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Articles 511 - 540 of 2595
Full-Text Articles in Mathematics
Formulas For Special Numbers And Polynomials Derived From Functional Equations Of Their Generating Functions, Nesli̇han Kilar
Formulas For Special Numbers And Polynomials Derived From Functional Equations Of Their Generating Functions, Nesli̇han Kilar
Turkish Journal of Mathematics
The main purpose of this paper is to investigate various formulas, identities and relations involving Apostol type numbers and parametric type polynomials. By using generating functions and their functional equations, we give many relations among the certain family of combinatorial numbers, the Vieta polynomials, the two-parametric types of the Apostol-Euler polynomials, the Apostol-Bernoulli polynomials, the Apostol-Genocchi polynomials, the Fibonacci and Lucas numbers, the Chebyshev polynomials, and other special numbers and polynomials. Moreover, we give some formulas related to trigonometric functions, special numbers and special polynomials. Finally, some remarks and observations on the results of this paper are given.
Integer-Valued Polynomials Satisfying The Lucas Property, Rattiya Meesa, Vichian Laohakosol, Tuangrat Chaichana
Integer-Valued Polynomials Satisfying The Lucas Property, Rattiya Meesa, Vichian Laohakosol, Tuangrat Chaichana
Turkish Journal of Mathematics
The classical theorem of Lucas states that the binomial polynomials, which form a basis for integer-valued polynomials, satisfy a congruence relation related to their integer parameters. We consider here three problems connected with this result in the setting of discrete valued structures. The first problem asks for the shapes of Lagrange-type interpolation polynomials which constitute a basis for integer-valued polynomials and satisfy the Lucas property; the result so obtained extends a 2001 result of Boulanger and Chabert. For the second problem, we show that the Carlitz polynomials, which form a basis for integer-valued polynomials in a function field, satisfy the …
Liftings And Covering Morphisms Of Crossed Modules In Group-Groupoids, Serap Demi̇r Karakaş, Osman Mucuk
Liftings And Covering Morphisms Of Crossed Modules In Group-Groupoids, Serap Demi̇r Karakaş, Osman Mucuk
Turkish Journal of Mathematics
In this work we introduce lifting and covering of a crossed module in the category of group-groupoids; and then we prove the categorical equivalence of horizontal actions of a double group-groupoid and lifting crossed modules of corresponding crossed module in group-groupoids. These allow us to produce more examples of double group-groupoids.
A Short Note On Generic Initial Ideals, Beki̇r Daniş
A Short Note On Generic Initial Ideals, Beki̇r Daniş
Turkish Journal of Mathematics
The definition of a generic initial ideal includes the assumption $x_1>x_2> \cdots >x_n$. A natural question is how generic initial ideals change when we permute the variables. In the article [1, §2], it is shown that the generic initial ideals are permuted in the same way when the variables in the monomial order are permuted. We give a different proof of this theorem. Along the way, we study the Zariski open sets which play an essential role in the definition of a generic initial ideal and also prove a result on how the Zariski open set changes after a …
On The Analytical Development Of Incomplete Riemann-Liouville Fractional Calculus, Arran Fernandez, Ceren Ustaoğlu, Mehmet Ali̇ Özarslan
On The Analytical Development Of Incomplete Riemann-Liouville Fractional Calculus, Arran Fernandez, Ceren Ustaoğlu, Mehmet Ali̇ Özarslan
Turkish Journal of Mathematics
The theoretical development of fractional calculus includes the formulation of different definitions, the extension of properties from standard calculus, and the application of fractional operators to special functions. In two recent papers, incomplete versions of classical fractional operators were formulated in connection with special functions. Here, we develop the theory of incomplete fractional calculus more deeply, investigating further properties of these operators and answering some fundamental questions about how they work. By considering appropriate function spaces, we discover that incomplete fractional calculus may be used to analyse a wider class of functions than classical fractional calculus can consider. By using …
Certain Subclasses Of Spirallike Univalent Functions Related To Poisson Distribution Series, Lakshminarayanan Vanitha, Chellakutti Ramachandran, Teodor Bulboaca
Certain Subclasses Of Spirallike Univalent Functions Related To Poisson Distribution Series, Lakshminarayanan Vanitha, Chellakutti Ramachandran, Teodor Bulboaca
Turkish Journal of Mathematics
The aim of the present study is to find the essential properties for some subclasses of analytic functions which are related to Poisson distribution that are member of the classes of spiral-like univalent functions. Further, we studied inclusion relations for such subclasses, and also we determined some properties of an integral operator related to Poisson distribution series. Several corollaries and consequences of the main results are also considered.
