Approximation By Integral Functions Of Finite Degree In Variable Exponentlebesgue Spaces On The Real Axis,
2018
TÜBİTAK
Approximation By Integral Functions Of Finite Degree In Variable Exponentlebesgue Spaces On The Real Axis, Ramazan Akgün, Arash Ghorbanalizadeh
Turkish Journal of Mathematics
We obtain several inequalities of approximation by integral functions of finite degree in generalized Lebesgue spaces with variable exponent defined on the real axis. Among them are direct, inverse, and simultaneous estimates of approximation by integral functions of finite degree in $L^{p\left( \cdot \right)}.$ An equivalence of modulus of continuity with Peetre's $K$ -functional is established. A constructive characterization of Lipschitz class is also obtained.
On The Rank Of Transformation Semigroup $T_{(N,M)}$,
2018
TÜBİTAK
On The Rank Of Transformation Semigroup $T_{(N,M)}$, Kemal Toker, Hayrullah Ayik
Turkish Journal of Mathematics
Let $T_{n}$ and $S_{n}$ be the full transformation semigroup and the symmetric group on $X_{n}=\{1,\ldots,n\}$, respectively. For $n,m\in \mathbb{Z}^{+}$ with $m\le n-1$ let $$T_{(n,m)}=\{ \alpha \in T_{n} : X_{m} \alpha = X_{m}\} .$$ In this paper we research generating sets and the rank of $T_{(n,m)}$. In particular, we prove that $$rank(T_{(n,m)})=\left\{ \begin{array}{lll} 2 & \mbox{ if }\, (n,m)=(2,1) \mbox{ or }(3,2)\\ 3 & \mbox{ if }\, (n,m)=(3,1) \mbox{ or } 4\leq n \mbox{ and } m=n-1\\ 4 & \mbox{ if }\, 4\leq n \mbox{ and } 1\leq m\leq n-2. \end{array}\right. $$ for $1\leq m\leq n-1$.
On A Solvable Nonlinear Difference Equation Of Higher Order,
2018
TÜBİTAK
On A Solvable Nonlinear Difference Equation Of Higher Order, Durhasan Turgut Tollu, Yasi̇n Yazlik, Necati̇ Taşkara
Turkish Journal of Mathematics
In this paper we consider the following higher-order nonlinear difference equation $$ x_{n}=\alpha x_{n-k}+\frac{\delta x_{n-k}x_{n-\left( k+l\right) }}{\beta x_{n-\left( k+l\right) }+\gamma x_{n-l}},\ n\in \mathbb{N} _{0}, $$ where $k$ and $l$ are fixed natural numbers, and the parameters $\alpha $, $ \beta $, $\gamma $, $\delta $ and the initial values $x_{-i}$, $i=\overline{ 1,k+l}$, are real numbers such that $\beta ^{2}+\gamma ^{2}\neq 0$. We solve the above-mentioned equation in closed form and considerably extend some results in the literature. We also determine the asymptotic behavior of solutions and the forbidden set of the initial values using the obtained formulae for the case …
Regular $\Mathscr{D}$-Classes Of The Semigroup Of $N\Times N$ Tropical Matrices,
2018
TÜBİTAK
Regular $\Mathscr{D}$-Classes Of The Semigroup Of $N\Times N$ Tropical Matrices, Lin Yang
Turkish Journal of Mathematics
In this paper we give the characterizations of Green's relations $\mathscr{R}$, $\mathscr{L}$, and $\mathscr{D}$ on the set of matrices with entries in a tropical semiring. An $m\times n$ tropical matrix $A$ is called regular if there exists an $n\times m$ tropical matrix $X$ satisfying $AXA = A$. Furthermore, we study the regular $\mathscr{D}$-classes of the semigroup of all $n\times n$ tropical matrices under multiplication and give a partition of a nonsingular regular $\mathscr{D}$-class.
First Order Self-Adjoint Multipoint Quasi-Differential Operators,
2018
TÜBİTAK
First Order Self-Adjoint Multipoint Quasi-Differential Operators, Ruki̇ye Öztürk Mert, Bülent Yilmaz, Zameddi̇n İsmai̇lov
Turkish Journal of Mathematics
In this paper, using the Calkin-Gorbachuk method, the general form of all self-adjoint operators generated by first order linear singular multipoint quasi-differential expressions in the direct sum of weighted Hilbert spaces of vector functions has been found. Later on, the geometry of the spectrum set of these type extensions was researched.
Chordality Of Graphs Associated To Commutative Rings,
2018
TÜBİTAK
Chordality Of Graphs Associated To Commutative Rings, Ashkan Nikseresht
Turkish Journal of Mathematics
We investigate when different graphs associated to commutative rings are chordal. In particular, we characterize commutative rings $R$ with each of the following conditions: the total graph of $R$ is chordal; the total dot product or the zero-divisor dot product graph of $R$ is chordal; the comaximal graph of $R$ is chordal; $R$ is semilocal; and the unit graph or the Jacobson graph of $R$ is chordal. Moreover, we state an equivalent condition for the chordality of the zero-divisor graph of an indecomposable ring and classify decomposable rings that have a chordal zero-divisor graph.
