Of Graded-Simple $\Mathfrak{Sl}_2(\Mathbb{C})$-Modules, Yuri Bahturin, Abdallah Shihadeh
Turkish Journal of Mathematics
In our paper [3] we have constructed the first example of simple graded torsion-free $\mathfrak{sl}_2(\mathbb{C})$-module denoted by $ M^{C}_{λ}$. Here we examine tensor product of $ M^{C}_{λ}$ with finite dimensional simple $\mathfrak{sl}_2(\mathbb{C})$-modules.
Jordan Maps And Zero Lie Product Determined Algebras, Matej Bresar
Jordan Maps And Zero Lie Product Determined Algebras, Matej Bresar
Turkish Journal of Mathematics
Let $A$ be an algebra over a field $F$ with $(F)\ne 2$. If $A$ is generated as an algebra by $[[A,A],[A,A]]$, then for every skew-symmetric bilinear map $\Phi:A\times A\to X$, where $X$ is an arbitrary vector space over $F$, the condition that $\Phi(x^2,x)=0 $ for all $x\in A$ implies that $\Phi(xy,z) +\Phi(zx,y) + \Phi(yz,x)=0$ for all $x,y,z\in A$. This is applicable to the question of whether $A$ is zero Lie product determined and is also used in proving that a Jordan homomorphism from $A$ onto a semiprime algebra $B$ is the sum of a homomorphism and an antihomomorphism.
Invariants Of Symplectic And Orthogonal Groups Acting On $Gl(N,Cc)$-Modules, Vesselin Drensky, Elitza Hristova
Invariants Of Symplectic And Orthogonal Groups Acting On $Gl(N,Cc)$-Modules, Vesselin Drensky, Elitza Hristova
Turkish Journal of Mathematics
Let $GL(n) = GL(n, CC)$ denote the complex general linear group and let $G \subset GL(n)$ be one of the classical complex subgroups $OO(n)$, $SO(n)$, and $Sp(2k)$ (in the case $n = 2k$). We take a finite dimensional polynomial $GL(n)$-module $W$ and consider the symmetric algebra $S(W)$. Extending previous results for $G=SL(n)$, we develop a method for determining the Hilbert series $H(S(W)^G, t)$ of the algebra of invariants $S(W)^G$. Our method is based on simple algebraic computations and can be easily realized using popular software packages. Then we give many explicit examples for computing $H(S(W)^G, t)$. As an application, we …
Symmetric Polynomials In The Free Metabelian Associative Algebra Of Rank 2, Şehmus Findik
Symmetric Polynomials In The Free Metabelian Associative Algebra Of Rank 2, Şehmus Findik
Turkish Journal of Mathematics
Let $F$ be the free metabelian associative algebra generated by $x$ and $y$ over a field of characteristic zero. We call a polynomial $f\in F$ symmetric, if $f(x,y)=f(y,x)$. The set of all symmetric polynomials coincides with the algebra $F^{S_2}$ of invariants of the symmetric group $S_2$. In this paper, we give the full description of the algebra $F^{S_2}$.
Nonlinear Evolution Equations Related To Kac-Moody Algebras $A_R^{(1)}$: Spectral Aspects, Vladimir S. Gerdjikov
Nonlinear Evolution Equations Related To Kac-Moody Algebras $A_R^{(1)}$: Spectral Aspects, Vladimir S. Gerdjikov
Turkish Journal of Mathematics
We analyze three types of integrable nonlinear evolution equations (NLEE) related to the Kac-Moody algebras $A_r^{(1)}$. These are $\mathbb{Z}_h$-reduced derivative NLS equations (DNLS), multicomponent mKdV equations and 2-dimensional Toda field theories (2dTFT). We outline the basic tools of this analysis: i) the gradings of the simple Lie algebras using their Coxeter automorphisms; ii) the construction of the relevant Lax representations; and iii) the spectral properties of the Lax operators and their reduction to Riemann-Hilbert problems. We also formulate the minimal set of scattering data which allow one to recover the asymptotics of the fundamental analytic solutions to $L$ and its …
Polynomial Identities In Matrix Algebras With Pseudoinvolution, Antonio Ioppolo
Polynomial Identities In Matrix Algebras With Pseudoinvolution, Antonio Ioppolo
Turkish Journal of Mathematics
Let $F$ be an algebraically closed field of characteristic zero. In this paper we deal with matrix superalgebras (i.e. algebras graded by $\mathbb{Z}_2$, the cyclic group of order $2$) endowed with a pseudoinvolution. The first goal is to present the classification of the pseudoinvolutions that it is possible to define, up to equivalence, in the full matrix algebra $M_n(F)$ of $n \times n$ matrices and on its subalgebra $UT_n(F)$ of upper-triangular matrices. Along the way we shall give the generators of the $T$-ideal of identities for the algebras $M_2(F)$, $UT_2(F)$ and $UT_3(F)$, endowed with all possible inequivalent pseudoinvolutions.
