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The Role Of Α-Inequalities In Examining The Singular Version Of The Big Bang Model, Samane Ijadi, S. Mansour Vaezpour, Mehdi Shabibi, Shahram Rezapour
The Role Of Α-Inequalities In Examining The Singular Version Of The Big Bang Model, Samane Ijadi, S. Mansour Vaezpour, Mehdi Shabibi, Shahram Rezapour
Turkish Journal of Mathematics
In this article, by extending Friedmann's equation, we propose a singular fractional differential system for the Big Bang model. In this model, the rate of increase in the size of the universe tends to infinity at time near to zero and causes the emergence of a singular differential equation,which physically justifies the near-infinity energy of the universe in the near-zero volume of the universe in the early moments of the Big Bang. Then, we investigate this type of strong singular boundary value problem, by using $\alpha$-inequalities. In the sequel, some examples, describe the main results. Moreover, we present numerical and …
Asymptotic Behavior Of The Kirchhoff Index For Square Lattice With Boundary Conditions, Fati̇h Ecevi̇t, Arzu Boysal
Asymptotic Behavior Of The Kirchhoff Index For Square Lattice With Boundary Conditions, Fati̇h Ecevi̇t, Arzu Boysal
Turkish Journal of Mathematics
We determine leading asymptotic behavior of the Kirchhoff index for the square lattice under free, cylindrical and toroidal boundary conditions. Our results provide correct forms of the eleven false theorems/results published in the following papers: L. Ye, On the Kirchhoff index of some toroidal lattices, Linear Multilinear Algebra, 59:6 (2011), 645--650; J.-B. Liu, X.-F. Pan, J. Cao, X. Huang, The Kirchhoff index of toroidal meshes and variant networks, Math. Probl. Eng., Article ID 286876, 8 pages (2014); J.-B. Liu, X.-F. Pan, A unified approach to the asymptotic topological indices of various lattices, Appl. Math. Comput., 270 (2015), 62--73.
Properties Of Frontier, Exterior And Border In Picture Topological Spaces, Shanmugasundharam Durga, Lakshmanadas Vidyarani, Mandarasalam Vigneshwaran, Tomasz Witczak
Properties Of Frontier, Exterior And Border In Picture Topological Spaces, Shanmugasundharam Durga, Lakshmanadas Vidyarani, Mandarasalam Vigneshwaran, Tomasz Witczak
Turkish Journal of Mathematics
The paper is dedicated to picture sets. They are crisp version of Cuong's picture fuzzy sets (just like intuitionistic sets introduced by Coker are crisp version of intuitionistic fuzzy sets). We have already defined several basic topological notions in this framework and we have analyzed its algebra. Now we continue our research. We introduce the notions of border, frontier and exterior. Many properties are studied. Moreover, we point out that there are some important differences between classical and non-classical approach.
Inverse Ordered Semigroups, Michael Tsingelis
Inverse Ordered Semigroups, Michael Tsingelis
Turkish Journal of Mathematics
Ένα στοιχείο x μιας διατεταγμένης ημιομάδας [[EQUATION]] ονομάζεται αντίστροφο στοιχείο του [[EQUATION]]if [[EQUATION]]και [[EQUATION]]. Μια αντίστροφη διατεταγμένη ημιομάδα είναι μια διατεταγμένη ημιομάδα S για την οποία κάθε στοιχείο του S έχει ένα αντίστροφο στοιχείο και τα αντίστροφα στοιχεία οποιουδήποτε στοιχείου του S βρίσκονται στην ίδια συνδεδεμένη συνιστώσα του διαγράμματος Hasse της σχέσης τάξης του. Παρουσιάζουμε ιδιότητες που ικανοποιούνται από αντίστροφα διατεταγμένες ημιομάδες και χαρακτηρίζουμε αντίστροφα διατεταγμένες ημιομάδες με βάση την έννοια της κανονικότητας των διατεταγμένων ημιομάδων, το σύνολο των αδυναμιών τους και τις σχέσεις του Green. Επίσης αποδεικνύουμε ότι η αντιστρεψιμότητα των διατεταγμένων ημιομάδων διατηρείται από ομομορφισμούς.