Extensions Of The Matrix-Valued$\ Q-$Sturm-Liouville Operators, Bi̇lender Paşaoğlu, Hüseyi̇n Tuna
Extensions Of The Matrix-Valued$\ Q-$Sturm-Liouville Operators, Bi̇lender Paşaoğlu, Hüseyi̇n Tuna
Turkish Journal of Mathematics
In this paper, we investigate the matrix-valued$\ q-$Sturm--Liouville problems. We establish an existence and uniqueness result. Later, we introduce the corresponding maximal and minimal operators for this system. Moreover, we give a criterion under which these operators are self-adjoint. Finally, we characterize extensions (maximal dissipative, maximal accumulative, and self-adjoint) of the minimal symmetric operator.
Statistically Multiplicative Convergence On Locally Solid Riesz Algebras, Abdullah Aydin, Mi̇kai̇l Et
Statistically Multiplicative Convergence On Locally Solid Riesz Algebras, Abdullah Aydin, Mi̇kai̇l Et
Turkish Journal of Mathematics
In this paper, we introduce the statistically multiplicative convergent sequences in locally solid Riesz algebras with respect to algebra multiplication and solid topology. We study this concept and the notion of $st_m$-bounded sequences, and also, we prove some relations between this convergence and the other convergences such as the order convergence and the statistical convergence in topological spaces. Also, we give some results related to semiprime $f$-algebras.
Generalized Stevi\'C-Sharma Type Operators From Hardy Spaces Into $N$Th Weighted Type Spaces, Ebrahim Abbasi, Yongmin Liu, Mostafa Hassanlou
Generalized Stevi\'C-Sharma Type Operators From Hardy Spaces Into $N$Th Weighted Type Spaces, Ebrahim Abbasi, Yongmin Liu, Mostafa Hassanlou
Turkish Journal of Mathematics
In this paper, some characterizations for boundedness, essential norm and compactness of generalized Stevic-Sharma type operators from Hardy spaces into $n$th weighted type spaces are given.
On B-Generalized Skew Derivations In Banach Algebras, Abdul Nadim Khan
On B-Generalized Skew Derivations In Banach Algebras, Abdul Nadim Khan
Turkish Journal of Mathematics
} Let $\mathscr{A}$ be a Banach algebra over $\mathbb{R}$ or $\mathbb{C}$. In this paper, we describe the behavior of recently defined $b$-generalized skew derivations which satisfy certain differential identities on some specific subsets of $\mathscr{A}$.
Fundamental Group Of Galois Covers Of Degree 5 Surfaces, Meirav Amram, Cheng Gong, Mina Teicher, Wan-Yuan Xu
Fundamental Group Of Galois Covers Of Degree 5 Surfaces, Meirav Amram, Cheng Gong, Mina Teicher, Wan-Yuan Xu
Turkish Journal of Mathematics
Let $X$ be an algebraic surface of degree $5$, which is considered a branch cover of $\mathbb{CP}^2$ with respect to a generic projection. The surface has a natural Galois cover with Galois group $S_5$. In this paper, we deal with the fundamental groups of Galois covers of degree $5$ surfaces that degenerate to nice plane arrangements; each of them is a union of five planes such that no three planes meet in a line.
Logarithmic Dimension And Bases In Whitney Spaces, Alexander Goncharov, Yasemi̇n Şengül Tezel
Logarithmic Dimension And Bases In Whitney Spaces, Alexander Goncharov, Yasemi̇n Şengül Tezel
Turkish Journal of Mathematics
We give a formula for the logarithmic dimension of the generalized Cantor-type set $K$. In the case when the logarithmic dimension of $K$ is smaller than $1$, we construct a Faber basis in the space of Whitney functions $\mathcal{E}(K)$.
B-Property Of Sublattices In Vector Lattices, Ömer Şafak Alpay, Svetlana Gorokhova
B-Property Of Sublattices In Vector Lattices, Ömer Şafak Alpay, Svetlana Gorokhova
Turkish Journal of Mathematics
We study $b$-property of a sublattice (or an order ideal) $F$ of a vector lattice $E$. In particular, $b$-property of $E$ in $E^\delta$, the Dedekind completion of $E$, $b$-property of $E$ in $E^u$, the universal completion of $E$, and $b$-property of $E$ in $\hat{E}(\hat{\tau})$, the completion of $E$.