On The Restricted Graded Jacobson Radical Of Rings Of Morita Context, Puguh Wahyu Prasetyo, Hidetoshi Marubayashi, Indah Emilia Wijayanti
On The Restricted Graded Jacobson Radical Of Rings Of Morita Context, Puguh Wahyu Prasetyo, Hidetoshi Marubayashi, Indah Emilia Wijayanti
Turkish Journal of Mathematics
The class of rings $\mathcal{J}=\{A (A,\circ)$ forms a group$\}$ forms a radical class and it is called the Jacobson radical class. For any ring $A$, the Jacobson radical $\mathcal{J}(A)$ of $A$ is defined as the largest ideal of $A$ which belongs to $\mathcal{J}$. In fact, the Jacobson radical is one of the most important radical classes since it is used widely in another branch of abstract algebra, for example, to construct a two-sided brace. On the other hand, for every ring of Morita context $T=\begin{pmatrix} R & V \\ W & S \end{pmatrix}$, we will show directly by the structure …
On Generalized Fibonacci And Lucas Hybrid Polynomials, N. Rosa Ait-Amrane, Hacene Belbachir, Eli̇f Tan
On Generalized Fibonacci And Lucas Hybrid Polynomials, N. Rosa Ait-Amrane, Hacene Belbachir, Eli̇f Tan
Turkish Journal of Mathematics
In this paper, we introduce a new generalization of Fibonacci and Lucas hybrid polynomials. We investigate some basic properties of these polynomials such as recurrence relations, the generating functions, the Binet formulas, summation formulas, and a matrix representation. We derive generalized Cassini's identity and generalized Honsberger formula for generalized Fibonacci hybrid polynomials by using their matrix representation.
Solvability In The Small Of $M$-Th Order Elliptic Equations In Weighted Grand Sobolev Spaces, Bilal Bilalov, Yusuf Zeren, Sabina Sadigova, Şeyma Çeti̇n
Solvability In The Small Of $M$-Th Order Elliptic Equations In Weighted Grand Sobolev Spaces, Bilal Bilalov, Yusuf Zeren, Sabina Sadigova, Şeyma Çeti̇n
Turkish Journal of Mathematics
In this work we consider the Sobolev spaces generated by the norm of the power weighted grand Lebesgue spaces. It is considered $m$-th order elliptic equation with nonsmooth coefficients on bounded domain in $R^{n} $. This space is nonseparable and by using shift operator we define the separable subspace of it, in which infinitely differentiable functions are dense. The investigation needs to establish boundedness property of convolution regarding weighted grand Lebesgue spaces. Then on scheme of nonweighted case we establish solvability (strong sense) in the small of $m$-th order elliptic equations in power weighted grand Sobolev spaces. Note that in …
On The Geometry Of Lift Metrics And Lift Connections On The Tangent Bundle, Esmaeil Peyghan, Davood Seifipour, Adara Blaga
On The Geometry Of Lift Metrics And Lift Connections On The Tangent Bundle, Esmaeil Peyghan, Davood Seifipour, Adara Blaga
Turkish Journal of Mathematics
We study lift metrics and lift connections on the tangent bundle $TM$ of a Riemannian manifold $(M,g)$. We also investigate the statistical and Codazzi couples of $TM$ and their consequences on the geometry of $M$. Finally, we prove a result on $1$-Stein and Osserman structures on $TM$, whenever $TM$ is equipped with the complete lift connection.
