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2016

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Articles 991 - 1020 of 1329

Full-Text Articles in Mathematics

On $Le$-Semigroups, Niovi Kehayopulu Jan 2016

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.

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Existence And Nonexistence Of Sign-Changing Solutions To Elliptic Critical Equations, Mokhless Hammami, Houria Ismail Jan 2016

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 …

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Uniqueness Of $P(F)$ And $P[F]$, Kuldeep Singh Charak, Banarsi Lal Jan 2016

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$\ddot{\text{u}}$.

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Some Topological Properties Of The Spaces Of Almost Null Andalmost Convergent Double Sequences, Medi̇ne Yeşi̇lkayagi̇l, Feyzi̇ Başar Jan 2016

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.

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Generalizations Of 2-Absorbing Primaryideals Of Commutative Rings, Ayman Badawi, Ünsal Teki̇r, Emel Aslankarayi̇ği̇t Uğurlu, Gülşen Ulucak, Ece Yetki̇n Celi̇kel Jan 2016

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.

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Detection Of Coherent Structures In Flows, Klodiana Shkembi Jan 2016

Detection Of Coherent Structures In Flows, Klodiana Shkembi

Theses, Dissertations and Culminating Projects

In this work, we have developed an experimental flow tank that can produce realistic ocean-like flows, including multi-gyre flows. By generating controllable ocean-like flow fields, we can study the flows to gain a better understanding of ocean dynamics. In particular, we use particle image velocimetry and finite-time Lyapunov exponents to determine the location of the Lagrangian Coherent Structures that determine transport in complex fluid flows. This understanding is useful for designing control algorithms and for optimizing the use of autonomous vehicles operating in the stochastic and time-dependent ocean environment.

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Homogenization Of Stokes Systems With Periodic Coefficients, Shu Gu Jan 2016

Homogenization Of Stokes Systems With Periodic Coefficients, Shu Gu

Theses and Dissertations--Mathematics

In this dissertation we study the quantitative theory in homogenization of Stokes systems. We study uniform regularity estimates for a family of Stokes systems with rapidly oscillating periodic coefficients. We establish interior Lipschitz estimates for the velocity and L∞ estimates for the pressure as well as Liouville property for solutions in ℝd. We are able to obtain the boundary W{1,p} estimates in a bounded C1 domain for any 1 < p < ∞. We also study the convergence rates in L2 and H1 of Dirichlet and Neumann problems for Stokes systems with rapidly oscillating periodic coefficients, without any regularity assumptions on the coefficients.

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Alexander And Writhe Polynomials For Virtual Knots, Blake Mellor Jan 2016

Alexander And Writhe Polynomials For Virtual Knots, Blake Mellor

Mathematics, Statistics and Data Science Faculty Works

We give a new interpretation of the Alexander polynomial Δ0 for virtual knots due to Sawollek and Silver and Williams, and use it to show that, for any virtual knot, Δ0 determines the writhe polynomial of Cheng and Gao (equivalently, Kauffman's affine index polynomial). We also use it to define a second-order writhe polynomial, and give some applications.

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Generalized Local And Nonlocal Master Equations For Some Stochastic Processes, Yanping Ma Jan 2016

Generalized Local And Nonlocal Master Equations For Some Stochastic Processes, Yanping Ma

Mathematics, Statistics and Data Science Faculty Works

In this paper, we present a study on generalized local and nonlocal equations for some stochastic processes. By considering the net flux change in a region determined by the transition probability, we derive the master equation to describe the evolution of the probability density function. Some examples, such as classical Fokker-Planck equations, models for Lévy process, and stochastic coagulation equations, are provided as illustrations. A particular application is a consistent derivation of coupled dynamical systems for spatially inhomogeneous stochastic coagulation processes.

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A Characteristic Averaging Property Of The Catenary, Vincent Coll, Jeff Dodd Jan 2016

A Characteristic Averaging Property Of The Catenary, Vincent Coll, Jeff Dodd

Research, Publications & Creative Work

It is well-known that the catenary is characterized by an extremal centroidal condition: It is the shape of the curve whose centroid is the lowest among all curves having a prescribed length and specified endpoints. Here, we establish a broad characteristic averaging property of the centenary that yields two new centroidal characterizations.

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Hom-Lie 2-Superalgebras, Chunyue Wang, Qingcheng Zhang, Jizhu Nan Jan 2016

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.

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Highly Non-Concurrent Longest Paths In Lattices, Yasir Bashir, Faisal Nadeem, Ayesha Shabbir Jan 2016

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.

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Abundance Of $E$-Order-Preserving Transformation Semigroups, Lei Sun, Xuefeng Han Jan 2016

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

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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 Jan 2016

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 …

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Extension Of Refinement Rings, Rahman Bahmani Sangesari, Marjan Sheibani Abdulyousefi, Nahid Ashrafi Jan 2016

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.

