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On Certain Semigroups Of Full Contraction Maps Of A Finite Chain, Goje Uba Garba, Muhammad Jamilu Ibrahim, Abdussamad Tanko Imam
On Certain Semigroups Of Full Contraction Maps Of A Finite Chain, Goje Uba Garba, Muhammad Jamilu Ibrahim, Abdussamad Tanko Imam
Turkish Journal of Mathematics
Let $X_{n}=\{1,2,\ldots,n\}$ with its natural order and let ${\cal T}_{n}$ be the full transformation semigroup on $X_{n}$. A map $\alpha\in{\cal T}_{n}$ is said to be order-preserving if, for all $x,y\in X_{n}$, $x\leq y\Rightarrow x\alpha\leq y\alpha$. The map $\alpha\in{\cal T}_{n}$ is said to be a contraction if, for all $x,y\in X_{n}$, $ x\alpha-y\alpha \leq x-y $. Let ${\cal CT}_{n}$ and ${\cal OCT}_{n}$ denote, respectively, subsemigroups of all contraction maps and all order-preserving contraction maps in ${\cal T}_{n}$. In this paper we present characterisations of Green's relations on ${\cal CT}_{n}$ and starred Green's relations on both ${\cal CT}_{n}$ and ${\cal OCT}_{n}$.
Andoyer Equations For Noncollinear Planar Central Configurations, Antonio Carlos Fernandes, Luis Fernando Mello
Andoyer Equations For Noncollinear Planar Central Configurations, Antonio Carlos Fernandes, Luis Fernando Mello
Turkish Journal of Mathematics
In this article we obtain the Andoyer equations for noncollinear planar central configurations taking into account the center of mass of the system. We apply these equations to study two configurations. In the first one we prove that it is not possible to put a square central configuration and an equilateral triangle central configuration as a cocircular central configuration. In the second one we give the central configurations for the noncollinear planar $4$-body problem with one pair of equal positive masses and two null masses.
Cyclic Codes Over $\Mathbb{Z}_{4}+U\Mathbb{Z}_{4}+U^{2}\Mathbb{Z}_{4}$, Mehmet Özen, Nazmi̇ye Tuğba Özzai̇m, Nuh Aydin
Cyclic Codes Over $\Mathbb{Z}_{4}+U\Mathbb{Z}_{4}+U^{2}\Mathbb{Z}_{4}$, Mehmet Özen, Nazmi̇ye Tuğba Özzai̇m, Nuh Aydin
Turkish Journal of Mathematics
In this paper, we study cyclic codes over the ring $R=\mathbb{Z}_{4}+u\mathbb{Z}_{4}+u^{2}\mathbb{Z}_{4}$,where $u^{3}=0$. We investigate Galois extensions of this ring and the ideal structure of these extensions.The results are then used to obtain facts about cyclic codes over $R$. We also determine the general form of the generator of a cyclic code and find its minimal spanning sets. Finally, we obtain many new linear codes over $\mathbb{Z}_4$ by considering Gray images of cyclic codes over $R$.
On Subdirectly Irreducible Regular Bands, Zheng-Pan Wang, Jing Leng, Hou-Yi Yu
On Subdirectly Irreducible Regular Bands, Zheng-Pan Wang, Jing Leng, Hou-Yi Yu
Turkish Journal of Mathematics
Subdirectly irreducible regular bands whose structural semilattices are finite chains are characterized in terms of arefined semilattice of semigroups.
On Focal Curves Of Null Cartan Curves, Hakan Şi̇mşek
On Focal Curves Of Null Cartan Curves, Hakan Şi̇mşek
Turkish Journal of Mathematics
The focal curve, which is determined as the locus of centers of osculatingpseudo-spheres of a null Cartan curve, is investigated in Minkowski(n+2)-space $\mathcal{M}^{n+2}.$ Moreover, a curve called \textit{accelerationfocal curve }of a null Cartan curve is introduced by using a new family of functions.
On The Equivalence Of Alexandrov Curvature And Busemann Curvature, Shijie Gu
On The Equivalence Of Alexandrov Curvature And Busemann Curvature, Shijie Gu
Turkish Journal of Mathematics
It is shown that the curvature bounded above (resp. below) in the sense of Alexandrov is equivalent to the curvature bounded above (resp. below) in the sense of Busemann if and only if the sum of adjacent average angles is at least (resp. at most) $\pi$.