On Congruences Related To Trinomial Coefficients And Harmonic Numbers, Neşe Ömür, Si̇bel Koparal, Laid Elkhiri
On Congruences Related To Trinomial Coefficients And Harmonic Numbers, Neşe Ömür, Si̇bel Koparal, Laid Elkhiri
Turkish Journal of Mathematics
In this paper, we establish some congruences involving the trinomial coefficients and harmonic numbers. For example, for any prime $p>3,$ \begin{equation*} \sum\limits_{k=0}^{p-1}\left( -1\right) ^{k}\binom{p-1}{k}_{2}H_{k}\equiv 0 \ \pmod {p}. \end{equation*}
Relative Conics And Their Brianchon Points, Magdalena Lampa-Baczynska, Daniel Wojcik
Relative Conics And Their Brianchon Points, Magdalena Lampa-Baczynska, Daniel Wojcik
Turkish Journal of Mathematics
The purpose of this paper is to study some additional relations between lines and points in the configuration of six lines tangent to the common conic. One of the most famous results concerning with this configuration is Brianchon theorem. It says that three diagonals of a hexagon circumscribing around conic are concurrent. They meet in the so called Brianchon point. In fact, by relabeling the vertices of hexagon, we obtain $60$ distinct Brianchon points. We prove, among others, that, in the set of all intersection points of six tangents to the same conic, there exist exactly $10$ sextuples of points …
Ideal Triangulation And Disc Unfolding Of A Singular Flat Surface, İsmai̇l Sağlam
Ideal Triangulation And Disc Unfolding Of A Singular Flat Surface, İsmai̇l Sağlam
Turkish Journal of Mathematics
An ideal triangulation of a singular flat surface is a geodesic triangulation such that its vertex set is equal to the set of singular points of the surface. Using the fact that each pair of points in a surface has a finite number of geodesics having length $\leq L$ connecting them, where $L$ is any positive number, we prove that each singular flat surface has an ideal triangulation provided that the surface has singular points when it has no boundary components, or each of its boundary components has a singular point. Also, we prove that such a surface contains a …
A Refinement Of The Bergström Inequality, Gülteki̇n Tinaztepe, İlknur Yeşi̇lce, Gabi̇l Adi̇lov
A Refinement Of The Bergström Inequality, Gülteki̇n Tinaztepe, İlknur Yeşi̇lce, Gabi̇l Adi̇lov
Turkish Journal of Mathematics
In this paper, the Bergstrom inequality is studied, and a refinement of this inequality is obtained by performing the optimality conditions based on abstract concavity. Some numerical experiments are given to illustrate the efficacy of the refinement.
On The Spectra Of Generalized Fibonomial And Jacobsthal-Binomial Graphs, Hati̇ce Topcu, Nurten Yücel
On The Spectra Of Generalized Fibonomial And Jacobsthal-Binomial Graphs, Hati̇ce Topcu, Nurten Yücel
Turkish Journal of Mathematics
In this work, we first give a more general form of the binomial, Fibonomial, and balance-binomial graphs that is called generalized Fibonomial graph. We also argue the spectra of generalized Fibonomial graph. Next, we introduce a new type of graph on Jacobsthal numbers that is called Jacobsthal-binomial graph and denoted by $JB_{n}$. We obtain the adjacency, Laplacian and signless Laplacian characteristic polynomials of $JB_{n}$, respectively. We lastly give inequalities for the adjacency, Laplacian and signless Laplacian energies of $JB_{n}$.
Ranks Of Nilpotent Subsemigroups Of Order-Preserving And Decreasing Transformation Semigroups, Emrah Korkmaz, Hayrullah Ayik
Ranks Of Nilpotent Subsemigroups Of Order-Preserving And Decreasing Transformation Semigroups, Emrah Korkmaz, Hayrullah Ayik
Turkish Journal of Mathematics
Let $\mathcal{C}_{n}$ be the semigroup of all order-preserving and decreasing transformations on $X=\{1,\ldots ,n\}$ under its natural order, and let $N(\mathcal{C}_{n})$ be the subsemigroup of all nilpotent elements of $\mathcal{C}_{n}$. For $1\leq r \leq n-1$, let \begin{eqnarray*} N(\mathcal{C}_{n,r})&=&\{ \alpha\in N(\mathcal{C}_{n}) : \lvert im(\alpha)\rvert \leq r\} ,\\ N_{r}(\mathcal{C}_{n})&=&\{\alpha\in N\mathcal({C}_{n}):\alpha\mbox{ is an } m\mbox{-potent for any } 1\leq m\leq r\} . \end{eqnarray*} In this paper we find the cardinality and the rank of the subsemigroup $N(\mathcal{C}_{n,r})$ of $\mathcal{C}_{n}$. Moreover, we show that the set $N_{r}(\mathcal{C}_{n})$ is a subsemigroup of $N(\mathcal{C}_{n})$ and then, we find a lower bound for the rank of $N_{r}(\mathcal{C}_{n})$.
