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Articles 1 - 30 of 223
Full-Text Articles in Physical Sciences and Mathematics
Harmonic Numbers Associated With Inversion Numbers In Terms Of Determinants, Takao Komatsu, Amalia Pizarro-Madariaga
Harmonic Numbers Associated With Inversion Numbers In Terms Of Determinants, Takao Komatsu, Amalia Pizarro-Madariaga
Turkish Journal of Mathematics
It has been known that some numbers, including Bernoulli, Cauchy, and Euler numbers, have such corresponding numbers in terms of determinants of Hessenberg matrices. There exist inversion relations between the original numbers and the corresponding numbers. In this paper, we introduce the numbers related to harmonic numbers in determinants. We also give several of their arithmetical and/or combinatorial properties and applications. These concepts can be generalized in the case of hyperharmonic numbers.
On The Cover Ideals Of Chordal Graphs, Nursel Erey
On The Cover Ideals Of Chordal Graphs, Nursel Erey
Turkish Journal of Mathematics
The independence complex of a chordal graph is known to be shellable which is equivalent to the fact that cover ideal of a chordal graph has linear quotients. We use this result to obtain recursive formulas for the Betti numbers of cover ideals of chordal graphs. Moreover, we give a new proof of such result which yields different shellings of the independence complex.
Ricci-Yamabe Maps For Riemannian Flows And Their Volume Variation And Volume Entropy, Si̇nem Güler, Mircea Crasmareanu
Ricci-Yamabe Maps For Riemannian Flows And Their Volume Variation And Volume Entropy, Si̇nem Güler, Mircea Crasmareanu
Turkish Journal of Mathematics
The aim of this short note is to produce new examples of geometrical flows associated to a given Riemannian flow $g(t)$. The considered flow in covariant symmetric $2$-tensor fields will be called Ricci-Yamabe map since it involves a scalar combination of Ricci tensor and scalar curvature of $g(t)$. Due to the signs of considered scalars the Ricci-Yamabe flow can be also a Riemannian or semi-Riemannian or singular Riemannian flow. We study the associated function of volume variation as well as the volume entropy. Finally, since the two-dimensional case was the most commonly addressed situation we express the Ricci flow equation …
On Congruences For $Q$-Analogues Of Ballot Numbers, Si̇bel Koparal
On Congruences For $Q$-Analogues Of Ballot Numbers, Si̇bel Koparal
Turkish Journal of Mathematics
In this paper, we examine some congruences with $q$-analogues of ballot numbers. For example, for $n>1$ and $% d=0,1,...,n-1$, \begin{eqnarray*} &&\sum\limits_{k=1}^{n-d}q^{k}B_{k,d}^{q}\equiv -2+\left( -1\right) ^{n-d}\left( \frac{n-d+1}{3}\right) q^{-\frac{1}{3}\binom{n-d}{2}}-\left( \frac{n-d-1% }{3}\right) q^{d+1-\frac{1}{3}\binom{n-d-2}{2}} \pmod{\Phi _{n}\left( q\right)} , \end{eqnarray*}% with the Legendre symbol $\left( \frac{.}{3}\right) ,~$the$~q$-analogue of ballot number $B_{n,d}^{q}$, and the $n$th cyclotomic polynomial $% \Phi _{n}\left( q\right) $.
Zeros Of The Extended Selberg Class Zeta-Functions And Of Their Derivatives, Ramunas Garunkstis
Zeros Of The Extended Selberg Class Zeta-Functions And Of Their Derivatives, Ramunas Garunkstis
Turkish Journal of Mathematics
Levinson and Montgomery proved that the Riemann zeta-function ζ(s) and its derivative have approximately the same number of nonreal zeros left of the critical line. Spira showed that ζ'(1/2+it) = 0 implies that ζ(1/2+it) = 0. Here we obtain that in small areas located to the left of the critical line and near it the functions ζ(s) and ζ'(s) have the same number of zeros. We prove our result for more general zeta-functions from the extended Selberg class S. We also consider zero trajectories of a certain family of zeta-functions from S.
