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On The Zero-Divisor Graphs Of Finite Free Semilattices, Kemal Toker
On The Zero-Divisor Graphs Of Finite Free Semilattices, Kemal Toker
Turkish Journal of Mathematics
Let $SL_{X}$ be the free semilattice on a finite nonempty set $X$. There exists an undirected graph $\Gamma(SL_{X})$ associated with $SL_{X}$ whose vertices are the proper subsets of $X$, except the empty set, and two distinct vertices $A$ and $B$ of $\Gamma(SL_{X})$ are adjacent if and only if $A\cup B=X$. In this paper, the diameter, radius, girth, degree of any vertex, domination number, independence number, clique number, chromatic number, and chromatic index of $\Gamma(SL_{X})$ have been established. Moreover, we have determined when $\Gamma(SL_{X})$ is a perfect graph and when the core of $\Gamma(SL_{X})$ is a Hamiltonian graph.
New Oscillation Tests And Some Refinements For First-Order Delay Dynamic Equations, Başak Karpuz, Özkan Öcalan
New Oscillation Tests And Some Refinements For First-Order Delay Dynamic Equations, Başak Karpuz, Özkan Öcalan
Turkish Journal of Mathematics
In this paper, we present new sufficient conditions for the oscillation of first-order delay dynamic equations on time scales. We also present some examples to which none of the previous results in the literature can apply.
Veronese Transform And Castelnuovo-Mumford Regularity Of Modules, Marcel Morales, Nguyen Thi Dung
Veronese Transform And Castelnuovo-Mumford Regularity Of Modules, Marcel Morales, Nguyen Thi Dung
Turkish Journal of Mathematics
Veronese rings, Segre embeddings, or more generally Segre--Veronese embeddings are very important rings in algebraic geometry. In this paper we present an original, elementary way to compute the Hilbert--Poincar\'e series of these rings; as a consequence we compute their Castelnuovo--Mumford regularity and also the highest graded Betti number. Moreover, using the Castelnuovo--Mumford regularity of a Cohen--Macaulay finitely generated graded module, we compute that of its Veronese transforms.
An Improved Singular Trudinger-Moser Inequality In Dimension Two, Anfeng Yuan, Zhiyong Huang
An Improved Singular Trudinger-Moser Inequality In Dimension Two, Anfeng Yuan, Zhiyong Huang
Turkish Journal of Mathematics
Let $\Omega\subset\mathbb{R}^2$ be a smooth bounded domain and $W_0^{1,2}(\Omega)$ be the usual Sobolev space. Let $\beta$, $0\leq\beta1$, $$\lambda_{p,\beta}(\Omega)=\inf_{u\in W_0^{1,2}(\Omega),\,u\not\equiv 0}{\ \nabla u\ _2^2}/{\ u\ _{p,\beta}^2},$$ where $\ \cdot\ _2$ denotes the standard $L^2$-norm in $\Omega$ and $\ u\ _{p,\beta}=({\int_{\Omega} x ^{-\beta} u ^pdx})^{1/p}$. Suppose that $\gamma$ satisfies $\f{\gamma}{4\pi}+\f{\beta}{2}=1$. Using a rearrangement argument, the author proves that $$\sup_{u\in W_0^{1,2}(\Omega), \ \nabla u\ _2\leq 1}\int_{\Omega} x ^{-\beta}e^{\gamma u^2 \le(1+\alpha\ u\ _{p,\beta}^2\ri) }dx$$ is finite for any $\alpha$, $0\leq\alpha
On $*$-Commuting Mappings And Derivations In Rings With Involution, Nadeem Ahmad Dar, Shakir Ali
On $*$-Commuting Mappings And Derivations In Rings With Involution, Nadeem Ahmad Dar, Shakir Ali
Turkish Journal of Mathematics
Let $R$ be a ring with involution $*$. A mapping $f:R\rightarrow R$ is said to be $*$-commuting on $R$ if $[f(x),x^*]=0$ holds for all $x\in R$. The purpose of this paper is to describe the structure of a pair of additive mappings that are $*$-commuting on a semiprime ring with involution. Furthermore, we study the commutativity of prime rings with involution satisfying any one of the following conditions: (i) $[d(x),d(x^*)]=0,$ (ii) $d(x)\circ d(x^*)=0$, (iii) $d([x,x^*])\pm [x,x^*]=0$ (iv) $d(x\circ x^*)\pm (x\circ x^*)=0,$ (v) $d([x,x^*])\pm (x\circ x^*)=0$, (vi) $d(x\circ x^*)\pm [x,x^*]=0$, where $d$ is a nonzero derivation of $R$. Finally, an example …
Overall Approach To Mizoguchi--Takahashi Type Fixed Point Results, Gülhan Minak, İshak Altun
Overall Approach To Mizoguchi--Takahashi Type Fixed Point Results, Gülhan Minak, İshak Altun
Turkish Journal of Mathematics
In this work, inspired by the recent technique of Jleli and Samet, we give a new generalization of the well-known Mizoguchi--Takahashi fixed point theorem, which is the closest answer to Reich's conjecture about the existence of fixed points of multivalued mappings on complete metric spaces. We also provide a nontrivial example showing that our result is a proper generalization of the Mizoguchi--Takahashi result.