On The Local And Global Stability Of An Sirs Epidemic Model With Logistic Growth And Information Intervention, İrem Çay
Turkish Journal of Mathematics
In this study, we investigate an susceptible-infected-recovered-susceptible (SIRS) epidemic model with logistic growth and information intervention. Firstly, the basic reproduction number $R_0$ is defined and the main results are given in terms of local stability. Then, sufficient conditions for the global stability of endemic equilibrium are obtained. Finally, some numerical simulations are given to validate our theoretical conclusions.
Decompositions Of Complete Symmetric Directed Graphs Into The Oriented Heptagons, Uğur Odabaşi
Decompositions Of Complete Symmetric Directed Graphs Into The Oriented Heptagons, Uğur Odabaşi
Turkish Journal of Mathematics
The complete symmetric directed graph of order $v$, denoted by $K_{v}$, is the directed graph on $v$~vertices that contains both arcs $(x,y)$ and $(y,x)$ for each pair of distinct vertices $x$ and~$y$. For a given directed graph $D$, the set of all $v$ for which $K_{v}$ admits a $D$-decomposition is called the spectrum of~$D$-decomposition. There are 10 nonisomorphic orientations of a $7$-cycle (heptagon). In this paper, we completely settled the spectrum problem for each of the oriented heptagons.
On Hilbert Genus Fields Of Imaginary Cyclic Quartic Fields, Moulay Ahmed Hajjami, Mohamed Mahmoud Chems Eddin
On Hilbert Genus Fields Of Imaginary Cyclic Quartic Fields, Moulay Ahmed Hajjami, Mohamed Mahmoud Chems Eddin
Turkish Journal of Mathematics
Let $p$ be a prime number such that $p=2$ or $p\equiv 1\pmod 4$. Let $\varepsilon_p$ denote the fundamental unit of $\mathbb{Q}(\sqrt{p})$ and let $a$ be a positive square-free integer. The main aim of this paper is to determine explicitly the Hilbert genus field of the imaginary cyclic quartic fields of the form $\mathbb{Q}(\sqrt{-a\varepsilon_p\sqrt{p}})$.
Conformal Bi-Slant Submersions, Sezi̇n Aykurt Sepet
Conformal Bi-Slant Submersions, Sezi̇n Aykurt Sepet
Turkish Journal of Mathematics
In this paper, we study conformal bi-slant submersions from almost Hermitian manifolds onto Riemannian manifolds as a generalized of conformal anti-invariant, conformal semi-invariant, conformal semi-slant, conformal slant, and conformal hemi-slant submersions. We investigate the integrability of distributions and obtain necessary and sufficient conditions for the maps to have totally geodesic fibers. Also, we consider some decomposition theorems for the new submersion and study the total geodesicity of such maps. Finally, we find curvature relations between the base space and the total space.
C_11 Modules Via Left Exact Preradicals, Ramazan Yaşar
C_11 Modules Via Left Exact Preradicals, Ramazan Yaşar
Turkish Journal of Mathematics
In this article, we study modules with the condition that every image of a submodule under a left exact preradical has a complement which is a direct summand. This new class of modules properly contains the class of $C_{11}$-modules (and hence also $CS$-modules). Amongst other structural properties, we deal with direct sums and decompositions with respect to the left exact preradicals of this new class of modules. It is obtained a decomposition such that the image of the module itself is a direct summand for the left exact radical, which enjoys the new condition.
Global Attractivity Of Delay Difference Equations In Banach Spaces Via Fixed-Point Theory, Abdullah Kalkan
Global Attractivity Of Delay Difference Equations In Banach Spaces Via Fixed-Point Theory, Abdullah Kalkan
Turkish Journal of Mathematics
We formulate initial value problems for delay difference equations in Banach spaces as fixed-point problems in sequence spaces. By choosing appropriate sequence spaces various types of attractivity can be described. This allows us to establish global attractivity by means of fixed-point results. Finally, we provide an application to delay integrodifference equations in the space of continuous functions over a compact domain.