Unitary Equivalence To Truncated Hankel Operators, Xi Zhao, Tao Yu
Unitary Equivalence To Truncated Hankel Operators, Xi Zhao, Tao Yu
Turkish Journal of Mathematics
In this paper, we characterize the operators which are unitarily equivalent to truncated Hankel operators. We show that every rank one operator and every $2\times 2$ matrix is unitarily equivalent to a truncated Hankel operator. Furthermore, we get that certain sum of tenser products of truncated Hankel operators is unitarily equivalent to a truncated Hankel operator.
Equicontinuity And Sensitivity On Countable Amenable Semigroup, Nader Asadi Karam, Mohammad Kbari Tootkaboni, Abbas Sahleh
Equicontinuity And Sensitivity On Countable Amenable Semigroup, Nader Asadi Karam, Mohammad Kbari Tootkaboni, Abbas Sahleh
Turkish Journal of Mathematics
In this paper, we obtain the classification of topological dynamical systems with a discrete action. The equicontinuity and sensitivity for amenable discrete countable semigroup action are shown by the left Følner sequence. We consider the notion of uniquely ergodic and mean equicontinuous on amenable discrete countable semigroup action and develop the notion of density with respect to the Følner sequence on equicontinuous and sensitivity.
$(P,Q)$-Chebyshev Polynomials For The Families Of Biunivalent Function Associating A New Integral Operator With $(P,Q)$-Hurwitz Zeta Function, Sarem H. Hadi, Maslina Darus
$(P,Q)$-Chebyshev Polynomials For The Families Of Biunivalent Function Associating A New Integral Operator With $(P,Q)$-Hurwitz Zeta Function, Sarem H. Hadi, Maslina Darus
Turkish Journal of Mathematics
In the present article, making use of the $(p,q)$-Hurwitz zeta function, we provide and investigate a new integral operator. Also, we define two families ${\mathcal{S}\mathcal{M}}_{p,q}\left(\xi ,\zeta,\delta,u,\tau \right)$ and ${\mathcal{S}\mathcal{C}}_{p,q}\left(\lambda, \zeta,\vartheta,u,\tau \right)$ of biunivalent and holomorphic functions in the unit disc connected with $(p,q)$-Chebyshev Polynomials. Then we find coefficient estimates $\left a_2\right $ and $\left a_3\right .$ Finally, we obtain Fekete-Szeg$\ddot{\mathrm{o}}$ inequalities for these families.
Bernstein-Walsh-Type Inequalities For Derivatives Of Algebraic Polynomials On The Regions Of Complex Plane, Naci̇ye Peli̇n Özkartepe, Cevahi̇r Doğanay Gün, Fahreddi̇n Abdullayev
Bernstein-Walsh-Type Inequalities For Derivatives Of Algebraic Polynomials On The Regions Of Complex Plane, Naci̇ye Peli̇n Özkartepe, Cevahi̇r Doğanay Gün, Fahreddi̇n Abdullayev
Turkish Journal of Mathematics
In this paper, we study Bernstein-Walsh-type estimates for the derivatives of an arbitrary algebraic polynomial on some general regions of the complex plane.
Quasi $J$-Submodules, Ece Yetki̇n Çeli̇kel, Hani Khashan
Quasi $J$-Submodules, Ece Yetki̇n Çeli̇kel, Hani Khashan
Turkish Journal of Mathematics
Let $R$ be a commutative ring with identity and $M$ be a unitary $R$-module. The aim of this paper is to extend the notion of quasi $J$-ideals of commutative rings to quasi $J$-submodules of modules. We call a proper submodule $N$ of $M$ a quasi $J$-submodule if whenever $r\in R$ and $m\in M$ such that $rm\in N$ and $r\notin(J(R)M:M)$, then $m\in M$-$rad(N)$. We present various properties and characterizations of this concept (especially in finitely generated faithful multiplication modules). Furthermore, we provide new classes of modules generalizing presimplifiable modules and justify their relation with (quasi) $J$-submodules. Finally, for a submodule $N$ …
Initial Value Problem For Elastic System In Transversely Isotropic Inhomogeneous Media, Meltem Altunkaynak
Initial Value Problem For Elastic System In Transversely Isotropic Inhomogeneous Media, Meltem Altunkaynak
Turkish Journal of Mathematics
In this paper, we consider an initial value problem (IVP) for three dimensional elasticity system in a transversely isotropic inhomogeneous media. We will rewrite the problem in the form of Fourier images by means of Fourier transform method. After some arrangements, the problem is reduced to integral equations in the vector form. Using the properties of the vector integral equation and successive approximations method, an explicit formula for the solution of the IVP in transversely isotropic inhomogeneous media is constructed, and existence and uniqueness of the solution is stated. By a computational example, we illustrate the robustness of the method.