Inverse Problem For Sturm-Liouville Differential Operators With Two Constant Delays, Mohammad Shahriari
Inverse Problem For Sturm-Liouville Differential Operators With Two Constant Delays, Mohammad Shahriari
Turkish Journal of Mathematics
In this manuscript, we study nonself-adjoint second-order differential operators with two constant delays. We investigate the properties of the spectral characteristics and the inverse problem of recovering operators from their spectra. An inverse spectral problem is studied of recovering the potential from spectra of two boundary value problems with one common boundary condition. The uniqueness theorem is proved for this inverse problem.
On The Divisors Of Shifted Primes, Jean Marie De Koninck, Imre Katai
On The Divisors Of Shifted Primes, Jean Marie De Koninck, Imre Katai
Turkish Journal of Mathematics
Let $\tau(n)$ stand for the number of positive divisors of $n$. Given an additive function $f$ and a real number $\alpha\in [0,1)$, let $\displaystyle{h_n(\alpha):= \frac 1{\tau(n)} \sum_{d\mid n \atop \{f(d)\}
Longest Increasing Subsequences In Involutions Avoiding Patterns Of Length Three, Toufi̇k Mansour, Gökhan Yildirim
Longest Increasing Subsequences In Involutions Avoiding Patterns Of Length Three, Toufi̇k Mansour, Gökhan Yildirim
Turkish Journal of Mathematics
We study the longest increasing subsequences in random involutions that avoid the patterns of length three under the uniform probability distribution. We determine the exact and asymptotic formulas for the average length of the longest increasing subsequences for such permutation classes.
Relative Ranks Of Some Partial Transformation Semigroups, Ebru Yi̇ği̇t, Gonca Ayik, Hayrullah Ayik
Relative Ranks Of Some Partial Transformation Semigroups, Ebru Yi̇ği̇t, Gonca Ayik, Hayrullah Ayik
Turkish Journal of Mathematics
Let $P_{n}$, $T_{n}$, $I_{n}$, and $S_{n}$ be the partial transformation semigroup, the (full) transformation semigroup, the symmetric inverse semigroup, and the symmetric group on $X_{n}=\{1,\ldots ,n \}$, respectively. For $1\leq r\leq n-1$, let $PK_{n,r}$ be the subsemigroup consisting $\alpha\in P_{n}$ such that $ \im\alpha \leq r$ and let $SPK_{n,r}=PK_{n,r}\setminus T_{n}$. In this paper, we first examine the subsemigroup $I_{n,r}=I_{n}\cup PK_{n,r}$ and we find the necessary and sufficient conditions for any nonempty subset of $PK_{n,r}$ to be a (minimal) relative generating set of the subsemigroup $I_{n,r}$ modulo $I_{n}$. Then we examine the subsemigroups $PI_{n,r}= SI_{n}\cup PK_{n,r}$ and $SI_{n,r}=SI_{n}\cup SPK_{n,r}$ for $1\leq …
Some Classes Of Harmonic Mappings With Analytic Part Defined By Subordination, Shuhai Li, Ma Li-Na, Ao En, Tang Huo
Some Classes Of Harmonic Mappings With Analytic Part Defined By Subordination, Shuhai Li, Ma Li-Na, Ao En, Tang Huo
Turkish Journal of Mathematics
Let $S_{H}$ be the class of functions $f=h+\bar{g}$ that are harmonic univalent and sense-preserving in the open unit disk $\mathbb{U}=\{z\in \mathbb{C}: z
Some Operator Inequalities Associated With Kantorovich And Hölder-Mccarthyinequalities And Their Applications, Hamdullah Başaran, Mehmet Gürdal, Ayşe Nur Güncan
Some Operator Inequalities Associated With Kantorovich And Hölder-Mccarthyinequalities And Their Applications, Hamdullah Başaran, Mehmet Gürdal, Ayşe Nur Güncan
Turkish Journal of Mathematics
We prove analogs of certain operator inequalities, including Hölder-McCarthy inequality, Kantorovich inequality, and Heinz-Kato inequality, for positive operators on the Hilbert space in terms of the Berezin symbols and the Berezin number of operators on the reproducing kernel Hilbert space.