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Parameterized Littlewood--Paley Operators And Their Commutators On Herz Spaces With Variable Exponents, Lijuan Wang, Shuangping Tao Jan 2016

Parameterized Littlewood--Paley Operators And Their Commutators On Herz Spaces With Variable Exponents, Lijuan Wang, Shuangping Tao

Turkish Journal of Mathematics

The aim of this paper is to deal with Littlewood--Paley operators with real parameters, including the parameterized Lusin area integrals and the parameterized Littlewood--Paley $g_{\lambda}^{\ast}$-functions, and their commutators on Herz spaces with two variable exponents $p(\cdot),~q(\cdot)$. By using the properties of the Lebesgue spaces with variable exponents, the boundedness of the parameterized Littlewood--Paley operators and their commutators generated respectively by BMO function and Lipschitz function is obtained on those Herz spaces.

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On The Twisted Modules For Finite Matrix Groups, Kübra Gül, Nurullah Ankaralioğlu Jan 2016

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}

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An Extension Of Cline''S Formula For A Generalized Drazin Inverse, Haifeng Lian, Qingping Zeng Jan 2016

An Extension Of Cline''S Formula For A Generalized Drazin Inverse, Haifeng Lian, Qingping Zeng

Turkish Journal of Mathematics

In this note we give an answer to a question recently posed by Zeng and Zhong, to note that Cline's formula for a generalized Drazin inverse extends to the case when $aba=aca$. Cline's formula for a pseudo Drazin inverse is also presented in this case.

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Quenching Behavior Of A Semilinear Reaction-Diffusion System With Singularboundary Condition, Burhan Selçuk Jan 2016

Quenching Behavior Of A Semilinear Reaction-Diffusion System With Singularboundary Condition, Burhan Selçuk

Turkish Journal of Mathematics

In this paper, we study the quenching behavior of the solution of a semilinear reaction-diffusion system with singular boundary condition. We first get a local exisence result. Then we prove that the solution quenches only on the right boundary in finite time and the time derivative blows up at the quenching time under certain conditions. Finally, we get lower bounds and upper bounds for quenching time.

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A Note On Gorenstein Projective Complexes, Bo Lu, Liu Zhongkui Jan 2016

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.

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Fixed Point Theory In Wc--Banach Algebras, Aref Jeribi, Bilel Krichen, Bilel Mefteh Jan 2016

Fixed Point Theory In Wc--Banach Algebras, Aref Jeribi, Bilel Krichen, Bilel Mefteh

Turkish Journal of Mathematics

In this paper, we will prove some fixed point theorems for the sum and the product of nonlinear weakly sequentially continuous operators acting on a WC--Banach algebra. Our results improve and correct some recent results given by Banas and Taoudi, and extend several earlier works using the condition $(\mathcal{P})$.

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Construction Of Biorthogonal Wavelet Packets On Local Fields Of Positive Characteristic, Firdous Ahmad Shah, Mohammad Younus Bhat Jan 2016

Construction Of Biorthogonal Wavelet Packets On Local Fields Of Positive Characteristic, Firdous Ahmad Shah, Mohammad Younus Bhat

Turkish Journal of Mathematics

Orthogonal wavelet packets lack symmetry, which is a much desired property in image and signal processing. The biorthogonal wavelet packets achieve symmetry where the orthogonality is replaced by biorthogonality. In the present paper, we construct biorthogonal wavelet packets on local fields of positive characteristic and investigate their properties by means of Fourier transforms. We also show how to obtain several new Riesz bases of the space $L^2(K)$ by constructing a series of subspaces of these wavelet packets. Finally, we provide algorithms for the decomposition and reconstruction using these biorthogonal wavelet packets.

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Solving An Initial Boundary Value Problem On Thesemiinfinite Interval, Feri̇he Atalan, Gusein Sh. Guseinov Jan 2016

Solving An Initial Boundary Value Problem On Thesemiinfinite Interval, Feri̇he Atalan, Gusein Sh. Guseinov

Turkish Journal of Mathematics

We explore the sign properties of eigenvalues and the basis properties of eigenvectors for a special quadratic matrix polynomial and use the results obtained to solve the corresponding linear system of differential equations on the half line subject to an initial condition at $t=0$ and a condition at $t=\infty$.

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The $Q$-Analogue Of The $E_{2;1}$-Transform And Its Applications, Ahmed Salem, Faruk Uçar Jan 2016

The $Q$-Analogue Of The $E_{2;1}$-Transform And Its Applications, Ahmed Salem, Faruk Uçar

Turkish Journal of Mathematics

In this paper, we introduce a new integral transform $\ _{q}\mathcal{E}_{2;1}$, which is the $q$-analogue of the $\mathcal{E}_{2;1}$-transform and can be regarded as a $\mathit{q}$-extension of the $\mathcal{E}_{2;1}$-transform. Some identities involving $~_{q}L_{2}$-transfom, $~_{q}\mathcal{L}_{2}$-transfom, and $\mathcal{P}_{q}$-transform are given. By making use of these identities and $\ _{q}\mathcal{E}_{2;1}$-transform, a new Parseval--Goldstein type theorem is obtained. Some examples are also given as an illustration of the main results presented here.

