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Full-Text Articles in Physical Sciences and Mathematics
Proximality And Transitivity In Relation To Points That Are Asymptotic To Themselves, Karol Gryszka
Proximality And Transitivity In Relation To Points That Are Asymptotic To Themselves, Karol Gryszka
Turkish Journal of Mathematics
We discuss dynamical systems that exhibit at least one weakly asymptotically periodic point. In the general case we prove that the system becomes trivial (it is either a periodic point or a fixed point) provided it is equicontinuous and transitive. This result can be used to provide a simple characterization of periodic points in transitive systems. We also discuss systems whose orbits are both proximal and weakly asymptotically periodic. As a result, we obtain a more general tool to detect mutual dynamics between two close orbits which need not be bounded (or have the empty limit set).
Some Congruences With $Q-$Binomial Sums, Neşe Ömür, Zehra Betül Gür, Si̇bel Koparal, Lai̇d Elkhiri
Some Congruences With $Q-$Binomial Sums, Neşe Ömür, Zehra Betül Gür, Si̇bel Koparal, Lai̇d Elkhiri
Turkish Journal of Mathematics
In this paper, using some combinatorial identities and congruences involving $q-$harmonic numbers, we establish congruences that for any odd prime $p$ and any positive integer $\alpha$,% \begin{equation*} \text{ }\sum\limits_{k=1 \pmod{2}}^{p-1}(-1)^{nk}\frac{% q^{-\alpha npk+ n\tbinom{k+1}{2}+2k}}{[k]_{q}}{\alpha p-1 \brack k}_{q}^{n} \pmod{[p]_{q}^{2}} , \end{equation*}% and \begin{equation*} \sum\limits_{k=1 \pmod{2}}^{p-1}(-1)^{nk}q^{-\alpha npk+ n\tbinom{k+1}{2}+k}{\alpha p-1 \brack k}_{q}^{n}% \widetilde{H}_{k}(q)\pmod{[p]_{q}^{2}} ,\text{ } \end{equation*}% where $n$ is any integer.
Operator Index Of A Nonsingular Algebraic Curve, Anar Dosi̇
Operator Index Of A Nonsingular Algebraic Curve, Anar Dosi̇
Turkish Journal of Mathematics
The present paper is devoted to a scheme-theoretic analog of the Fredholm theory. The continuity of the index function over the coordinate ring of an algebraic variety is investigated. It turns out that the index is closely related to the filtered topology given by finite products of maximal ideals. We prove that a variety over a field possesses the index function on nonzero elements of its coordinate ring iff it is an algebraic curve. In this case, the index is obtained by means of the multiplicity function from its normalization if the ground field is algebraically closed.
On The Existence Of $6$-Cycles For Some Families Of Difference Equations Of Third Order, Antonio Linero Bas, Daniel Nieves Roldán
On The Existence Of $6$-Cycles For Some Families Of Difference Equations Of Third Order, Antonio Linero Bas, Daniel Nieves Roldán
Turkish Journal of Mathematics
We prove that there are no $6$-cycles of the form $x_{n+3}=x_i f(x_j,x_k),$ with $i,j,k\in\{n,n+1,n+2\}$ pairwise distinct, whenever $f:(0,\infty)\times (0,\infty)\rightarrow (0,\infty)$ is a continuous symmetric function, that is, $f(x,y)=f(y,x)$, for all $x,y>0$. Moreover, we obtain all the $6$-cycles of potential form and present some open questions relative to the search of $p$-cycles whenever symmetry does not hold.
Inequalities Involving General Fractional Integrals Of P-Convex Functions, İlknur Yeşi̇lce Işik, Gülteki̇n Tinaztepe, Serap Kemali̇, Gabi̇l Adi̇lov
Inequalities Involving General Fractional Integrals Of P-Convex Functions, İlknur Yeşi̇lce Işik, Gülteki̇n Tinaztepe, Serap Kemali̇, Gabi̇l Adi̇lov
Turkish Journal of Mathematics
The Hermite-Hadamard type inequalities involving fractional integral operations for p-convex functions with respect to another function are studied. Then, the inequalities via Riemann-Liouville and Hadamard fractional integrals are presented specially. Using the obtained results, some inequality relations among special functions including beta and incomplete beta functions, gamma and incomplete gamma functions, and hypergeometric functions are presented.