On The Comaximal Ideal Graph Of A Commutative Ring, Mehrdad Azadi, Zeinab Jafari, Changiz Eslahchi
On The Comaximal Ideal Graph Of A Commutative Ring, Mehrdad Azadi, Zeinab Jafari, Changiz Eslahchi
Turkish Journal of Mathematics
Let $R$ be a commutative ring with identity. We use $\Gamma ( R )$ to denote the comaximal ideal graph. The vertices of $\Gamma ( R )$ are proper ideals of R that are not contained in the Jacobson radical of $R$, and two vertices $I$ and $J$ are adjacent if and only if $I + J = R$. In this paper we show some properties of this graph together with the planarity and perfection of $\Gamma ( R )$.
A Contribution To The Analysis Of A Reduction Algorithm For Groups With An Extraspecial Normal Subgroup, Abdullah Çağman, Nurullah Ankaralioğlu
A Contribution To The Analysis Of A Reduction Algorithm For Groups With An Extraspecial Normal Subgroup, Abdullah Çağman, Nurullah Ankaralioğlu
Turkish Journal of Mathematics
Reduction algorithms are an important tool for understanding structural properties of groups. They play an important role in algorithms designed to investigate matrix groups over a finite field. One such algorithm was designed by Brooksbank et al. for members of the class $C_6$ in Aschbacher's theorem, namely groups $N$ that are normalizers in $GL(d,q)$ of certain absolutely irreducible symplectic-type $r$-groups $R$, where $r$ is a prime and $d=r^n$ with $n>2$. However, the analysis of this algorithm has only been completed when $d=r^2$ and when $d=r^n$ and $n>2$, in the latter case under the condition that $G/RZ(G)\cong N/RZ(N)$. We …
On Coprimely Structured Rings, Nesli̇han Ayşen Özki̇ri̇şci̇, Kürşat Hakan Oral, Ünsal Teki̇r
On Coprimely Structured Rings, Nesli̇han Ayşen Özki̇ri̇şci̇, Kürşat Hakan Oral, Ünsal Teki̇r
Turkish Journal of Mathematics
In this paper, we define coprimely structured rings, which are the generalization of strongly 0-dimensional rings. Furthermore, we investigate coprimely structured rings and give some relations between other rings such as Artinian rings, strongly 0-dimensional rings, and h-local domains.
Almost Co-K\"{A}Hler Manifolds Satisfying Some Symmetry Conditions, Yaning Wang
Almost Co-K\"{A}Hler Manifolds Satisfying Some Symmetry Conditions, Yaning Wang
Turkish Journal of Mathematics
Let $M^{2n+1}$ be an almost co-K\"{a}hler manifold of dimension $>3$ with K\"{a}hlerian leaves. In this paper, we first prove that if $M^{2n+1}$ is locally symmetric, then either it is a co-K\"{a}hler manifold with locally symmetric K\"{a}hlerian leaves, or the Reeb vector field $\xi$ is harmonic and in this case $M^{2n+1}$ is non-co-K\"{a}hler. We also prove that any almost co-K\"{a}hler manifold of dimension $3$ is $\phi$-symmetric if and only if it is locally isometric to either a flat Euclidean space $\mathbb{R}^3$ or a Riemannian product $\mathbb{R}\times N^2(c)$, where $N^2(c)$ denotes a K\"{a}hler surface of constant curvature $c\neq0$.
A Lower Bound For Stanley Depth Of Squarefree Monomial Ideals, Guangjun Zhu
A Lower Bound For Stanley Depth Of Squarefree Monomial Ideals, Guangjun Zhu
Turkish Journal of Mathematics
Let $S=K[x_{1},\dots,x_{n}]$ be a polynomial ring over a field $K$ in $n$ variables and $I$ a squarefree monomial ideal of $S$ with Schmitt--Vogel number $sv(I)$. In this paper, we show that $\mbox{sdepth}\,(I)\geq \mbox{max}\,\{1, n-1-\lfloor \frac{sv(I)}{2}\rfloor\},$ which improves the lower bound obtained by Herzog, Vladoiu, and Zheng. As some applications, we show that Stanley's conjecture holds for the edge ideals of some special $n$-cyclic graphs with a common edge.