On Minimal Hypersurfaces In Euclidean Spaces And Riemannian Manifolds, Josef Mikeš, Sergey Stepanov, Irina Tsyganok
On Minimal Hypersurfaces In Euclidean Spaces And Riemannian Manifolds, Josef Mikeš, Sergey Stepanov, Irina Tsyganok
Turkish Journal of Mathematics
In this paper, we present the conditions under which minimal and stable minimal hypersurfaces are as hyperplanes in Euclidean spaces ands a totally geodesic submanifolds in Riemannian manifolds.
Local Dynamic Analysis Of The Covid-19 Mathematical Model Based On Discrete-Time Predator-Prey Population Model, Fi̇gen Kangalgi̇l, Ni̇lüfer Topsakal, Özge Kuzucu
Local Dynamic Analysis Of The Covid-19 Mathematical Model Based On Discrete-Time Predator-Prey Population Model, Fi̇gen Kangalgi̇l, Ni̇lüfer Topsakal, Özge Kuzucu
Turkish Journal of Mathematics
In this article, the local dynamics of a discrete-time Covid-19 pandemic model based on the Lotka Volterra model with topological classifications, bifurcation analysis and chaos control are investigated. It is shown that under some parametric conditions, the discrete-time Covid-19 pandemic model has two equilibrium points. With linear stability theory, local dynamics are investigated with topological classifications about the equilibrium points of the discrete-time Covid-19 epidemic model. In addition, the existence of a Neimark-Sacker bifurcation at the internal equilibrium point is proved and this bifurcation is analysed using explicit criteria. Furthermore, the chaos in the discrete Covid-19 pandemic model is also …
Generalization Of Dual Numbers And Dual Euclidean 3-Space, Şükran Duygu Soylu, Harun Bariş Çolakoğlu, Mustafa Özdemi̇r
Generalization Of Dual Numbers And Dual Euclidean 3-Space, Şükran Duygu Soylu, Harun Bariş Çolakoğlu, Mustafa Özdemi̇r
Turkish Journal of Mathematics
In this study, we consider the generalized dual numbers and determine their algebraic and geometric properties. Then we generalize the well-known D3 module and introduce the generalized dual Euclidean 3-space with its scalar product and norm. After determining the conditions for being a unit generalized dual Euclidean vector, we derive the generalized Euclidean Study map, which states that there is a bijective correspondence between directed lines of the space and the elements of the unit generalized dual Euclidean sphere. Finally, we define the dual Euclidean angle between two generalized dual Euclidean vectors.
Estimates Of The Numerical Radius Utilizing Various Function Properties, Vuk Stojiljkovic, Mehmet Gürdal
Estimates Of The Numerical Radius Utilizing Various Function Properties, Vuk Stojiljkovic, Mehmet Gürdal
Turkish Journal of Mathematics
Numerous inequalities of the vector and numerical radius types have been found. We achieved several extensions of the well-known numerical radius type inequalities by using the function [[EQUATION]] described in the publication by Stojiljkovi\'{c} and Dragomir in [30] and convexity characteristics with standard operator theory approaches. In particular, the following integral type numerical radius inequality has been obtained, that is [[EQUATION]]
Nearly Toric Varieties Of Type A, Mahi̇r Bi̇len Can, Nestor Fernando Diaz Morera
Nearly Toric Varieties Of Type A, Mahi̇r Bi̇len Can, Nestor Fernando Diaz Morera
Turkish Journal of Mathematics
A notion of a nearly toric variety is introduced. The examples of nearly toric varieties in the context of Schubert varieties are discussed. In particular, combinatorial characterizations of the smooth and singular nearly toric Schubert varieties are found. Furthermore, the counts and generating series are determined. Additionally, a connection between Dyck paths and a certain family of nearly toric Schubert varieties is established.