A Regularized Trace Formula For "Weighted" Sturm-Liouville Equation With Point Delta-Interaction, Manaf Manafli
A Regularized Trace Formula For "Weighted" Sturm-Liouville Equation With Point Delta-Interaction, Manaf Manafli
Turkish Journal of Mathematics
In this study, we obtain a formula for the regularized trace formula for "weighted" Sturm--Liouville equation with point $\delta $- interaction. At the begining, for the correct determination of solutions of analyzed equation at the point of discontinuty, the matching conditions are required. As a result, an equation is derived for the eigenvalues of the differential operator given in this study.
Some Properties Of The Semigroup $Pg_Y(X)$: Green's Relations, Ideals, Isomorphism Theorems And Ranks, Worachead Sommanee
Some Properties Of The Semigroup $Pg_Y(X)$: Green's Relations, Ideals, Isomorphism Theorems And Ranks, Worachead Sommanee
Turkish Journal of Mathematics
Let $T(X)$ be the full transformation semigroup on the set $X$. For a fixed nonempty subset $Y$ of $X$, let \begin{equation*} PG_Y(X) = \{\alpha\in T(X) : \alpha _Y\in G(Y)\} \end{equation*} where $G(Y)$ is the permutation group on $Y$. It is known that $PG_Y(X)$ is a regular subsemigroup of $T(X)$. In this paper, we give a simpler description of Green's relations and characterize the ideals of $PG_Y(X)$. Moreover, we prove some isomorphism theorems for $PG_Y(X)$. For finite sets, we investigate the cardinalities of $PG_Y(X)$ and of its subsets of idempotents, and we also calculate their ranks.
Domination Parameters On Cayley Digraphs Of Transformation Semigroups With Fixed Sets, Nuttawoot Nupo, Chollawat Pookpienlert
Domination Parameters On Cayley Digraphs Of Transformation Semigroups With Fixed Sets, Nuttawoot Nupo, Chollawat Pookpienlert
Turkish Journal of Mathematics
For a nonempty subset $Y$ of a nonempty set $X$, denote by $Fix(X,Y)$ the semigroup of full transformations on the set $X$ in which all elements in $Y$ are fixed. The Cayley digraph $Cay$ $(Fix(X,Y),A)$ of $Fix(X,Y)$ with respect to a connection set $A\subseteq Fix(X,Y)$ is defined as a digraph whose vertex set is $Fix(X,Y)$ and two vertices $\alpha, \beta$ are adjacent in sense of drawing a directed edge (arc) from $\alpha$ to $\beta$ if there exists $\mu\in A$ such that $\beta = \alpha\mu$. In this paper, we determine domination parameters of $Cay$ $(Fix(X,Y),A)$ where $A$ is a subset of …
General Characteristics Of A Fractal Sturm-Liouville Problem, Fatma Ayça Çeti̇nkaya, Alireza Khalili Golmankaneh
General Characteristics Of A Fractal Sturm-Liouville Problem, Fatma Ayça Çeti̇nkaya, Alireza Khalili Golmankaneh
Turkish Journal of Mathematics
In this paper, we consider a regular fractal Sturm-Liouville boundary value problem. We prove the self-adjointness of the differential operator which is generated by the $F^\alpha$-derivative introduced in [32]. We obtained the $F^\alpha$-analogue of Liouville's theorem, and we show some properties of eigenvalues and eigenfunctions. We present examples to demonstrate the efficiency and applicability of the obtained results. The findings of this paper can be regarded as a contribution to an emerging field.
Half Inverse Problems For The Impulsive Quadratic Pencil With The Discontinouty Coefficient, Rauf Ami̇rov, Sevi̇m Durak
Half Inverse Problems For The Impulsive Quadratic Pencil With The Discontinouty Coefficient, Rauf Ami̇rov, Sevi̇m Durak
Turkish Journal of Mathematics
In this paper, we study the inverse spectral problem for the quadratic differential pencils with discontinuity coefficient on $\left[ 0,\pi\right] $ with separable boundary conditions and the impulsive conditions at the point $x=\dfrac{\pi}{2}$. We prove that two potential functions on the interval $\left[ 0,\pi\right] $, and the parameters in the boundary and impulsive conditions can be determined from a sequence of eigenvalues for two cases: (i) The potentials are given on $\left( 0,\dfrac{\pi}{4}\left( 1+\alpha\right) \right) ,$ (ii) The potentials are given on $\left( \dfrac{\pi}{4}\left( 1+\alpha\right) ,\pi\right) $, where $0