On The Zariski Topology Over An $L$-Module $M$, Fethi̇ Çallialp, Gülşen Ulucak, Ünsal Teki̇r
On The Zariski Topology Over An $L$-Module $M$, Fethi̇ Çallialp, Gülşen Ulucak, Ünsal Teki̇r
Turkish Journal of Mathematics
Let $L$ be a multiplicative lattice and $M$ be an $L$-module. In this study, we present a topology said to be the Zariski topology over $\sigma (M),$ the collection of all prime elements of an $L$-module $M.$ We research some results on the Zariski topology over $\sigma (M).$ We show that the topology is a $T_{0}$-space and a $T_{1}$-space under some conditions. Some properties and results are studied for the topology over $\sigma (L)$, the collection of all prime elements of a multiplicative lattice $L.$
Value Distribution And Normality Of Meromorphic Functions Involving Partial Sharing Of Small Functions, Kuldeep Singh Charak, Shittal Sharma
Value Distribution And Normality Of Meromorphic Functions Involving Partial Sharing Of Small Functions, Kuldeep Singh Charak, Shittal Sharma
Turkish Journal of Mathematics
In this paper, we generalize a value distribution result and use it to prove a normality criterion using partial sharing of small functions. Further in the sequel, various known normality criteria are improved and generalized on the domain $D:=\{z: z \lt R, 0\lt R\leq\infty \}$.
Existence And Global Attractivity Of Periodic Solutions In A Max-Type System Of Difference Equations, Imane Dekkar, Nouressadat Touafek
Existence And Global Attractivity Of Periodic Solutions In A Max-Type System Of Difference Equations, Imane Dekkar, Nouressadat Touafek
Turkish Journal of Mathematics
We consider in this paper the following system of difference equations with maximum $$ \left\{ \begin{array}{lll} x(n+1)= & \max\{f_1(n,x(n)),g_1(n,y(n))\}& \\ & &, ~~ n=0,1,2, \ldots, \\ y(n+1)= & \max\{f_2(n,x(n)),g_2(n,y(n))\} & \\ \end{array} \right.$$ where $f_i, g_i$, $i=1,2$, are real-valued functions with periodic coefficients. We use the Banach fixed point theorem to get a sufficient condition under which this system admits a unique periodic solution. Moreover, we show that this periodic solution attracts all the solutions of the current system. Some examples are also given to illustrate our results.
$F$-Biminimal Immersions, Fatma Gürler, Ci̇han Özgür
$F$-Biminimal Immersions, Fatma Gürler, Ci̇han Özgür
Turkish Journal of Mathematics
In the present paper, we define $f$-biminimal immersions. We consider $f$-biminimal curves in a Riemannian manifold and $f$-biminimal submanifolds of codimension $1$ in a Riemannian manifold, and we give examples of $f$-biminimal surfaces. Finally, we consider $f$-biminimal Legendre curves in Sasakian space forms and give an example.
Second Hankel Determinant For Certain Subclasses Ofbi-Univalent Functions, Murat Çağlar, Erhan Deni̇z, Hari Mohan Srivastava
Second Hankel Determinant For Certain Subclasses Ofbi-Univalent Functions, Murat Çağlar, Erhan Deni̇z, Hari Mohan Srivastava
Turkish Journal of Mathematics
In the present paper, we obtain the upper bounds for the second Hankel determinant for certain subclasses of analytic and bi-univalent functions. Moreover, several interesting applications of the results presented here are also discussed.