Computing Exterior Isoclinism Of Crossed Modules, Zekeri̇ya Arvasi̇, Alper Odabaş
Computing Exterior Isoclinism Of Crossed Modules, Zekeri̇ya Arvasi̇, Alper Odabaş
Turkish Journal of Mathematics
In this paper, we introduce exterior isoclinism for crossed modules, extending the concept of isoclinism from groups to these 2-dimensional algebraic structures. Motivated by work on tensor and exterior products of non-abelian groups, we utilize non-abelian exterior products, exterior squares, and exterior centers to define this new equivalence relation. Additionally, we provide computational tools implemented in the GAP system to identify exterior isoclinism families of small groups and crossed modules.
The Multiples Of A Numerical Semigroup, Ignacio Ojeda, José Carlos Rosales
The Multiples Of A Numerical Semigroup, Ignacio Ojeda, José Carlos Rosales
Turkish Journal of Mathematics
Given two numerical semigroups $S$ and $T$ we say that $T$ is a multiple of $S$ if there exists an integer $d \in \mathbb{N} \setminus \{0\}$ such that $S = \{x \in \mathbb{N} \mid d x \in T\}$. In this paper we study the family of multiples of a (fixed) numerical semigroup. We also address the open problem of finding numerical semigroups of embedding dimension $e$ without any quotient of embedding dimension less than $e$, and provide new families with this property.
Moment-Based Approximation For Variance Of Semi-Markovian Random Walk With Gamma Distributed Interference Of Chance, Büşra Alakoç, Asli Bektaş Kamişlik, Tülay Yazir, Tahi̇r Khaniyev
Moment-Based Approximation For Variance Of Semi-Markovian Random Walk With Gamma Distributed Interference Of Chance, Büşra Alakoç, Asli Bektaş Kamişlik, Tülay Yazir, Tahi̇r Khaniyev
Turkish Journal of Mathematics
This study proposed moment-based approximations for the expected value and variance of the ergodic distribution of the semi-Markovian random walk process (X(t)) with gamma distributed interference of chance. Many studies have investigated analogous moment problems by using asymptotic approach. The key distinguishing aspect of this study from others in the literature is obtaining Kambo’s approximations for the moments of X(t) instead of asymptotic expansions. Firstly, the approximation formulas for the moments of boundary functional SN(z) of X(t) were obtained. Then using these results, approximation formulas for the first two moments of the ergodic distributions of X(t) were derived. Finally, the …
Free Weakly K-Nilpotent N-Tuple Semigroups, Anatolii V. Zhuchok, Jorg Koppitz
Free Weakly K-Nilpotent N-Tuple Semigroups, Anatolii V. Zhuchok, Jorg Koppitz
Turkish Journal of Mathematics
In this paper, we construct a free object in the variety of weakly k-nilpotent n-tuple semigroups and characterize the least weakly k-nilpotent congruence on a free n-tuple semigroup. Moreover, we present separately free weakly k-nilpotent n-tuple semigroups of rank 1, calculate the cardinality of the free weakly k-nilpotent n-tuple semigroup for the finite case, emphasize that the semigroups of the free weakly k-nilpotent n-tuple semigroup are isomorphic and the automorphism group of the free weakly k-nilpotent n-tuple semigroup is isomorphic to the symmetric group. We also describe all maximal n-tuple subsemigroups of the free weakly k-nilpotent n-tuple semigroup and all …
Explicit Solution Of System Of Two Higher-Order Recurrences, László Németh, László Szalay
Explicit Solution Of System Of Two Higher-Order Recurrences, László Németh, László Szalay
Turkish Journal of Mathematics
We give a method to determine an explicit solution to a system of two inhomogeneous linear recursive sequences of higher order. Our approach can be used efficiently in solving certain combinatorial problems. We finish the paper by considering a tiling problem with black and white dominoes, and we use the method as a demonstration to find the solution.
