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Articles 1381 - 1410 of 2494
Full-Text Articles in Physical Sciences and Mathematics
On Armendariz-Like Properties In Amalgamated Algebras Along Ideals, Abdeslam Mimouni, Najib Mahdou, Mounir El Ourrachi
On Armendariz-Like Properties In Amalgamated Algebras Along Ideals, Abdeslam Mimouni, Najib Mahdou, Mounir El Ourrachi
Turkish Journal of Mathematics
Let $f: A\rightarrow B$ be a ring homomorphism and $J$ be an ideal of $B$. In this paper, we investigate the transfer of Armendariz-like properties to the amalgamation of $A$ with $B$ along $J$ with respect to $f$ (denoted by $A\bowtie^fJ)$ introduced and studied by D'Anna, Finocchiaro, and Fontana in 2009. Our aim is to provide necessary and sufficient conditions for $A\bowtie^fJ$ to be an Armendariz ring, nil-Armendariz ring, and weak Armendariz ring.
On The Bounds Of The Forgotten Topological Index, Suresh Elumalai, Toufik Mansour, Mohammad Ali Rostami
On The Bounds Of The Forgotten Topological Index, Suresh Elumalai, Toufik Mansour, Mohammad Ali Rostami
Turkish Journal of Mathematics
The forgotten topological index is defined as the sum of cubes of the degrees of the vertices of the molecular graph $G.$ In this paper, we obtain, analyze, and compare various lower bounds for the forgotten topological index involving the number of vertices, edges, and maximum and minimum vertex degree. Then we give Nordhaus--Gaddum-type inequalities for the forgotten topological index and coindex. Finally, we correct the number of extremal chemical trees on 15 vertices.
New Inequalities For Fractional Integrals And Their Applications, Hsiow Ru Hwang, Kuei Lin Tseng, Kai Chen Hsu
New Inequalities For Fractional Integrals And Their Applications, Hsiow Ru Hwang, Kuei Lin Tseng, Kai Chen Hsu
Turkish Journal of Mathematics
In this paper, we establish some Hermite--Hadamard-type, Bullen-type, and Simpson-type inequalities for fractional integrals. Some applications for the beta function are also given.
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$.
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.
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$.
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.
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.
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 $\Gamma ( R )$.
Generalized Bertrand Curves With Spacelike $\Left(1,3\Right) $-Normal Plane In Minkowski Space-Time, Ali̇ Uçum, Osman Keçi̇li̇oğlu, Kazim İlarslan
Generalized Bertrand Curves With Spacelike $\Left(1,3\Right) $-Normal Plane In Minkowski Space-Time, Ali̇ Uçum, Osman Keçi̇li̇oğlu, Kazim İlarslan
Turkish Journal of Mathematics
In this paper, we reconsider the $(1,3)$-Bertrand curves with respect to the casual characters of a $\left( 1,3\right) $-normal plane that is a plane spanned by the principal normal and the second binormal vector fields of the given curve. Here, we restrict our investigation of $(1,3)$-Bertrand curves to the spacelike $\left( 1,3\right) $-normal plane in Minkowski space-time. We obtain the necessary and sufficient conditions for the curves with spacelike $\left( 1,3\right) $-normal plane to be $(1,3)$-Bertrand curves and we give the related examples for these curves.