On Finite Nonsolvable Groups Whose Cyclic $P$-Subgroups Of Equal Order Are Conjugate, Robert Van Der Waall, Sezgi̇n Sezer
On Finite Nonsolvable Groups Whose Cyclic $P$-Subgroups Of Equal Order Are Conjugate, Robert Van Der Waall, Sezgi̇n Sezer
Turkish Journal of Mathematics
The structure of the nonsolvable (P)-groups is completely described in this article. By definition, a finite group $G$ is called a (P)-group if any two cyclic $p$-subgroups of the same order are conjugate in $G$, whenever $p$ is a prime number dividing the order of $G$.
Ulam's Type Stability Analysis Of Fractional Difference Equation With Impulse: Gronwall Inequality Approach, Rabia Ilyas, Mujeeb Ur Rehman
Ulam's Type Stability Analysis Of Fractional Difference Equation With Impulse: Gronwall Inequality Approach, Rabia Ilyas, Mujeeb Ur Rehman
Turkish Journal of Mathematics
In this paper, we present a new Gronwall inequality with an impulsive effect. The existence and uniqueness of the solution is investigated through fixed point theorems. Moreover, with the help of newly developed inequality Ulam's type stability criterion is developed for impulsive fractional difference equation. At last, a model is given to help the hypothetical outcome.
$K$-Generalized Pell Numbers Which Are Repdigits In Base $B$, Zafer Şi̇ar, Refi̇k Keski̇n
$K$-Generalized Pell Numbers Which Are Repdigits In Base $B$, Zafer Şi̇ar, Refi̇k Keski̇n
Turkish Journal of Mathematics
Let $k\geq 2$ be an integer and let $(P_{n}^{(k)})_{n\geq 2-k}$ be the $k$ -generalized Pell sequence defined by \begin{equation*} P_{n}^{(k)}=2P_{n-1}^{(k)}+P_{n-2}^{(k)}+...+P_{n-k}^{(k)} \end{equation*} for $n\geq 2$ with initial conditions \begin{equation*} P_{-(k-2)}^{(k)}=P_{-(k-3)}^{(k)}=\cdot \cdot \cdot =P_{-1}^{(k)}=P_{0}^{(k)}=0,P_{1}^{(k)}=1. \end{equation*} In this study, we deal with the Diophantine equation \begin{equation*} P_{n}^{(k)}=d\left( \frac{b^{m}-1}{b-1}\right) \end{equation*} in positive integers $n,m,k,b,d$ such that $m\geq 2,$ $2\leq b\leq 9$ and $ 1\leq d\leq b-1$. We show that the repdigits in the base $b$ in the $k-$ generalized Pell sequence, which have at least two digits, are the numbers \begin{eqnarray*} \ P_{7}^{(4)} &=&228=(444)_{7},\text{ }P_{4}^{(2)}=12=(22)_{5}\text{, }% P_{6}^{(2)}=70=(77)_{9}\text{;} \\ P_{4}^{(k)} &=&13=(111)_{3}\text{ } \end{eqnarray*} for $k\geq …
On The Behaviour Of Solutions To A Kind Of Third Order Nonlinear Neutral Differential Equation With Delay, Adeleke Ademola, Peter Arawomo, Olufemi Adesina, Samuel Okoya
On The Behaviour Of Solutions To A Kind Of Third Order Nonlinear Neutral Differential Equation With Delay, Adeleke Ademola, Peter Arawomo, Olufemi Adesina, Samuel Okoya
Turkish Journal of Mathematics
This paper presents a novel class of third order nonlinear nonautonomous neutral differential equation with delay. The third order neutral differential equation is cut down to a system of first order, a suitable complete Lyapunov-Krasovskii's functional is constructed and used, to obtain standard conditions on the nonlinear functions to ensure stability and uniform asymptotic stability of the trivial solutions, the existence of a unique periodic solution, uniform boundedness and uniform ultimate boundedness of solutions when the forcing term is nonzero. The obtained results are new and include many prominent results on neutral and nonneutral delay differential equations in literature. Finally, …
2-Colored Rogers-Ramanujan Partition Identities, Mohammad Zadehdabbagh
2-Colored Rogers-Ramanujan Partition Identities, Mohammad Zadehdabbagh
Turkish Journal of Mathematics
In this paper, we combined two types of partitions and introduced 2-colored Rogers-Ramanujan partitions. By finding some functional equations and using a constructive method, some identities have been found. Some overpartition identities coincide with our findings. A correspondence between colored partitions and overpartitions is provided.