Canonical Involution On Double Jet Bundles, Hülya Kadioğlu
Canonical Involution On Double Jet Bundles, Hülya Kadioğlu
Turkish Journal of Mathematics
In this study, we generalize double tangent bundles to double jet bundles. We present a secondary vector bundle structure on a 1-jet of a vector bundle. We show that the 1-jet of a vector bundle carries two vector bundle structures, namely primary and secondary structures. We also show that the manifold charts induced by primary and secondary structures belong to the same atlas. We prove that double jet bundles can be considered as a quotient of the second order jet bundle. We show that there exists a natural involution that interchanges between primary and secondary vector bundle structures on double …
Solvability Of Boundary Value Problems For Coupled Impulsive Differential Equations With One-Dimensional P-Laplacians, Yuji Liu
Turkish Journal of Mathematics
This paper is concerned with a boundary value problem of impulsive differential systems on the whole line with one-dimensional p-Laplacians. By constructing a weighted Banach space and defining a nonlinear operator, together with Schauder's fixed point theorem, sufficient conditions to guarantee the existence of at least one solution are established (Theorems 3.1-3.3). Two examples are given to illustrate the main results.
Generalized Convolution Product For An Integral Transform On A Wiener Space, Byoung Soo Kim, Il Yoo
Generalized Convolution Product For An Integral Transform On A Wiener Space, Byoung Soo Kim, Il Yoo
Turkish Journal of Mathematics
We introduce a generalized convolution product $(F*G)_{\vec\alpha,\vec\beta}$ for integral transform ${\mathcal F}_{\gamma,\eta}$ for functionals defined on $K[0,T]$, the space of complex valued continuous functions on $[0,T]$ that vanish at zero. We study some interesting properties of our generalized convolution product and establish various relationships that exist among the generalized convolution product, the integral transform, and the first variation for functionals defined on $K[0,T]$. We also discuss the associativity of the generalized convolution product.
P-Subordination Chains And P-Valence Integral Operators, Erhan Deni̇z, Hali̇t Orhan, Murat Çağlar
P-Subordination Chains And P-Valence Integral Operators, Erhan Deni̇z, Hali̇t Orhan, Murat Çağlar
Turkish Journal of Mathematics
In the present investigation we obtain some sufficient conditions for the analyticity and the $p$-valence of an integral operator in the unit disk $\mathbb{D}$. Using these conditions we give some applications for a few different integral operators. The significant relationships and relevance to other results are also given. A number of known univalent conditions would follow upon specializing the parameters involved in our main results.
New Recurrences For Euler's Partition Function, Mircea Merca
New Recurrences For Euler's Partition Function, Mircea Merca
Turkish Journal of Mathematics
In this paper, the author invokes some consequences of the bisectional pentagonal number theorem to derive two linear recurrence relations for Euler's partition function $p(n)$. As a corollary of these results, we obtain an efficient method to compute the parity of Euler's partition function $p(n)$ that requires only the parity of $p(k)$ with $k \leq n/4$.
Stability Analysis Of Nonlinear Fractional Differential Order Systems With Caputo And Riemann--Liouville Derivatives, Javad Alidousti, Reza Khoshsiar Ghaziani, Ali Bayati Eshkaftaki
Stability Analysis Of Nonlinear Fractional Differential Order Systems With Caputo And Riemann--Liouville Derivatives, Javad Alidousti, Reza Khoshsiar Ghaziani, Ali Bayati Eshkaftaki
Turkish Journal of Mathematics
In this paper we establish stability theorems for nonlinear fractional orders systems (FDEs) with Caputo and Riemann--Liouville derivatives. In particular, we derive conditions for $ {\bf \cal{F}}$-stability of nonlinear FDEs. By numerical simulations, we verify numerically our theoretical results on a test example.
Chaos-Related Properties On The Product Of Semiflows, Alica Miller, Chad Money
Chaos-Related Properties On The Product Of Semiflows, Alica Miller, Chad Money
Turkish Journal of Mathematics
In this paper we generalize some results about the chaos-related properties on the product of two semiflows, which appeared in the lite\-rature in the last few years, to the case of the most general possible acting monoids. In order to do that we introduce some new notions, namely the notions of a directional, psp and sip monoid, and the notion of a strongly transitive semiflow. In particular, we obtain a sufficient condition for the Devaney chaoticity of a product, which works for the (very large) class of the psp acting monoids.
