On Congruences Related To Trinomial Coefficients And Harmonic Numbers,
2021
TÜBİTAK
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,
2021
TÜBİTAK
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,
2021
TÜBİTAK
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,
2021
TÜBİTAK
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,
2021
TÜBİTAK
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,
2021
TÜBİTAK
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,
2021
TÜBİTAK
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,
2021
TÜBİTAK
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,
2021
TÜBİTAK
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,
2021
TÜBİTAK
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,
2021
TÜBİTAK
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,
2021
TÜBİTAK
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,
2021
TÜBİTAK
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,
2021
TÜBİTAK
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,
2021
TÜBİTAK
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,
2021
TÜBİTAK
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,
2021
TÜBİTAK
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
On Some Nonlocal Inverse Boundary Problem For Partial Differential Equations Of Third Order,
2021
TÜBİTAK
On Some Nonlocal Inverse Boundary Problem For Partial Differential Equations Of Third Order, Ziyatkhan S. Aliyev, Yashar T. Mehraliyev, Elmira H. Yusifova
Turkish Journal of Mathematics
In this paper, we consider the inverse boundary value problem for a partial differential equation of third order with nonlocal boundary conditions, including an integral condition. Using analytical and operator-theoretic methods, as well as the Fourier method, the existence and uniqueness of the classical solution of this problem is proved.
Normalized Null Hypersurfaces In Non-Flat Lorentzian Space Forms Satisfying $L_R X =\Mathcal U X +B$,
2021
TÜBİTAK
Normalized Null Hypersurfaces In Non-Flat Lorentzian Space Forms Satisfying $L_R X =\Mathcal U X +B$, Hans Fotsing Tetsing
Turkish Journal of Mathematics
In the present work, we classify normalized null hypersurfaces $x:(M,g,N)\to Q^{n+2}_1(c)$ immersed into one of the two real standard nonflat Lorentzian space-forms and satisfying the equation $L_r x=\mathcal U x+b$ for some field of screen constant matrices $\mathcal U$ and some field of screen constant vectors $b\in\mathbb{R}^{n+2}$, where $L_r$ is the linearized operator of the $(r+1)-$mean curvature of the normalized null hypersurface for $r=0,...,n$. We show that if the immersion $x$ is a solution of the equation $L_r x=\mathcal U x+b$ for $1\leq r\leq n$ and the normalization $N$ is quasi-conformal, then $M$ is either an $(r+1)-$maximal null hypersurface, or …
Weak And Injective Dimensional Analogues Of Kaplansky's And Auslander's Lemmas For Purity,
2021
TÜBİTAK
Weak And Injective Dimensional Analogues Of Kaplansky's And Auslander's Lemmas For Purity, Laszlo Fuchs, Sang Bum Lee
Turkish Journal of Mathematics
We prove a stronger form of an analogue of a Kaplansky lemma on homological dimensions by showing that in a pure-exact sequence $0 \to A \to B \to C \to 0$, the weak dimensions of the modules satisfy $ {\rm w.d.} B = \max\{{\rm w.d.} A, {\rm w.d.} C\}$. We also show that the same equality holds for the injective dimensions whenever the ring is noetherian. In addition, a version of Auslander's lemma for chains of pure submodules $M_{\rho}$ is proved: the weak dimension of the union of the chain equals the supremum of the weak dimensions of the factor …