Some Complementary Results On Asymptotic Behavior Of Solutions Of Neutral Difference Equations, Nour H. M. Alsharif, Başak Karpuz
Some Complementary Results On Asymptotic Behavior Of Solutions Of Neutral Difference Equations, Nour H. M. Alsharif, Başak Karpuz
Turkish Journal of Mathematics
This paper focuses on examining the boundedness and asymptotic behavior of all solutions of the neutral difference equations\begin{equation}\Delta[x_{n}-p_{n}x_{n-\kappa}]+q_{n}x_{n-\ell}=0\quad\text{for}\ n=0,1,\cdots,\label{abseq1}\tag{$\star$}\end{equation}and\begin{equation}\Delta[x_{n}-px_{n-\kappa}]+q_{n}x_{n-\ell}=0\quad\text{for}\ n=0,1,\cdots,\label{abseq2}\tag{$\star\star$}\end{equation}where $\kappa,\ell\in\N$, $\{p_{n}\}\subset[0,1)$, $p\in[0,1)$ and $\{q_{n}\}\subset[0,\infty)$.Diverging from much of the existing literature, our results accommodate the scenario where$\{p_{n}\}\subset[\frac{1}{2},1)$ and $p\in[\frac{1}{2},1)$ for \eqref{abseq1} and \eqref{abseq2}, respectively.Furthermore, we underscore the practical implications of our results through the presentation of numerical examples. This paper focuses on examining the boundedness and asymptotic behavior of all solutions of the neutral difference equations \begin{equation} \Delta[x_{n}-p_{n}x_{n-\kappa}]+q_{n}x_{n-\ell}=0\quad\text{for}\ n=0,1,\cdots,\label{abseq1}\tag{$\star$} \end{equation} and \begin{equation} \Delta[x_{n}-px_{n-\kappa}]+q_{n}x_{n-\ell}=0\quad\text{for}\ n=0,1,\cdots,\label{abseq2}\tag{$\star\star$} \end{equation} where $\kappa,\ell\in\N$, $\{p_{n}\}\subset[0,1)$, $p\in[0,1)$ and $\{q_{n}\}\subset[0,\infty)$. Diverging from much of the existing literature, our results …
Fibration Category Structures Induced By Enrichments, Mehmet Aki̇f Erdal
Fibration Category Structures Induced By Enrichments, Mehmet Aki̇f Erdal
Turkish Journal of Mathematics
We study fibration category structures induced by enrichments over symmetric monoidal categories that are also fibration categories. Let $\mathcal V$ be a monoidal category that is also a fibration category. Assume that $\mathcal V$ has an interval object. We show that the fibration category structure on $\mathcal V$ can be transferred over any $\mathcal V$-enriched category through corepresentable functors provided that certain power objects exists. We also give its $G$-equivariant extension for a group $G$, so that under mild conditions the category of $G$-objects in a $\mathcal V$-enriched category admits a (non-trivial) fibration category structure. We later show that several …
The 2-Adic Valuation Of Shifted Padovan And Perrin Numbers And Applications, Eric Bravo, Nuretti̇n Irmak
The 2-Adic Valuation Of Shifted Padovan And Perrin Numbers And Applications, Eric Bravo, Nuretti̇n Irmak
Turkish Journal of Mathematics
We characterize the 2-adic valuation of (Pn − 1)n≥0 , where (Pn)n≥0 denotes the Padovan sequence. In addition, we use this formula to find all the Cullen and Proth numbers that are Padovan numbers. We also fully describe the 2-adic order of (Rn + 1)n≥0 , where (Rn)n≥0 denotes the Perrin sequence, and use it to find all Woodall and Proth numbers of the second kind which are Perrin numbers. As a consequence we find that 3, 5, 9, and 65 are the only Fermat numbers in the Padovan sequence; while 3 and 7 and 2 and 5 are the …
Coefficient Problems For A Certain Subclass Of Analytic And Univalent Functions, Osman Altintaş, Ni̇zami̇ Mustafa
Coefficient Problems For A Certain Subclass Of Analytic And Univalent Functions, Osman Altintaş, Ni̇zami̇ Mustafa
Turkish Journal of Mathematics
In the present work, some new subclasses of analytic and univalent functions are introduced and some 5 geometric properties such as coefficient estimates problem are studied for them. Furthermore, we show that our results 6 are generalization for some earlier works in the literature and we show this by comparing ours with those related.