Dissipative Operator And Its Cayley Transform, Eki̇n Uğurlu, Kenan Taş
Dissipative Operator And Its Cayley Transform, Eki̇n Uğurlu, Kenan Taş
Turkish Journal of Mathematics
In this paper, we investigate the spectral properties of the maximaldissipative extension of the minimal symmetric differential operatorgenerated by a second order differential expression and dissipative andeigenparameter dependent boundary conditions. For this purpose we use thecharacteristic function of the maximal dissipative operator and inverseoperator. This investigation is done by the characteristic function of theCayley transform of the maximal dissipative operator, which is a completelynonunitary contraction belonging to the class $C_{0}.$ Using Solomyak'smethod we also introduce the self-adjoint dilation of the maximal dissipativeoperator and incoming/outgoing eigenfunctions of the dilation. Moreover, weinvestigate other properties of the Cayley transform of the maximaldissipative operator.
Corrigendum: On Density Theorems For Rings Of Krull Type With Zero Divisors, Başak Ay Saylam
Corrigendum: On Density Theorems For Rings Of Krull Type With Zero Divisors, Başak Ay Saylam
Turkish Journal of Mathematics
This corrigendum is written to correct some parts of the paper "On density theorems for rings of Krull type with zero divisors". The proofs of Proposition 2.4 and Proposition 4.3 are incorrect and the current note makes the appropriate corrections.
Braided Regular Crossed Modules Bifibered Over Regular Groupoids, Alper Odabaş, Erdal Ulualan
Braided Regular Crossed Modules Bifibered Over Regular Groupoids, Alper Odabaş, Erdal Ulualan
Turkish Journal of Mathematics
We show that the forgetful functor from the category ofbraided regular crossed modules to the category of regular (or whiskered) groupoids is a fibration and also a cofibration.
Unions And Ideals Of Locally Strongly Porous Sets, Maya Altinok, Oleksiy Dovgoshey, Mehmet Küçükaslan
Unions And Ideals Of Locally Strongly Porous Sets, Maya Altinok, Oleksiy Dovgoshey, Mehmet Küçükaslan
Turkish Journal of Mathematics
For subsets of $\mathbb R^+ = [0,∞)$ we introduce a notion of coherently porous sets as the sets for which the upper limit in the definition of porosity at a point is attained along the same sequence. We prove that the union of two strongly porous at $0$ sets is strongly porous if and only if these sets are coherently porous. This result leads to a characteristic property of the intersection of all maximal ideals contained in the family of strongly porous at $0$ subsets of $\mathbb R^+$. It is also shown that the union of a set $A \subseteq …
Generalized Crossed Modules And Group-Groupoids, Mustafa Habi̇l Gürsoy, Hati̇ce Aslan, İlhan İçen
Generalized Crossed Modules And Group-Groupoids, Mustafa Habi̇l Gürsoy, Hati̇ce Aslan, İlhan İçen
Turkish Journal of Mathematics
In this present work, we present the concept of a crossed module over generalized groupsand we call it a "generalized crossed module". We also define a generalizedgroup-groupoid. Furthermore, we show that the category of generalized crossedmodules is equivalent to that of generalized group-groupoids whose object sets are abelian generalized group.
Extension Of The Darboux Frame Into Euclidean 4-Space And Its Invariants, Mustafa Düldül, Bahar Uyar Düldül, Nuri̇ Kuruoğlu, Ertuğrul Özdamar
Extension Of The Darboux Frame Into Euclidean 4-Space And Its Invariants, Mustafa Düldül, Bahar Uyar Düldül, Nuri̇ Kuruoğlu, Ertuğrul Özdamar
Turkish Journal of Mathematics
In this paper, by considering a Frenet curve lying on an oriented hypersurface, we extend the Darboux frame field into Euclidean 4-space $\mathbb{E}^4$. Depending on the linear independency of the curvature vector with the hypersurface's normal, we obtain two cases for this extension. For each case, we obtain some geometrical meanings of new invariants along the curve on the hypersurface. We also give the relationships between the Frenet frame curvatures and Darboux frame curvatures in $\mathbb{E}^4$. Finally, we compute the expressions of the new invariants of a Frenet curve lying on an implicit hypersurface.
On Algebraic Properties Of Veronese Bi-Type Ideals Arising From Graphs, Maurizio Imbesi, Monica La Barbiera
On Algebraic Properties Of Veronese Bi-Type Ideals Arising From Graphs, Maurizio Imbesi, Monica La Barbiera
Turkish Journal of Mathematics
Some algebraic properties of the ideals of Veronese bi-type arising from graphs with loops are studied. More precisely, the property of these ideals to be bi-polymatroidal is discussed. Moreover, we are able to determine the structure of the ideals of vertex covers for such generalized graph ideals.