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A Note On Riesz Space Valued Measures, Neşet Özkan Tan Jan 2016

A Note On Riesz Space Valued Measures, Neşet Özkan Tan

Turkish Journal of Mathematics

In this paper, some properties of Riesz space valued measures that are defined on an algebra of sets are obtained. The question of under what conditions $oba(\mathcal{F},E)$ =$a(\mathcal{F},E)$ for a given Dedekind complete Riesz space $E$ is answered under natural conditions. The outer measure, which is generated by order bounded Riesz space valued measure, is obtained and its properties are investigated. The concept of hazy convergence that is valid for real valued signed measures is extended to Riesz space valued measures. The consequences of order convergence of $f:X\rightarrow E$, which implies hazy convergence, are given.

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Evaluation Of Spectrum Of 2-Periodic Tridiagonal-Sylvester Matrix, Emrah Kiliç, Talha Arikan Jan 2016

Evaluation Of Spectrum Of 2-Periodic Tridiagonal-Sylvester Matrix, Emrah Kiliç, Talha Arikan

Turkish Journal of Mathematics

The Sylvester matrix was first defined by JJ Sylvester. Some authors have studied the relationships between certain orthogonal polynomials and the determinant of the Sylvester matrix. Chu studied a generalization of the Sylvester matrix. In this paper, we introduce its $2$-periodic generalization. Then we compute its spectrum by left eigenvectors with a similarity trick.

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Notes On Cotorsion Dimension Of Hopf--Galois Extensions, Xiaoyan Zhou, Min Wei Jan 2016

Notes On Cotorsion Dimension Of Hopf--Galois Extensions, Xiaoyan Zhou, Min Wei

Turkish Journal of Mathematics

Let $H$ be a finite dimensional Hopf algebra over a field $k$ and $A/B$ be a right $H$-Galois extension. In this note the relationship of cotorsion dimensions between $A$ and $B$ will be studied. We prove that $\mbox{r.cot.D}(A)\leq\mbox{r.cot.D}(B)+\mbox{l.D}(H)$. Moreover, we give some sufficient conditions for which $\mbox{r.cot.D}(A)=\mbox{r.cot.D}(B)$. As applications, we obtain some results about cotorsion dimension of the smash product.

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Shellability Of Simplicial Complexes And Simplicial Complexes With The Free Vertex Property, Guangjun Zhu Jan 2016

Shellability Of Simplicial Complexes And Simplicial Complexes With The Free Vertex Property, Guangjun Zhu

Turkish Journal of Mathematics

To a simplicial complex $\Delta$, we associate a square-free monomial ideal $\mathcal{F}(\Delta)$ in the polynomial ring generated by its facet over a field. Furthermore, we could consider $\mathcal{F}(\Delta)$ as the Stanley--Reisner ideal of another simplicial complex $\delta_{N}(\mathcal{F}(\Delta))$ from facet ideal theory and Stanley--Reisner theory. In this paper, we determine what families of simplicial complexes $\Delta$ have the property that their Stanley--Reisner complexes $\delta_{N}(\mathcal{F}(\Delta))$ are shellable. Furthermore, we show that the simplicial complex with the free vertex property is sequentially Cohen--Macaulay. This result gives a new proof for a result of Faridi on the sequentially Cohen--Macaulayness of simplicial forests.

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Zero-Divisor Graph Of Matrix Rings And Hurwitz Rings, Ci̇hat Abdi̇oğlu Jan 2016

Zero-Divisor Graph Of Matrix Rings And Hurwitz Rings, Ci̇hat Abdi̇oğlu

Turkish Journal of Mathematics

Let $R$ be ring a with identity $1\neq 0$, $S_n(R)$ be a subring of the ring $T_n(R)$ of $n\times n$ upper triangular matrices over $R$, and $H_n(R)$ be the ring defined in the next section using $HR$, the ring of the Hurwitz series over $R$. In this paper, we introduce the zero-divisor graph $\overset{\rightarrow}{\Gamma}(S_n(R))$ and its underlying undirected graph $\Gamma(S_n(R))$ of $S_n(R)$. We give some basic graph theory properties of $\overset{\rightarrow}{\Gamma}(S_n(R))$. Moreover, we obtain some results of the zero-divisor directed graph of $\overset{\rightarrow}{\Gamma}(H_n(R))$.

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Rectifying Curves In The $N$-Dimensional Euclidean Space, Stijn Cambie, Wendy Goemans, Iris Van Den Bussche Jan 2016

Rectifying Curves In The $N$-Dimensional Euclidean Space, Stijn Cambie, Wendy Goemans, Iris Van Den Bussche

Turkish Journal of Mathematics

In this article, we study the so-called rectifying curves in an arbitrary dimensional Euclidean space. A curve is said to be a rectifying curve if, in all points of the curve, the orthogonal complement of its normal vector contains a fixed point. If this fixed point is chosen to be the origin, then this condition is equivalent to saying that the position vector of the curve in every point lies in the orthogonal complement of its normal vector. Here we characterize rectifying curves in the $n$-dimensional Euclidean space in different ways: using conditions on their curvatures, with an expression for …

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