Fourth-Order Birkhoff Regular Problems With Eigenvalue Parameter Dependent Boundary Conditions, Bertin Zinsou
Fourth-Order Birkhoff Regular Problems With Eigenvalue Parameter Dependent Boundary Conditions, Bertin Zinsou
Turkish Journal of Mathematics
A regular fourth-order differential equation that depends quadratically on the eigenvalue parameter $\lambda$ is considered with classes of separable boundary conditions independent of $\lambda$ or depending on $\lambda$ linearly. Conditions are given for the problems to be Birkhoff regular.
Global Regularity For Unsteady Flow Of Third Grade Fluid In An Annular Region, Saeed Ur Rahman, Tasawar Hayat, Hamed H. Alsulami
Global Regularity For Unsteady Flow Of Third Grade Fluid In An Annular Region, Saeed Ur Rahman, Tasawar Hayat, Hamed H. Alsulami
Turkish Journal of Mathematics
This article develops global regularity criteria for unsteady and magnetohydrodynamic flow of third grade fluid in terms of bounded mean oscillations. Uniqueness of the solution is also verified.
Simulations Of The Helmholtz Equation At Any Wave Number For Adaptive Grids Using A Modified Central Finite Difference Scheme, Hafiz Abdul Wajid
Simulations Of The Helmholtz Equation At Any Wave Number For Adaptive Grids Using A Modified Central Finite Difference Scheme, Hafiz Abdul Wajid
Turkish Journal of Mathematics
In this paper, a modified central finite difference scheme for a three-point nonuniform grid is presented for the one-dimensional homogeneous Helmholtz equation using the Bloch wave property. The modified scheme provides highly accurate solutions at the nodes of the nonuniform grid for very small to very large range of wave numbers irrespective of how the grid is adapted throughout the domain. A variety of numerical examples are considered to validate the superiority of the modified scheme for a nonuniform grid over a standard central finite difference scheme.
$H$-Admissible Fourier Integral Operators, Chafika Amel Aitemrar, Abderrahmane Senoussaoui
$H$-Admissible Fourier Integral Operators, Chafika Amel Aitemrar, Abderrahmane Senoussaoui
Turkish Journal of Mathematics
We study in this work a class of $h$-admissible Fourier integral operators. These operators are bounded (respectively compact) in $L^{2}$ if the weight of the amplitude is bounded (respectively tends to 0).
Coefficient Bounds For Subclasses Of M-Fold Symmetric Bi-Univalent Functions, Sevtap Sümer Eker
Coefficient Bounds For Subclasses Of M-Fold Symmetric Bi-Univalent Functions, Sevtap Sümer Eker
Turkish Journal of Mathematics
In this study, we introduce and investigate two new subclasses of the bi-univalent functions; both $f(z)$ and $f^{-1}(z)$ are m-fold symmetric analytic functions. Among other results, upper bounds for the coefficients $\left a_{m+1}\right $ and $\left a_{2m+1}\right $ are found in this investigation.
Stability And Data Dependence Results For The Jungck--Khan Iterative Scheme, Abdul Rahim Khan, Fai̇k Gürsoy, Vivek Kumar
Stability And Data Dependence Results For The Jungck--Khan Iterative Scheme, Abdul Rahim Khan, Fai̇k Gürsoy, Vivek Kumar
Turkish Journal of Mathematics
The Jungck--Khan iterative scheme for a pair of nonself operators contains as a special case Jungck--Ishikawa and Jungck--Mann iterative schemes. In this paper, we establish improved results about convergence, stability, and data dependence for the Jungck--Khan iterative scheme.
On The Asymptotic Criterion For The Zero-Free Regions Of Certain $L$-Functions, Almasa Odzak
On The Asymptotic Criterion For The Zero-Free Regions Of Certain $L$-Functions, Almasa Odzak
Turkish Journal of Mathematics
We investigate relations between zero-free regions of certain $L$-functions and the asymptotic behavior of corresponding generalized Li coefficients. Precisely, we prove that violation of the $\tau/2$-generalized Riemann hypothesis implies oscillations of corresponding $\tau$-Li coefficients with exponentially growing amplitudes. Results are obtained for class $\shfs$ that contains the Selberg class, the class of all automorphic $L$-functions, the Rankin--Selberg $L$-functions, and products of suitable shifts of the mentioned functions.