Dynamical Complexity Of A Predator-Prey Model With A Prey Refuge And Allee Effect, Jianping Gao, Jianghong Zhang, Wenyan Lian
Dynamical Complexity Of A Predator-Prey Model With A Prey Refuge And Allee Effect, Jianping Gao, Jianghong Zhang, Wenyan Lian
Turkish Journal of Mathematics
We consider a predator-prey model with a non-monotonic functional response encompassing a prey refuge and a strong Allee effect on the prey. The multiple existence and stability of interior equilibria are investigated. The bifurcation analysis shows this model can exhibit numerous kinds of bifurcations (e.g., saddle-node, Hopf-Andronov and Bogdanov-Takens bifurcations). It is found that there exist diverse parameter values for which the model exhibits a limit cycle, a homoclinic orbit, and even many heteroclinic curves. The results obtained reveal the prey refuge in the model brings rich dynamics and makes the system more sensitive to parameter values. The main purpose …
Adjunction Greatest Element To Ordered Hypersemigroups, Niovi Kehayopulu
Adjunction Greatest Element To Ordered Hypersemigroups, Niovi Kehayopulu
Turkish Journal of Mathematics
As a continuation of the paper "Adjunction Identity to Hypersemigroup" in Turk J Math 2022; 46 (7): 2834--2853, it has been proved here that the adjunction of a greatest element to an ordered hypersemigroup is actually an embedding problem. The concept of pseudoideal has been introduced and has been proved that for each ordered hypersemigroup $S$ an ordered hypersemigroup $V$ having a greatest element ($poe$-hypersemigroup) can be constructed in such a way that there exists a pseudoideal $T$ of $S$ such that $S$ is isomorphic to $T$. If $S$ does not have a greatest element, then this can be regarded …
On The Eigenstructure Of The $Q$-Durrmeyer Operators, Övgü Gürel Yilmaz
On The Eigenstructure Of The $Q$-Durrmeyer Operators, Övgü Gürel Yilmaz
Turkish Journal of Mathematics
The purpose of this paper is to establish the eigenvalues and the eigenfunctions of both the $q$-Durrmeyer operators $D_{n,q}$ and the limit $q$-Durrmeyer operators $D_{\infty,q}$ introduced by V. Gupta in the case 0<$q$<1. All moments for $D_{n,q}$ and $D_{\infty,q}$ are provided. The coefficients for the eigenfunctions of the operators are explicitly derived and the eigenfunctions of these operators are illustrated by graphical examples.
Higher Topological Complexity Of A Map, Cesar Augusto Ipanaque Zapata, Jesús González
Higher Topological Complexity Of A Map, Cesar Augusto Ipanaque Zapata, Jesús González
Turkish Journal of Mathematics
The higher topological complexity of a space $X$, $\text{TC}_r(X)$, $r=2,3,\ldots$, and the topological complexity of a map $f$, $\text{TC}(f)$, have been introduced by Rudyak and Pavesiç, respectively, as natural extensions of Farber's topological complexity of a space. In this paper we introduce a notion of higher topological complexity of a map $f$, $\text{TC}_{r,s}(f)$, for $1\leq s\leq r\geq2$, which simultaneously extends Rudyak's and Pavesiç notions. Our unified concept is relevant in the $r$-multitasking motion planning problem associated to a robot devise when the forward kinematics map plays a role in $s$ prescribed stages of the motion task. We study the homotopy …
Operators Affiliated To Banach Lattice Properties And Their Enveloping Norms, Eduard Emelyanov, Svetlana Gorokhova
Operators Affiliated To Banach Lattice Properties And Their Enveloping Norms, Eduard Emelyanov, Svetlana Gorokhova
Turkish Journal of Mathematics
Several recent papers were devoted to various modifications of limited, Grothendieck, and Dunford-Pettis operators, etc., through involving the Banach lattice structure. In the present paper, it is shown that many of these operators appear as operators affiliated to well-known properties of Banach lattices, like the disjoint (dual) Schur property, the disjoint Grothendieck property, the property (d), the sequential w$^\ast$-continuity of the lattice operations, etc. We also introduce new classes of operators such as the s-GPP-operators, s-BDP-operators, and bi-sP-operators. It is proved that the spaces consisting of regular versions of the above-mentioned operators are all the Banach spaces. The domination problem …
Extended Calculus On ${\Cal O}({\Mathbb C}_{H}^{1\Vert1})$, Sali̇h Çeli̇k
Extended Calculus On ${\Cal O}({\Mathbb C}_{H}^{1\Vert1})$, Sali̇h Çeli̇k
Turkish Journal of Mathematics
We give an extended calculus over the function algebra on $h$-deformed superplane. For this, we extend the $(h_1,h_2)$-deformed differential calculus on the $h$-deformed superplane by adding inner derivations. We reformulate the results with an $R$-matrix and present the tensor product realization of the wedge product. We also discuss Cartan calculus via a contraction.