Curves Over Finite Fields And Permutations Of The Form $X^K-\Gamma \Mathrm{Tr}(X)$, Nurdagül Anbar Meidl
Curves Over Finite Fields And Permutations Of The Form $X^K-\Gamma \Mathrm{Tr}(X)$, Nurdagül Anbar Meidl
Turkish Journal of Mathematics
We consider the polynomials of the form $P(x)=x^k-\gamma \mathrm{Tr}(x)$ over $\mathbb{F}_{q^n}$ for $n\geq 2$. We show that $P(x)$ is not a permutation of $\mathbb{F}_{q^n}$ in the case $\gcd(k, q^n-1)>1$. Our proof uses an absolutely irreducible curve over $\mathbb{F}_{q^n}$ and the number of rational points on it.
Nonnegative Integer Solutions Of The Equation $F_{N}-F_{M}=5^{A}$, Fati̇h Erduvan, Refi̇k Keski̇n
Nonnegative Integer Solutions Of The Equation $F_{N}-F_{M}=5^{A}$, Fati̇h Erduvan, Refi̇k Keski̇n
Turkish Journal of Mathematics
In this study, we solve the Diophantine equation in the title in nonnegative integers $m,n,$ and $a$. The solutions are given by $F_{1}-F_{0}=F_{2}-F_{0}=F_{3}-F_{2}=F_{3}-F_{1}=F_{4}-F_{3}=5^{0}$ and $F_{5}-F_{0}=F_{6}-F_{4}=F_{7}-F_{6}=5.$ Then we give a conjecture that says that if $a\geq 2$ and $p>7$ is prime, then the equation $F_{n}-F_{m}=p^{a}$ has no solutions in nonnegative integers $m,n.$
On Oscillatory And Nonoscillatory Behavior Of Solutions For A Class Of Fractional Orderdifferential Equations, Arjumand Seemab, Mujeeb Ur Rehman
On Oscillatory And Nonoscillatory Behavior Of Solutions For A Class Of Fractional Orderdifferential Equations, Arjumand Seemab, Mujeeb Ur Rehman
Turkish Journal of Mathematics
This work aims to develop oscillation criterion and asymptotic behavior of solutions for a class of fractional order differential equation: $D^{\alpha}_{0}u(t)+\lambda u(t)=f(t,u(t)),~~t> 0,$ $D^{\alpha-1}_{0}u(t) _{t=0}=u_{0},~~\lim_{t\to 0}J^{2-\alpha}_{0}u(t)=u_{1}$ where $D^{\alpha}_{0}$ denotes the Riemann--Liouville differential operator of order $\alpha$ with $1
Star-Likeness Associated With The Exponential Function, Adiba Naz, Sumit Nagpal, V. Ravichandran
Star-Likeness Associated With The Exponential Function, Adiba Naz, Sumit Nagpal, V. Ravichandran
Turkish Journal of Mathematics
Given a domain $\Omega$ in the complex plane $\mathbb{C}$ and a univalent function $q$ defined in an open unit disk $\mathbb{D}$ with nice boundary behaviour, Miller and Mocanu studied the class of admissible functions $\Psi(\Omega,q)$ so that the differential subordination $\psi(p(z),zp'(z),z^2p''(z);z)\prec h(z)$ implies $p(z)\prec q(z)$, where $p$ is an analytic function in $\mathbb{D}$ with $p(0)=1$, $\psi:\mathbb{C}^3\times \mathbb{D}\to\mathbb{C}$ and $\Omega=h(\mathbb{D})$. This paper investigates the properties of this class for $q(z)=e^z$. As application, several sufficient conditions for normalized analytic functions $f$ to be in the subclass of star-like functions associated with the exponential function are obtained.
Value Sets Of Folding Polynomials Over Finite Fields, Ömer Küçüksakalli
Value Sets Of Folding Polynomials Over Finite Fields, Ömer Küçüksakalli
Turkish Journal of Mathematics
Let $k$ be a positive integer that is relatively prime to the order of the Weyl group of a semisimple complex Lie algebra $\mf{g}$. We find the cardinality of the value sets of the folding polynomials $P_\mf{g}^k(\mb{x}) \in \Z[\mb{x}]$ of arbitrary rank $n \geq 1$, over finite fields. We achieve this by using a characterization of their fixed points in terms of exponential sums.