Pointwise Slant Submersions From Cosymplectic Manifolds, Sezi̇n Aykurt Sepet, Mahmut Ergüt
Pointwise Slant Submersions From Cosymplectic Manifolds, Sezi̇n Aykurt Sepet, Mahmut Ergüt
Turkish Journal of Mathematics
In this paper, we characterize the pointwise slant submersions from cosymplectic manifolds onto Riemannian manifolds and give several examples.
On The Evolute Offsets Of Ruled Surfaces In Minkowski 3-Space, Dae Won Yoon
On The Evolute Offsets Of Ruled Surfaces In Minkowski 3-Space, Dae Won Yoon
Turkish Journal of Mathematics
In this paper, we classify evolute offsets of a ruled surface in Minkowski 3-space $\Bbb L^3$ with constant Gaussian curvature and mean curvature. As a result, we investigate linear Weingarten evolute offsets of a ruled surface in $\Bbb L^3$.
On $Le$-Semigroups, Niovi Kehayopulu
On $Le$-Semigroups, Niovi Kehayopulu
Turkish Journal of Mathematics
We characterize the idempotent ideal elements of the $le$-semigroups in terms of semisimple elements and we prove, among others, that the ideal elements of an $le$-semigroup $S$ are prime (resp. weakly prime) if and only if they form a chain and $S$ is intraregular (resp. semisimple). The corresponding results on semigroups (without order) can be also obtained as an application of the results of this paper. The study of $poe$-semigroups plays an essential role in the theory of fuzzy semigroups and the theory of hypersemigroups.
Existence And Nonexistence Of Sign-Changing Solutions To Elliptic Critical Equations, Mokhless Hammami, Houria Ismail
Existence And Nonexistence Of Sign-Changing Solutions To Elliptic Critical Equations, Mokhless Hammami, Houria Ismail
Turkish Journal of Mathematics
We consider the nonlinear equation $ -\Delta u = u ^{p-1}u -\varepsilon u \quad \mbox{in } \Omega , u =0 \quad \mbox{on } \partial \Omega ,$ where $\Omega $ is a smooth bounded domain in $\mathbb{R}^n$, $n \geq 4$, $ \varepsilon$ is a small positive parameter, and $p=(n+2)/(n-2)$. We study the existence of sign-changing solutions that concentrate at some points of the domain. We prove that this problem has no solutions with one positive and one negative bubble. Furthermore, for a family of solutions with exactly two positive bubbles and one negative bubble, we prove that the limits of the …
Uniqueness Of $P(F)$ And $P[F]$, Kuldeep Singh Charak, Banarsi Lal
Uniqueness Of $P(F)$ And $P[F]$, Kuldeep Singh Charak, Banarsi Lal
Turkish Journal of Mathematics
Let $f$ be a nonconstant meromorphic function, $a (\not\equiv 0, \infty)$ be a meromorphic function satisfying $T(r,a) = o(T(r,f))$ as $r \rightarrow \infty$, and $p(z)$ be a polynomial of degree $n \geq 1$ with $p(0) = 0$. Let $P[f]$ be a nonconstant differential polynomial of $f$. Under certain essential conditions, we prove that $p(f) \equiv P[f]$, when $p(f)$ and $P[f]$ share $a$ with weight $l \geq 0$. Our result generalizes the results due to Zhang and L$\ddot{\text{u}}$, Banerjee and Majumdar, and Bhoosnurmath and Kabbur and answers a question asked by Zhang and L$\ddot{\text{u}}$.
Some Topological Properties Of The Spaces Of Almost Null Andalmost Convergent Double Sequences, Medi̇ne Yeşi̇lkayagi̇l, Feyzi̇ Başar
Some Topological Properties Of The Spaces Of Almost Null Andalmost Convergent Double Sequences, Medi̇ne Yeşi̇lkayagi̇l, Feyzi̇ Başar
Turkish Journal of Mathematics
Let $\mathcal{C}_{f_0}$ and $\mathcal{C}_{f}$ denote the spaces of almost null and almost convergent double sequences, respectively. We show that $\mathcal{C}_{f_0}$ and $\mathcal{C}_{f}$ are BDK-spaces, barreled and bornological, but they are not monotone and so not solid. Additionally, we establish that both of the spaces $\mathcal{C}_{f_0}$ and $\mathcal{C}_{f}$ include the space $\mathcal{BS}$ of bounded double series.