Congruences Modulo 9 For Bipartitions Withdesignated Summands,
2018
TÜBİTAK
Congruences Modulo 9 For Bipartitions Withdesignated Summands, Robert Xiaojian Hao, Erin Yiying Shen
Turkish Journal of Mathematics
Andrews, Lewis, and Lovejoy studied arithmetic properties of partitions with designated summands that are defined on ordinary partitions by tagging exactly one part among parts with equal size. A bipartition of $n$ is an ordered pair of partitions $(\pi_1, \pi_2)$ with the sum of all of the parts being $n$. In this paper, we investigate arithmetic properties of bipartitions with designated summands. Let $PD_{-2}(n)$ denote the number of bipartitions of $n$ with designated summands. We establish several Ramanujan-like congruences and an infinite family of congruences modulo $9$ satisfied by $PD_{-2}(n)$.
Positive Solutions Of Neumann Problems For A Discrete System Coming From Models Of House Burglary,
2018
TÜBİTAK
Positive Solutions Of Neumann Problems For A Discrete System Coming From Models Of House Burglary, Tianlan Chen, Ruyun Ma, Yongwen Liang
Turkish Journal of Mathematics
We show existence results of positive solutions of Neumann problems for a discrete system: $$\aligned &\eta\Delta^2(A_{k-1}-A^0_{k-1})-A_{k}+A^0_{k}+N_kA_{k}=0,\ \ k\in[2, n-1]_\mathbb{Z},\\ &\Delta\big(\Delta N_{k-1}-2N_k\frac{\Delta A_{k-1}}{A_{k}}\big)-N_kA_{k}+A^1_{k}-A^0_{k}=0,\ \ k\in[2, n-1]_\mathbb{Z},\\ &\Delta A_{1}=0=\Delta A_{n-1},\ \ \Delta N_{1}=0=\Delta N_{n-1}, \endaligned $$ where the assumptions on $\eta,\ A_k^0$, and $A_k^1$ are motivated by some mathematics models for house burglary. Our results are based on the topological degree theory.
On The Type And Generators Of Monomial Curves,
2018
TÜBİTAK
On The Type And Generators Of Monomial Curves, Nguyen Thi Dung
Turkish Journal of Mathematics
Let $n_1, n_2,\ldots, n_d$ be positive integers and $H $ be the numerical semigroup generated by $n_1,n_2, \ldots, n_d$. Let $A:=k[H]:=k[t^{n_1}, t^{n_2},\ldots, t^{n_d}]\cong k[x_1,x_2,\ldots,x_d]/I$ be the numerical semigroup ring of $H $ over $k.$ In this paper we give a condition $(*)$ that implies that the minimal number of generators of the defining ideal $I$ is bounded explicitly by its type. As a consequence for semigroups with $d=4$ satisfying the condition $(*)$ we have $\mu ({\rm in}(I))\leq 2(t(H))+1$.
Some Subclasses Of Analytic Functions Of Complex Order,
2018
TÜBİTAK
Some Subclasses Of Analytic Functions Of Complex Order, Ni̇zami̇ Mustafa
Turkish Journal of Mathematics
In this paper, we introduce and investigate two new subclasses of analytic functions in the open unit disk in the complex plane. Several interesting properties of the functions belonging to these classes are examined. Here, sufficient, and necessary and sufficient, conditions for the functions belonging to these classes, respectively, are also given. Furthermore, various properties like order of starlikeness and radius of convexity of the subclasses of these classes and radii of starlikeness and convexity of these subclasses are examined.
Difference Uniqueness Theorems On Meromorphic Functions In Several Variables,
2018
TÜBİTAK
Difference Uniqueness Theorems On Meromorphic Functions In Several Variables, Zhixue Liu, Qingcai Zhang
Turkish Journal of Mathematics
In this paper, we mainly investigate the uniqueness problem on meromorphic functions in $\mathbb{C}^m$ sharing small functions with their difference operators or shifts, and we obtain some interesting results that act as some extensions of previous results from one complex variable to several complex variables.
Limit Behaviors Of Nonoscillatory Solutions Of Three-Dimensional Time Scale Systems,
2018
TÜBİTAK
Limit Behaviors Of Nonoscillatory Solutions Of Three-Dimensional Time Scale Systems, Özkan Öztürk, Raegan Higgins
Turkish Journal of Mathematics
In this article, we investigate the oscillatory behavior of a three-dimensional system of dynamic equations on an unbounded time scale. A time scale $\T$ is a nonempty closed subset of real numbers. An example is given to illustrate some of the results.