Numerical Solutions Of Sird Model Of Covid-19 By Utilizing Pell-Lucascollocation Method, Gamze Yildirim, Şuayi̇p Yüzbaşi
Numerical Solutions Of Sird Model Of Covid-19 By Utilizing Pell-Lucascollocation Method, Gamze Yildirim, Şuayi̇p Yüzbaşi
Turkish Journal of Mathematics
This article presents an SIRD model based on the evolution of Coronavirus Disease 2019 (COVID-19) caused by SARS-CoV-2 from the coronavirus family. Firstly, we constitute Pell-Lucas collocation method (PLCM) for this model. According to method, the matrix forms of the Pell-Lucas polynomials (PLPs) are constituted. By utilizing this matrix forms, solution forms and all terms in this model are expressed in matrix form. Thus, PLCM transforms our model into a system of the matrix equations. By solving this system, the approximate solutions are obtained. In addition, the error analysis is also presented. In the examples of this study, we analyzed …
Some Free Boundary Problem Arising In Rock Mechanics, Anvarbek Meirmanov, Koblandy Yerzhanov
Some Free Boundary Problem Arising In Rock Mechanics, Anvarbek Meirmanov, Koblandy Yerzhanov
Turkish Journal of Mathematics
An initial boundary value problem for the in-situ leaching of rare metals with the acid solution in the elastic skeleton is considered. First, we describe physical processes at the microscopic level with a dimensional pore size [[EQUATION]]1 by the model [[EQUATION]], where dynamics of the incompressible solid skeleton is described by the Lamé equations and the physical process in the pore space by the Stokes equations for the incompressible fluid in combination with the diffusion and transport equations for the concentration of acid and product of chemical reactions. Since the solid skeleton changes its geometry upon dissolution, the “pore space …
The Compositions Derived From By Changing Variable In Singular Distributions, Emi̇n Özçağ
The Compositions Derived From By Changing Variable In Singular Distributions, Emi̇n Özçağ
Turkish Journal of Mathematics
In this paper we concern further results of \cite{kn:oz9,kn:oz8} by using the method mainly related to the finite part of divergent integral, in fact we consider the powers for positive integers of the composition of the Dirac delta function and an infinitely differentiable function having any number of distinct multiple roots which will be defined as the neutrix limit of the regular sequence $\delta^k_n(f(x))$. Moreover we show that the powers of the composition $\delta(f(x))$ for negative integers can be also defined via neutrix settings. Some compositions as examples to better understand will be given.
The Heat Kernel On A Finite Graph In Different Time-Scales, Yang Chen, Jay Jorgenson, Luis Lopez, Lejla Smajlovic
The Heat Kernel On A Finite Graph In Different Time-Scales, Yang Chen, Jay Jorgenson, Luis Lopez, Lejla Smajlovic
Turkish Journal of Mathematics
Let G be a finite, weighted graph, and let [[EQUATION]] be a Time-scale with a fixed point [[EQUATION]] such that sup[[EQUATION]]. In this paper we construct the heat kernel on G in Time-scale [[EQUATION]] in terms of a certain convolution series involving he heat operator acting on a parametrix, which is a fairly general function depending on the vertex set of G and the time variable [[EQUATION]]. We develop some applications by choosing different parametrices and various Time-scales. The results we obtain here do extend, in part, aspects of the recent articles in that the Time-scale considered in this paper …
Φ−Pluriharmonicity And Φ−Invariance Of Pointwise Bislant Riemanniansubmersions, Grayson Light, Cem Sayar, Mehmet Aki̇f Akyol
Φ−Pluriharmonicity And Φ−Invariance Of Pointwise Bislant Riemanniansubmersions, Grayson Light, Cem Sayar, Mehmet Aki̇f Akyol
Turkish Journal of Mathematics
In this research, we investigate the intriguing realm of pointwise bislant Riemannian submersions, a generalizationof many previous submersions, such as antiinvariant, slant, semislant, pointwise slant, pointwise semislant,and bislant submersions, within the framework of almost product manifolds. After giving an original example, wedelve into the submersion’s integrability conditions and geodesics. We explore the concept of φ−pluriharmonicity andφ−invariance within this context. The study sheds light on the profound interplay between pointwise bislant submersions’fibers and their being either geodesic or mixed geodesic, offering valuable insights into these intriguing mappings’geometric properties.