Stressed Or Just Running? Differentiation Of Mental Stress And Physical Activityby Using Machine Learning, Yekta Sai̇d Can
Stressed Or Just Running? Differentiation Of Mental Stress And Physical Activityby Using Machine Learning, Yekta Sai̇d Can
Turkish Journal of Electrical Engineering and Computer Sciences
Recently, modern people have excessive stress in their daily lives. With the advances in physiological sensors and wearable technology, people?s physiological status can be tracked, and stress levels can be recognized for providing beneficial services. Smartwatches and smartbands constitute the majority of wearable devices. Although they have an excellent potential for physiological stress recognition, some crucial issues need to be addressed, such as the resemblance of physiological reaction to stress and physical activity, artifacts caused by movements and low data quality. This paper focused on examining and differentiating physiological responses to both stressors and physical activity. Physiological data are collected …
Synthesis Of Titanium Dioxide Nanoparticles With Renewable Resources And Their Applications: Review, Umut Şafak Öztürk, Ali̇me Çitak
Synthesis Of Titanium Dioxide Nanoparticles With Renewable Resources And Their Applications: Review, Umut Şafak Öztürk, Ali̇me Çitak
Turkish Journal of Chemistry
Metal-oxide nanoparticles have reached a wide range of applications in the last ten years. Titanium dioxide nanoparticles stand out with their unique crystal structure and near-perfect physical and chemical properties at nanoscales (crystal size between 10-100 nm). It has created many applications with its white pigment, semiconductor state, and effective photocatalytic properties, but the synthesis of these nanoparticles is very damaging to nature. Titanium dioxide nanoparticles, which can be synthesized with toxic solvents or high-energy machines, have started to be synthesized by the green synthesis method, which has been a cheap and easy method in recent years. The application areas …
Photocatalytic Degradation Of Aquatic Organic Pollutants With Zn- And Zr-Based Metalorganic Frameworks: Zif-8 And Uio-66, Fatma Defne Çalik, Bi̇lgesu Erdoğan, Esra Yilmaz, Gi̇zem Saygi, Seher Fehi̇me Çakicioğlu Özkan
Photocatalytic Degradation Of Aquatic Organic Pollutants With Zn- And Zr-Based Metalorganic Frameworks: Zif-8 And Uio-66, Fatma Defne Çalik, Bi̇lgesu Erdoğan, Esra Yilmaz, Gi̇zem Saygi, Seher Fehi̇me Çakicioğlu Özkan
Turkish Journal of Chemistry
Water treatment has been an essential issue with the increasing population over 40 years. Researchers center on the major organic pollutants, such as dyes, pesticides, and pharmaceutical products. Photocatalytic degradation is one of the promising methods for aquatic organic pollutant treatment. Over the years, scientists have been working on developments for photocatalysts to enhance their pollutant degradation performances. From the reviewed studies, it is seen that properties like surface area, chemical, mechanical, and thermal stability, and uniform distribution of active sites are crucial, and an increase in these properties provides better degradation efficiency. In this sense, metal-organic frameworks as photocatalysts …
A Review On The Achievement Of Enzymatic Glycerol Carbonate Production, Selda Aydoğdu, Nurcan Kapucu
A Review On The Achievement Of Enzymatic Glycerol Carbonate Production, Selda Aydoğdu, Nurcan Kapucu
Turkish Journal of Chemistry
High energy demand driven by decreasing fossil fuels, and global warming because of the burning of fossil fuels necessitates the utilization of renewable and clean energy. One of these renewable energy sources is biodiesel. The increasing trend of biodiesel over the last 20 years tends to result in increasing glycerol (Gly), which is produced during the biodiesel production in 10% ratio (w/w) as a by-product. Using Gly as raw material is an alternative way to produce bio-based new products such as glycerol carbonate (GlyC). GlyC is a value-added product of Gly/vegetable oil and this product can be used as a …