Olsen-Type Inequalities For The Generalized Commutator Of Multilinear Fractional Integrals,
2018
TÜBİTAK
Olsen-Type Inequalities For The Generalized Commutator Of Multilinear Fractional Integrals, Xiao Yu, Shanzhen Lu
Turkish Journal of Mathematics
In this paper, we study certain multilinear operators of fractional integral type defined by \[ I^{\vec{A}}_{\alpha}\vec{f}(x)=\int_{% %TCIMACRO{\U{211d} }% %BeginExpansion (\mathbb{R} %EndExpansion ^{n})^m}\frac{f_1(y_1)\cdots f_m(y_m)}{ (x-y_1,\cdots,x-y_m) ^{mn-\alpha+\sum\limits_{i=1}^m(N_i-1)}}\prod\limits_{i=1}^mR_{N_i}(A_i;x,y_i)d\vec{y}, \] where $0< \alpha
Delta-Shocks And Vacuums As Limits Of Flux Approximation For The Pressureless Type System,
2018
TÜBİTAK
Delta-Shocks And Vacuums As Limits Of Flux Approximation For The Pressureless Type System, Jinjing Liu, Hanchun Yang
Turkish Journal of Mathematics
In this paper, we investigate the phenomena of concentration and cavitation and the formation of delta-shocks and vacuum states in solutions of the pressureless type system with flux approximation. First, the Riemann problem of the pressureless type system with a flux perturbation is considered. A parameterized delta-shock and generalized constant density solution are obtained. Then we rigorously prove that, as the flux perturbation vanishes, they converge to the delta-shock and vacuum state of the pressureless type system, respectively. Secondly, by adding an artificial pressure term in the pressureless type system, we solve the Riemann problem of the system with a …
Quasinilpotents In Rings And Their Applications,
2018
TÜBİTAK
Quasinilpotents In Rings And Their Applications, Jian Cui
Turkish Journal of Mathematics
An element $a$ of an associative ring $R$ is said to be quasinilpotent if $1-ax$ is invertible for every $x\in R$ with $xa=ax$. Nilpotents and elements in the Jacobson radical of a ring are well-known examples of quasinilpotents. In this paper, properties and examples of quasinilpotents in a ring are provided, and the set of quasinilpotents is applied to characterize rings with some certain properties.
Natural Mates Of Frenet Curves In Euclidean 3-Space,
2018
TÜBİTAK
Natural Mates Of Frenet Curves In Euclidean 3-Space, Sharief Deshmukh, Bang-Yen Chen, Azeb Alghanemi
Turkish Journal of Mathematics
For each Frenet curve $\alpha $ in the Euclidean 3-space $\mathbb{E}^{3}$, there exists a unique unit speed curve $\beta$ tangent to the principal normal vector field of $\alpha $. We simply call this curve $\beta $ the natural mate of $\alpha$. The main purpose of this paper is to prove some relationships between a Frenet curve and its natural mate. In particular, we obtain some necessary and sufficient conditions for the natural mate of a Frenet curve to be a helix, a spherical curve, or a curve of constant curvature. Several applications of our main results are also presented.
Equidimensional Adic Eigenvarieties For Groups With Discrete Series,
2018
Illinois Mathematics and Science Academy
Equidimensional Adic Eigenvarieties For Groups With Discrete Series, Daniel Robert Gulotta '03
Doctoral Dissertations
We extend Urban's construction of eigenvarieties for reductive groups G such that G(R) has discrete series to include characteristic p points at the boundary of weight space. In order to perform this construction, we define a notion of "locally analytic" functions and distributions on a locally Qp-analytic manifold taking values in a complete Tate Zp-algebra in which p is not necessarily invertible. Our definition agrees with the definition of locally analytic distributions on p-adic Lie groups given by Johansson and Newton.
Abelian Subalgebras Of Maximal Dimension In Euclidean Lie Algebras,
2018
Wilfrid Laurier University
Abelian Subalgebras Of Maximal Dimension In Euclidean Lie Algebras, Mark Curro
Theses and Dissertations (Comprehensive)
In this paper we define, discuss and prove the uniqueness of the abelian subalgebra of maximal dimension of the Euclidean Lie algebra. We also construct a family of maximal abelian subalgebras and prove that they are maximal.
The Local And Semilocal Convergence Analysis Of New Newton-Like Iteration Methods,
2018
TÜBİTAK
The Local And Semilocal Convergence Analysis Of New Newton-Like Iteration Methods, Vatan Karakaya, Kadri̇ Doğan, Yunus Atalan, Nour El Houda Bouzara
Turkish Journal of Mathematics
The aim of this paper is to find new iterative Newton-like schemes inspired by the modified Newton iterative algorithm and prove that these iterations are faster than the existing ones in the literature. We further investigate their behavior and finally illustrate the results by numerical examples.
Strongly $Cm$-Semicommutative Rings,
2018
TÜBİTAK
Strongly $Cm$-Semicommutative Rings, Liang Zhao, Jiaqun Wei
Turkish Journal of Mathematics
We study the strongly semicommutative properties relative to a monoid crossed product. The concept of strongly $CM$-semicommutative rings is introduced and investigated. Many results related to semicommutative properties over polynomial rings, skew polynomial rings, monoid rings, and skew monoid rings are extended and unified.