Fractional Semilinear Neumann Problem With Critical Nonlinearity, Zhenfeng Jin, Hongrui Sun
Fractional Semilinear Neumann Problem With Critical Nonlinearity, Zhenfeng Jin, Hongrui Sun
Turkish Journal of Mathematics
In this paper, we consider the following critical fractional semilinear Neumann problem \begin{equation*} \begin{cases} (-\Delta)^{1/2}u+\lambda u=u^{\frac{n+1}{n-1}},~u>0\quad&\, \mathrm{in}\ \Omega,\\ \partial_\nu{u}=0 &\mathrm{on}\ \partial\Omega, \end{cases} \end{equation*} where $\Omega\subset\mathbb{R}^n~(n\geq5)$ is a smooth bounded domain, $\lambda>0$ and $\nu$ is the outward unit normal to $\partial\Omega$. We prove that there exists a constant $\lambda_0>0$ such that the above problem admits a minimal energy solution for $\lambda<\lambda_0$. Moreover, if $\Omega$ is convex, we show that this solution is constant for sufficiently small $\lambda$.
On The Weak And Strong Solutions Of The Velocity-Vorticity Model Of The $G$-Navier-Stokes Equations, Özge Kazar, Meryem Kaya
On The Weak And Strong Solutions Of The Velocity-Vorticity Model Of The $G$-Navier-Stokes Equations, Özge Kazar, Meryem Kaya
Turkish Journal of Mathematics
In this work, we consider a velocity-vorticity formulation for the $g$-Navier-Stokes equations. The system is constructed by combining the velocity-pressure system which is included by using the rotational formulation of the nonlinearity and the vorticity equation for the $g$ -Navier-Stokes equations. We prove the existence and uniqueness of weak and strong solutions of this system with the periodic boundary conditions.
Liouville-Type Theorem For One-Dimensional Porous Medium Systems With Sources, Anh Tuan Duong
Liouville-Type Theorem For One-Dimensional Porous Medium Systems With Sources, Anh Tuan Duong
Turkish Journal of Mathematics
In this paper, we are concerned with the one-dimensional porous medium system with sources \begin{align*} \begin{cases}u_t-( u^m)_{xx} =a_{11}u^{p}+a_{12} u^rv^{r+m}, (x,t)\in J\times I\subset\mathbb{R}\times \mathbb{R}\\ v_t-(v^m)_{xx} =a_{21} u^{r+m}v^{r}+a_{22}v^{p},\;(x,t)\in J\times I\subset \mathbb{R}\times \mathbb{R}, \end{cases} \end{align*} where $p=2r+m$, $m>1$, $r>0$. Under the conditions $a_{12}\geq 0, a_{21}\geq 0$, $a_{11}>0$, and $a_{22}>0$, we prove that the system does not possess any nontrivial nonnegative weak solution.