A New Comprehensive Subclass Of Analytic Bi-Close-To-Convex Functions, Serap Bulut
A New Comprehensive Subclass Of Analytic Bi-Close-To-Convex Functions, Serap Bulut
Turkish Journal of Mathematics
In a very recent work, Şeker and Sümer Eker [On subclasses of bi-close-to-convex functions related to the odd-starlike functions. Palestine Journal of Mathematics 2017; 6: 215-221] defined two subclasses of analytic bi-close-to-convex functions related to the odd-starlike functions in the open unit disk $\mathbb{U}$. The main purpose of this paper is to generalize and improve the results of Şeker and Sümer Eker (in the aforementioned study) defining a comprehensive subclass of bi-close-to-convex functions. Also, we investigate the Fekete-Szegö type coefficient bounds for functions belonging to this new class.
Generalized Helices In Three-Dimensional Lie Groups, Alexander Yampolsky, Anastasiya Opariy
Generalized Helices In Three-Dimensional Lie Groups, Alexander Yampolsky, Anastasiya Opariy
Turkish Journal of Mathematics
We introduce three types of helices in three-dimensional Lie groups with left-invariant metric and give their geometrical description similar to that of Lancret. We generalize the results known for the case of three-dimensional Lie groups with bi-invariant metric.
Uncountably Many Nonoscillatory Bounded Solutions To Second-Order Nonlinear Neutral Dynamic Equations, Magdalena Nockowska Rosiak
Uncountably Many Nonoscillatory Bounded Solutions To Second-Order Nonlinear Neutral Dynamic Equations, Magdalena Nockowska Rosiak
Turkish Journal of Mathematics
This work is devoted to the study of the existence of uncountably many nonoscillatory bounded solutions to second-order nonlinear neutral dynamic equations by means of the Darbo fixed point theorem. We construct assumptions without sign conditions on the nonlinear part of the equation. Moreover, we prove the necessary condition for the existence of an asymptotically zero solution to the problem under consideration.
Cremona Transformations Of Plane Configurations Of 6 Points, Remzi̇ye Arzu Zabun
Cremona Transformations Of Plane Configurations Of 6 Points, Remzi̇ye Arzu Zabun
Turkish Journal of Mathematics
We analyze how a set of 6 points of $\Rp 2$ in general position changes under quadratic Cremona transformations based at triples of points of the given six. As an application, we give an alternative approach to determining the deformation types (i.e. icosahedral, bipartite, tripartite and hexagonal) of 36 real Schlafli double sixes on any nonsingular real cubic surface performed by Segre.
Basicity Of A System Of Exponents With A Piecewise Linear Phase In Morrey-Type Spaces, Bilal Bilalov, Fidan Seyidova
Basicity Of A System Of Exponents With A Piecewise Linear Phase In Morrey-Type Spaces, Bilal Bilalov, Fidan Seyidova
Turkish Journal of Mathematics
In this paper a perturbed system of exponents with a piecewise linear phase depending on two real parameters is considered. The sufficient conditions for these parameters are found, under which the considered system of exponents is complete, minimal, or it forms a basis for a Morrey-type space.
On Uniformly $Pr$-Ideals In Commutative Rings, Rabi̇a Nagehan Üregen
On Uniformly $Pr$-Ideals In Commutative Rings, Rabi̇a Nagehan Üregen
Turkish Journal of Mathematics
Let $R\ $be a commutative ring with nonzero identity and $I\ $a proper ideal of $R.\ $Then $I\ $is called a uniformly $pr$-ideal if there exists $N\in% \mathbb{N} $ such that $ab\in I\ $with $ann(a)=0\ $then $b^{N}\in I.\ $We say that the smallest $N\in% \mathbb{N} $ is called order of $I\ $and denoted by $ord_{R}(I)=N.\ $In this paper, we give some examples and characterizations of this new class of ideals.
Fekete-Szegö Problem For A General Subclass Of Analytic Functions, Nesli̇han Uyanik
Fekete-Szegö Problem For A General Subclass Of Analytic Functions, Nesli̇han Uyanik
Turkish Journal of Mathematics
In this present investigation, we introduced a certain subclass of starlike and convex functions of complex order $b$, using a linear multiplier differential operator $D_{\lambda ,\mu }^{m}f(z)$. For this class, the Fekete-Szegö problem is completely solved. Various new special cases are considered.