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 …
Anti-Invariant Riemannian Submersions From Kenmotsu Manifolds Onto Riemannian Manifolds, Ayşe Beri̇, İrem Küpeli̇ Erken, Cengi̇zhan Murathan
Anti-Invariant Riemannian Submersions From Kenmotsu Manifolds Onto Riemannian Manifolds, Ayşe Beri̇, İrem Küpeli̇ Erken, Cengi̇zhan Murathan
Turkish Journal of Mathematics
The purpose of this paper is to study anti-invariant Riemannian submersions from Kenmotsu manifolds onto Riemannian manifolds. Several fundamental results in this respect are proved. The integrability of the distributions and the geometry of foliations are investigated. We proved the nonexistence of (anti-invariant) Riemannian submersions from Kenmotsu manifolds onto Riemannian manifolds such that the characteristic vector field $\xi $ is a vertical vector field. We gave a method to get horizontally conformal submersion examples from warped product manifolds onto Riemannian manifolds. Furthermore, we presented an example of anti-invariant Riemannian submersions in the case where the characteristic vector field $\xi $ …
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 …
On The Twisted Modules For Finite Matrix Groups, Kübra Gül, Nurullah Ankaralioğlu
On The Twisted Modules For Finite Matrix Groups, Kübra Gül, Nurullah Ankaralioğlu
Turkish Journal of Mathematics
Suppose that $W$ is an irreducible $F_{q}G$-module of dimension $n$ $% (d^{2}
A Note On Gorenstein Projective Complexes, Bo Lu, Liu Zhongkui
A Note On Gorenstein Projective Complexes, Bo Lu, Liu Zhongkui
Turkish Journal of Mathematics
As we know, a complex $Q$ is projective if and only if $Q$ is exact and $\mathrm{Z}_n(Q)$ is projective in $R$-$\mathrm{Mod}$ for each $n\in\mathbb{Z}$. In this article, we show that a complex $G$ is Gorenstein projective with Hom$_R(P,G)$ and Hom$_R(G,P)$ exact for any Cartan--Eilenberg projective complex $P$ if and only if $G$ is exact and $\mathrm{Z}_n(G)$ is Gorenstein projective in $R$-$\mathrm{Mod}$ for each $n\in\mathbb{Z}$. Using the above result, a new equivalent characterization of some $\mathcal{A}$ complexes is obtained.
Weakly $2$-Absorbing Submodules Of Modules, Sedigheh Moradi, Abdulrasool Azizi
Weakly $2$-Absorbing Submodules Of Modules, Sedigheh Moradi, Abdulrasool Azizi
Turkish Journal of Mathematics
Let $M$ be a module over a commutative ring $R.$ A proper submodule $N$ of $M$ is called weakly $2$-absorbing, if for $r,s\in R$ and $x\in M$ with $0\neq rsx\in N,$ either $rs\in (N:M)$ or $rx\in N$ or $sx\in N.$ We study the behavior of $(N:M)$ and $\sqrt{(N:M)},$ when $N$ is weakly $2$-absorbing. The weakly $2$-absorbing submodules when $R=R_1\oplus R_2$ are characterized. Moreover we characterize the faithful modules whose proper submodules are all weakly $2$-absorbing.
The Sharpening Hölder Inequality Via Abstract Convexity, Gülteki̇n Tinaztepe
The Sharpening Hölder Inequality Via Abstract Convexity, Gülteki̇n Tinaztepe
Turkish Journal of Mathematics
In this work, a new inequality by sharpening the well-known Hölder inequality by means of a theorem based on abstract convexity is derived.
Problems In Matricially Derived Solid Banach Sequence Spaces, Peter D. Johnson, Faruk Polat
Problems In Matricially Derived Solid Banach Sequence Spaces, Peter D. Johnson, Faruk Polat
Turkish Journal of Mathematics
Let $\mathbb{F}^\mathbb{N}$ denote the vector space of all scalar sequences. If $A$ is an infinite matrix with nonnegative entries and $\lambda$ is a solid subspace of $\mathbb{F}^\mathbb{N}$, then $ sol-A^{-1}(\lambda)=\{x\in \mathbb{F}^\mathbb{N} : A x \in \lambda\} $ is also a solid subspace of $\mathbb{F}^\mathbb{N}$ that, under certain conditions on $A$ and $\lambda$, inherits a solid topological vector space topology from any such topology on $\lambda$. Letting $\Lambda_0=\lambda$ and $\Lambda_m=sol-A^{-1}(\Lambda_{m-1})$ for $m>0$, we derive an infinite sequence $\Lambda_0, \Lambda_1, \Lambda_2,...$ of solid subspaces of $\mathbb{F}^\mathbb{N}$ from the inputs $A$ and $\lambda$. For $A$ and $\lambda$ confined to certain classes, we …
Combining Euclidean And Adequate Rings, Huanyin Chen, Marjan Sheibani
Combining Euclidean And Adequate Rings, Huanyin Chen, Marjan Sheibani
Turkish Journal of Mathematics
We combine Euclidean and adequate rings, and introduce a new type of ring. A ring $R$ is called an E-adequate ring provided that for any $a,b\in R$ such that $aR+bR=R$ and $c\neq 0$ there exists $y\in R$ such that $(a+by,c)$ is an E-adequate pair. We shall prove that an E-adequate ring is an elementary divisor ring if and only if it is a Hermite ring. Elementary matrix reduction over such rings is also studied. We thereby generalize Domsha, Vasiunyk, and Zabavsky's theorems to a much wider class of rings.
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 …
$H$-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).