On The Monoid Of Partial Isometries Of A Cycle Graph, Vitor H. Fernandes, Tania Paulista
On The Monoid Of Partial Isometries Of A Cycle Graph, Vitor H. Fernandes, Tania Paulista
Turkish Journal of Mathematics
In this paper we consider the monoid $DPC_n$ of all partial isometries of an $n$-cycle graph $C_n$. We show that $DPC_n$ is the submonoid of the monoid of all oriented partial permutations on an $n$-chain whose elements are precisely all restrictions of a dihedral group of order $2n$. Our main aim is to exhibit a presentation of $DPC_n$. We also describe Green's relations of $DPC_n$ and calculate its cardinality and rank.
The Application Of Brzdek's Fixed Point Theorem In The Stability Problem Of The Drygas Functional Equation, Mehdi Dehghanian, Yamin Sayyari
The Application Of Brzdek's Fixed Point Theorem In The Stability Problem Of The Drygas Functional Equation, Mehdi Dehghanian, Yamin Sayyari
Turkish Journal of Mathematics
Using the Brzdek fixed point theorem, we establish the Hyers?Ulam stability problem of Drygas functional equations \begin{equation} \delta(x+y-z)+\delta(x-y)+\delta(-y-z)+\delta(y)=\delta(x-y-z)+\delta(y-z)+\delta(x+y)+\delta(-y)\nonumber \end{equation} for all $x,y,z\in A$.
Modification Of The Sector Theorem Of Kondo-Tanaka, Eric Choi
Modification Of The Sector Theorem Of Kondo-Tanaka, Eric Choi
Turkish Journal of Mathematics
Kondo-Tanaka proved that if a rotationally symmetric plane $M_m$ is von Mangoldt or Cartan-Hadamard outside a compact set and has finite total curvature, then it has a sector with no pair of cut points. We show that the condition of finite total curvature can be removed. %The abstract should provide clear information about the research and the results obtained, and should not exceed 200 words. The abstract should not contain citations.
A Short Note On A New Approach To Rayleigh-Bénard-Chandrasekhar Convection In Weakly Electrically Conducting Viscoelastic Liquids, Hati̇ce Muti̇
A Short Note On A New Approach To Rayleigh-Bénard-Chandrasekhar Convection In Weakly Electrically Conducting Viscoelastic Liquids, Hati̇ce Muti̇
Turkish Journal of Mathematics
The onset of magnetoconvection (known as Rayleigh-Bénard-Chandrasekhar convection) in two relaxation time viscoelastic liquids is studied here without seeking explicit recourse to a normal stress formulation as is usually done in these studies. Magnetoconvection refers to the flow of fluid in the presence of both thermal gradients (Rayleigh-Bénard convection) and a magnetic field. When these two effects are combined, they can lead to interesting and complex patterns of fluid motion. Understanding magnetoconvection in viscoelastic liquids is crucial for various industrial and scientific applications. The hyperbolic-type of linear momentum equation is decomposed into two first-order equations in time by cleverly separating …
On Positive Periodic Solutions To Third-Order Integro-Differential Equations With Distributed Delays, Mimia Benhadri, Tomas Caraballo
On Positive Periodic Solutions To Third-Order Integro-Differential Equations With Distributed Delays, Mimia Benhadri, Tomas Caraballo
Turkish Journal of Mathematics
In this paper, we investigate the existence of positive periodic solutions of a third-order nonlinear integro-differential equation with distributed delays, by using the Green function and the Krasnosel'skii fixed point theorem in cones of Banach spaces, providing new results on this field. Three examples are analyzed to illustrate the effectiveness of the abstract results.
Identities Involving Special Functions From Hypergeometric Solution Of Algebraic Equations, Juan Luis Gonzalez-Santander
Identities Involving Special Functions From Hypergeometric Solution Of Algebraic Equations, Juan Luis Gonzalez-Santander
Turkish Journal of Mathematics
From the algebraic solution of $x^{m}-x+t=0$ for $m=2,3,4$ and the corresponding solution in terms of hypergeometric functions, we obtain a set of reduction formulas for hypergeometric functions. By differentiation and integration of these results, and applying other known reduction formulas of hypergeometric functions, we derive new reduction formulas of special functions as well as the calculation of some definite integrals in terms of elementary functions.