A Note On Reduction Numbers And Hilbert-Samuel Functions Of Ideals Over Cohen-Macaulay Rings, Amir Mafi, Dler Naderi
A Note On Reduction Numbers And Hilbert-Samuel Functions Of Ideals Over Cohen-Macaulay Rings, Amir Mafi, Dler Naderi
Turkish Journal of Mathematics
Let $(R,\fm)$ be a Cohen--Macaulay local ring of dimension $d\geq 2$ with infinite residue field and $I$ an $\fm$-primary ideal of $R$. Let $I$ be integrally closed and $J$ be a minimal reduction of $I$. In this paper, we show that the following are equivalent: $(i)$ $P_I(n)=H_I(n)$ for $n=1,2$; $(ii)$ $P_I(n)=H_I(n)$ for all $n\geq 1$; $(iii)$ $I^3=JI^2$. Moreover, if $\Dim R=3$, $n(I)\leq 1$ and $\grade gr_I(R)_+>0$, then the reduction number $r(I)$ is independent.
Sharp Bounds For The First Nonzero Steklov Eigenvalues For$F$-Laplacians, Guangyue Huang, Bingqing Ma
Sharp Bounds For The First Nonzero Steklov Eigenvalues For$F$-Laplacians, Guangyue Huang, Bingqing Ma
Turkish Journal of Mathematics
Let $M$ be an $n$-dimensional compact Riemannian manifold with a boundary. In this paper, we consider the Steklov first eigenvalue with respect to the $f$-divergence form: $$ e^{f}{\rm div}(e^{-f}A\nabla u)=0\ {\rm in}\ \ M, \ \ \ \ \ \langle A(\nabla u),\nu\rangle-\eta u=0 \ \ {\rm on}\ \partial M,$$ where $A$ is a smooth symmetric and positive definite endomorphism of $TM$, and the following three fourth order Steklov eigenvalue problems: $$ (\Delta_f)^2u=0\ \ {\rm in}\ M, \ \ \ \ \ u=\Delta_f u-q\frac{\partial u}{\partial \nu}=0\ \ {\rm on}\ \partial M; $$ $$ (\Delta_f)^2u=0\ {\rm in}\ \ M, \ \ \ …
A Remark On Singularity Of Homeomorphisms And Hausdorff Dimension, Chun Wei, Shengyou Wen
A Remark On Singularity Of Homeomorphisms And Hausdorff Dimension, Chun Wei, Shengyou Wen
Turkish Journal of Mathematics
We prove that there is a homeomorphism of the unit interval onto itself that is so singular that it maps some set $E$ of $\dim_HE=0$ onto a set $F$ of $\dim_H[0,1]\setminus F=0$.
Idempotents Of The Green Algebras Of Finite Dimensionalpointed Rank One Hopf Algebras Of Nilpotent Type, Zhihua Wang
Idempotents Of The Green Algebras Of Finite Dimensionalpointed Rank One Hopf Algebras Of Nilpotent Type, Zhihua Wang
Turkish Journal of Mathematics
In this paper, we intend to study idempotents of the Green algebra (complexified Green ring) of any finite dimensional pointed rank one Hopf algebra of nilpotent type over the complex number field. We first determine all one dimensional representations of the quotient algebra of the Green algebra modulo its Jacobson radical. This gives rise to all primitive idempotents of the quotient algebra. Then we present explicitly primitive idempotents of the Green algebra by lifting the ones of the quotient algebra. Finally, as an example, we describe all primitive idempotents of the Green algebra of the Taft algebra $T_3$.
A New Aspect To Picard Operators With Simulation Functions, Murat Olgun, Tuğçe Alyildiz, Özge Bi̇çer
A New Aspect To Picard Operators With Simulation Functions, Murat Olgun, Tuğçe Alyildiz, Özge Bi̇çer
Turkish Journal of Mathematics
In the present paper, considering the simulation function, we give a new class of Picard operators on complete metric spaces. We also provide a nontrivial example that shows the aforementioned class properly contains some earlier such classes.