Ideals In Semigroups Of Partial Transformations With Invariant Set, Jitsupa Srisawat, Yanisa Chaiya
Ideals In Semigroups Of Partial Transformations With Invariant Set, Jitsupa Srisawat, Yanisa Chaiya
Turkish Journal of Mathematics
This paper explores the ideals and their structural properties in two generalizations of the partial transformationsemigroup. Furthermore, principal, maximal, and minimal ideals within these semigroups are elucidated.
Comprehensive Computational Study On Transient Heat Transfer In Functionally Graded Longitudinal Fins Under Time-Varying Laser Heating, Hüseyi̇n Demi̇r, İnci̇ Çi̇li̇ngi̇r Süngü, İbrahi̇m Keleş
Comprehensive Computational Study On Transient Heat Transfer In Functionally Graded Longitudinal Fins Under Time-Varying Laser Heating, Hüseyi̇n Demi̇r, İnci̇ Çi̇li̇ngi̇r Süngü, İbrahi̇m Keleş
Turkish Journal of Mathematics
The present study assumes that the material properties of the fin vary by a force rule in the axial direction, with the exception of the thermal relaxation coefficient, which is assumed to be constant. The temperature distribution in the longitudinal fin with homogeneous cross-section exposed to the laser heat source is numerically investigated. This is because these constraints lead to a linear differential equation with partial solutions that can't be analytically resolved using conventional methods, except for a few elementary order functions. Consequently, a linear or non-linear system of equations as a function of time is obtained by transforming a …
A Note On The Hull And Linear Complementary Pair Of Cyclic Codes, Zohreh Aliabadi, Tekgül Kalayci
A Note On The Hull And Linear Complementary Pair Of Cyclic Codes, Zohreh Aliabadi, Tekgül Kalayci
Turkish Journal of Mathematics
The Euclidean hull of a linear code C is defined as C ∩ C⊥ , where C⊥ denotes the dual of C underthe Euclidean inner product. A linear code with the trivial hull is called a linear complementary dual (LCD) code. Apair (C,D) of linear codes of length n over the finite field Fq is called a linear complementary pair (LCP) of codes ifC ⊕ D = Fnq. More generally, a pair (C,D) of linear codes of the same length over Fq is called a linear ℓ -intersectionpair of codes if C ∩D has dimension ℓ as a vector space …
A Short Note On Generalized Robertson Walker Spacetimes, Uday Chand De, Aydin Gezer
A Short Note On Generalized Robertson Walker Spacetimes, Uday Chand De, Aydin Gezer
Turkish Journal of Mathematics
In this article, generalized Robertson Walker spacetimes are investigated in light of perfect fluid spacetimes. First, we establish that a perfect fluid spacetime with non-vanishing vorticity whose associated scalars are constant along the velocity vector field becomes a generalized Robertson Walker spacetime. Among others, it is also shown that a Ricci parallel perfect fluid spacetime is either a generalized Robertson Walker spacetime or a static spacetime. Finally, we acquire that in a conformally semi-symmetric generalized Robertson Walker spacetime of dimension $4$, the scalar curvature vanishes and the spacetime is locally isometric to the Minkowski spacetime, provided the electric part of …