Existence Results For Impulsive Dynamic Singular Nonlinear Sturm-Liouville Equations On Infinite Intervals, Bi̇lender Paşaoğlu Allahverdi̇ev, Hüseyi̇n Tuna, Hamlet Abdullaoğlu Isayev
Existence Results For Impulsive Dynamic Singular Nonlinear Sturm-Liouville Equations On Infinite Intervals, Bi̇lender Paşaoğlu Allahverdi̇ev, Hüseyi̇n Tuna, Hamlet Abdullaoğlu Isayev
Turkish Journal of Mathematics
The purpose of this study is to investigate an impulsive dynamic singular nonlinear Sturm-Liouville problem on infinite intervals. The existence and uniqueness of the solutions of such problem will be investigated by considering Weyl's limit-circle case.
Pell-Lucas Collocation Method For Solving A Class Of Second Order Nonlinear Differential Equations With Variable Delays, Şuayi̇p Yüzbaşi, Gamze Yildirim
Pell-Lucas Collocation Method For Solving A Class Of Second Order Nonlinear Differential Equations With Variable Delays, Şuayi̇p Yüzbaşi, Gamze Yildirim
Turkish Journal of Mathematics
In this study, the approximate solution of the nonlinear differential equation with variable delays is investigated by means of a collocation method based on the truncated Pell-Lucas series. In the first stage of the method, the assumed solution form (the truncated Pell-Lucas polynomial solution) is expressed in the matrix form of the standard bases. Next, the matrix forms of the necessary derivatives, the nonlinear terms, and the initial conditions are written. Then, with the help of the equally spaced collocation points and these matrix relations, the problem is reduced to a system of nonlinear algebraic equations. Finally, the obtained system …
An Invariant Of Regular Isotopy For Disoriented Links, İsmet Altintaş, Hati̇ce Parlatici
An Invariant Of Regular Isotopy For Disoriented Links, İsmet Altintaş, Hati̇ce Parlatici
Turkish Journal of Mathematics
In this paper, we define a two-variable polynomial invariant of regular isotopy, $M_{K}$ for a disoriented link diagram $K$. By normalizing the polynomial $M_{K}$ using complete writhe, we obtain a polynomial invariant of ambient isotopy, $N_{K}$, for a disoriented link diagram $K$. The polynomial $N_{K}$ is a generalization of the expanded Jones polynomial for disoriented links and is an expansion of the Kauffman polynomial $F$ to the disoriented links. Moreover, the polynomial $M_{K}$ is an expansion of the Kauffman polynomial $L$ to the disoriented links.
Bipolar Soft Ideal Rough Set With Applications In Covid-19, Heba I. Mustafa
Bipolar Soft Ideal Rough Set With Applications In Covid-19, Heba I. Mustafa
Turkish Journal of Mathematics
Bipolar soft rough set represents an important mathematical model to deal with uncertainty. This theory represents a link between bipolar soft set and rough set theories. This study introduced the concept of topological bipolar soft set by combining a bipolar soft set with topologies. Also, the topological structure of bipolar soft rough set has been discussed by defining the bipolar soft rough topology. The main objective of this paper is to present some solutions to develop and modify the approach of the bipolar soft rough sets. Two kinds of bipolar soft ideal approximation operators which represent extensions of bipolar soft …
A New Approach To Matrix Isomorphisms Of Complex Clifford Algebras Via Cantor Set, Derya Çeli̇k
A New Approach To Matrix Isomorphisms Of Complex Clifford Algebras Via Cantor Set, Derya Çeli̇k
Turkish Journal of Mathematics
We give a new way to obtain the standard isomorphisms of complex Clifford algebras, known as the tensor product of Pauli matrices, by representing the complex Clifford algebras on the space of complex valued functions defined over a finite subset of the Cantor set.