Generalizations Of 2-Absorbing Primaryideals Of Commutative Rings, Ayman Badawi, Ünsal Teki̇r, Emel Aslankarayi̇ği̇t Uğurlu, Gülşen Ulucak, Ece Yetki̇n Celi̇kel
Generalizations Of 2-Absorbing Primaryideals Of Commutative Rings, Ayman Badawi, Ünsal Teki̇r, Emel Aslankarayi̇ği̇t Uğurlu, Gülşen Ulucak, Ece Yetki̇n Celi̇kel
Turkish Journal of Mathematics
ideals of $R$. In this paper, we extend the concept of 2-absorbing primary ideals to the context of $\phi $-2-absorbing primary ideals. Let $\phi :S(R)\rightarrow S(R)\cup \emptyset $ be a function. A proper ideal $I$ of $% R $ is said to be a $\phi $-2-absorbing primary ideal of $R$ if whenever $% a,b,c\in R$ with $abc\in I-\phi (I)$ implies $ab\in I$ or $ac\in \sqrt{I}$ or $bc\in \sqrt{I}$. A number of results concerning $\phi $-2-absorbing primary ideals are given.
Hom-Lie 2-Superalgebras, Chunyue Wang, Qingcheng Zhang, Jizhu Nan
Hom-Lie 2-Superalgebras, Chunyue Wang, Qingcheng Zhang, Jizhu Nan
Turkish Journal of Mathematics
Hom-Lie 2-superalgebras can be considered as the categorification of Hom-Lie superalgebras. We give the definition of Hom-Lie 2-superalgebras and study their superderivations. We obtain the representation, deformation, and abelian extensions related to the 2-cocycle and Hom-Nijenhuis operators. Moreover, we also construct a skeletal (strict) Hom-Lie 2-superalgebra from a Hom-associative Rota--Baxter superalgebra.
Highly Non-Concurrent Longest Paths In Lattices, Yasir Bashir, Faisal Nadeem, Ayesha Shabbir
Highly Non-Concurrent Longest Paths In Lattices, Yasir Bashir, Faisal Nadeem, Ayesha Shabbir
Turkish Journal of Mathematics
In this paper we consider graphs in which any pair of vertices is missed by some longest path. We are proving the existence of such graphs in the infinite triangular, square and hexagonal lattices in the plane. Moreover, we extend our investigation to lattices on several surfaces such as the torus, the M\"obius strip and the Klein bottle.
Abundance Of $E$-Order-Preserving Transformation Semigroups, Lei Sun, Xuefeng Han
Abundance Of $E$-Order-Preserving Transformation Semigroups, Lei Sun, Xuefeng Han
Turkish Journal of Mathematics
Let ${\cal T}_X$ be the full transformation semigroup on a finite totally ordered set $X=\{1<2<\ldots
Note On The Divisoriality Of Domains Of The Form $K[[X^{P}, X^{Q}]]$, $K[X^{P}, X^{Q}]$, $K[[X^{P}, X^{Q}, X^{R}]]$, And $K[X^{P}, X^{Q}, X^{R}]$, Abdeslam Mimouni
Note On The Divisoriality Of Domains Of The Form $K[[X^{P}, X^{Q}]]$, $K[X^{P}, X^{Q}]$, $K[[X^{P}, X^{Q}, X^{R}]]$, And $K[X^{P}, X^{Q}, X^{R}]$, Abdeslam Mimouni
Turkish Journal of Mathematics
Let $k$ be a field and $X$ an indeterminate over $k$. In this note we prove that the domain $k[[X^{p}, X^{q}]]$ (resp. $k[X^{p}, X^{q}]$) where $p, q$ are relatively prime positive integers is always divisorial but $k[[X^{p}, X^{q}, X^{r}]]$ (resp. $k[X^{p}, X^{q}, X^{r}]$) where $p, q, r$ are positive integers is not. We also prove that $k[[X^{q}, X^{q+1}, X^{q+2}]]$ (resp. $k[X^{q}, X^{q+1}, X^{q+2}]$) is divisorial if and only if $q$ is even. These are very special cases of well-known results on semigroup rings, but our proofs are mainly concerned with the computation of the dual (equivalently the inverse) of the …
Extension Of Refinement Rings, Rahman Bahmani Sangesari, Marjan Sheibani Abdulyousefi, Nahid Ashrafi
Extension Of Refinement Rings, Rahman Bahmani Sangesari, Marjan Sheibani Abdulyousefi, Nahid Ashrafi
Turkish Journal of Mathematics
In this paper we prove that a ring $R$ in which every finitely generated projective $R$-module lifts modulo $J(R)$ is a refinement ring if and only if $ \frac{R}{J(R)}$ is a refinement ring. We also prove that the refinement property for rings is Morita invariant. Several examples are constructed as well.