Radii Of Starlikeness And Convexity Of $Q$-Mittag-Leffler Functions, Evri̇m Toklu
Radii Of Starlikeness And Convexity Of $Q$-Mittag-Leffler Functions, Evri̇m Toklu
Turkish Journal of Mathematics
In this paper we deal with the radii of starlikeness and convexity of the $q$-Mittag-Leffler function for three different kinds of normalization by making use of their Hadamard factorization in such a way that the resulting functions are analytic in the unit disk of the complex plane. By applying Euler-Rayleigh inequalities for the first positive zeros of these functions tight lower and upper bounds for the radii of starlikeness of these functions are obtained. The Laguerre-P\'olya class of real entire functions plays a pivotal role in this investigation.
The Intrinsic Metric And Geodesics On The Sierpinski Gasket Sg(3), Yunus Özdemi̇r
The Intrinsic Metric And Geodesics On The Sierpinski Gasket Sg(3), Yunus Özdemi̇r
Turkish Journal of Mathematics
We give an explicit expression for the intrinsic metric on the Sierpinski gasket SG(3) (the mod-3 Sierpinski gasket) via code representation of its points. We also investigate the geodesics of SG(3) and determine the number of geodesics between two points.
On The Regularity Of The Solution Map Of The Euler-Poisson System, Hasan İnci̇
On The Regularity Of The Solution Map Of The Euler-Poisson System, Hasan İnci̇
Turkish Journal of Mathematics
In this paper we consider the Euler--Poisson system (describing a plasma consisting of positive ions with a negligible temperature and massless electrons in thermodynamical equilibrium) on the Sobolev spaces $H^s(\mathbb{R}^3)$, $s > 5/2$. Using a geometric approach we show that for any time $T > 0$ the corresponding solution map, $(\rho_0,u_0) \mapsto (\rho(T),u(T))$, is nowhere locally uniformly continuous. On the other hand it turns out that the trajectories of the ions are analytic curves in $\mathbb{R}^3$.
A Variational Study On A Natural Hamiltonian For Curves, Gözde Özkan Tükel
A Variational Study On A Natural Hamiltonian For Curves, Gözde Özkan Tükel
Turkish Journal of Mathematics
A variational study of finding critical points of the total squared torsion functional for curves in Euclidean 3-spaces is presented. Critical points of this functional also known as one of the natural Hamiltonians of curves are characterized by two Euler-Lagrange equations in terms of curvature and torsion of a curve. To solve these balance equations, the curvature of the critical curve is expressed by its torsion so that equations are completely solved by quadratures. Then two Killing fields along the critical curve are found for integrating the structural equations of the critical curve and this curve is expressed by quadratures …
On A Pair Of Ramanujan's Modular Equations And $P$-$Q$ Theta Functions Of Level 35, K. R. Vasuki, Anusha T
On A Pair Of Ramanujan's Modular Equations And $P$-$Q$ Theta Functions Of Level 35, K. R. Vasuki, Anusha T
Turkish Journal of Mathematics
S. Ramanujan recorded several modular equations and $P$-$Q$ theta function identities in his notebooks and lost notebook without recording the proofs. In this paper, we provide an elementary proof of two modular equations and two $P$-$Q$ theta function identities of level 35, which have been proved by B.C. Berndt using the theory of modular forms.
Degenerate Maximal Hyponormal Differential Operators For The First Order, Meltem Sertbaş, Fati̇h Yilmaz
Degenerate Maximal Hyponormal Differential Operators For The First Order, Meltem Sertbaş, Fati̇h Yilmaz
Turkish Journal of Mathematics
In this study, all maximal hyponormal extensions are given for the degenerate first order in the Hilbert space of vector-functions on a finite interval. The extensions are defined in terms of the boundary values. The structure of the spectrum of the maximal hyponormal extensions is also investigated.
On The Starlikeness Of P-Valent Functions, Mamoru Nunokawa, Nak Eun Cho, Oh Sang Kwon, Janusz Sokol
On The Starlikeness Of P-Valent Functions, Mamoru Nunokawa, Nak Eun Cho, Oh Sang Kwon, Janusz Sokol
Turkish Journal of Mathematics
For an analytic function in open unit disk $\mathbb{D}$, we consider the $p$-valent analogue of the Noshiro-Warschawski univalence condition. We apply the Fejér-Riesz inequality to establish some sufficient conditions for functions to be $p$-valent or to be a Bazilevič function or to be in some other classes.