Forming Coupled Dispersionless Equations Of Families Of Bertrand Curves, Kemal Eren
Forming Coupled Dispersionless Equations Of Families Of Bertrand Curves, Kemal Eren
Turkish Journal of Mathematics
In this study, we establish a link of the coupled dispersionless (CD) equations system with the motion of Bertrand curve pairs. Moreover, we find the Lax equations that provide the integrability of these equations. By taking an appropriate choice of variables we show the link of the short pulse (SP) equation with the motion of Bertrand curve pairs via the reciprocal (hodograph) transformation. Finally, we prove that the conserved quantity of the corresponding coupled dispersionless equations obtained from each of these curve pairs is constant.
On The Distribution Of Adjacent Zeros Of Solutions To First-Order Neutral Differential Equations, Emad R. Attia, Ohoud N. Al-Masarer, Irena Jadlovska
On The Distribution Of Adjacent Zeros Of Solutions To First-Order Neutral Differential Equations, Emad R. Attia, Ohoud N. Al-Masarer, Irena Jadlovska
Turkish Journal of Mathematics
The purpose of this paper is to study the distribution of zeros of solutions to a first-order neutral differential equation of the form \begin{equation*} \left[x(t) + p(t) x(t-\tau)\right]' + q(t) x(t-\sigma) = 0, \quad t \geq t_0, \end{equation*} where $p\in C([t_0,\infty),[0,\infty))$, $q \in C([t_0,\infty),(0,\infty))$, $\tau,\sigma>0$, and $\sigma>\tau$. We obtain new upper bound estimates for the distance between consecutive zeros of solutions, which improve upon many of the previously known ones. The results are formulated so that they can be generalized without much effort to equations for which the distribution of zeros problem is related to the study of …
Novel Correlation Coefficients For Interval-Valued Fermatean Hesitant Fuzzy Sets With Pattern Recognition Application, İbrahi̇m Demi̇r
Novel Correlation Coefficients For Interval-Valued Fermatean Hesitant Fuzzy Sets With Pattern Recognition Application, İbrahi̇m Demi̇r
Turkish Journal of Mathematics
A combination of interval-valued Fermatean fuzzy sets with Fermatean hesitant fuzzy elements in the form of interval values is known as an interval-valued Fermatean hesitant fuzzy set. Since Fermatean hesitant fuzzy sets are effective instruments for representing more complex, ambiguous, and hazy information, interval-valued Fermatean hesitant fuzzy sets are expansions of these sets. This investigation will concentrate on four different types of correlation coefficients for Fermatean hesitant fuzzy sets and expand them to include correlation coefficients and weighted correlation coefficients for interval-valued Fermatean hesitant fuzzy sets. Finally, the numerical examples demonstrate the viability and usefulness of the suggested methodologies in …
Geodesics And Isocline Distributions In Tangent Bundles Of Nonflat Lorentzian-Heisenberg Spaces, Murat Altunbaş
Geodesics And Isocline Distributions In Tangent Bundles Of Nonflat Lorentzian-Heisenberg Spaces, Murat Altunbaş
Turkish Journal of Mathematics
Let $(H_{3},g_{1})$ and $(H_{3},g_{2})$ be the Lorentzian-Heisenberg spaces with nonflat metrics $g_{1}$ and $g_{2},\ $and $(TH_{3},g_{1}^{s}),\ (TH_{3},g_{2}^{s})$ be their tangent bundles with the Sasaki metric, respectively. In the present paper, we find nontotally geodesic distributions in tangent bundles by using lifts of contact forms from the base manifold $H_{3}.$We give examples for totally geodesic but not isocline distributions. We study the geodesics of tangent bundles by considering horizontal and natural lifts of geodesics of the base manifold $H_{3}$. We also investigate more general classes of geodesics which are not obtained from horizontal and natural lifts of geodesics.
On The Band Functions And Bloch Functions, Oktay Veli̇ev
On The Band Functions And Bloch Functions, Oktay Veli̇ev
Turkish Journal of Mathematics
In this paper, we consider the continuity of the band functions and Bloch functions of the differential operators generated by the differential expressions with periodic matrix coefficients.