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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.
Transmission Eigenvalues Problem Of A Schrödinger Equation, Emel Yildirim, Elgiz Bairamov
Transmission Eigenvalues Problem Of A Schrödinger Equation, Emel Yildirim, Elgiz Bairamov
Turkish Journal of Mathematics
In this paper, transmission eigenvalues of a Schrödinger equation have been studied by constructing a new inner product and using Weyl theory. Necessary conditions for these eigenvalues to be negative, real and finite have been examined. This method has provided a new framework related to transmission eigenvalue problems and investigation of their properties. The conclusions has been verified for special case of the problem.
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 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 …
Individual Stability Of Representations Of Abelian Semigroups, Heybetkulu Mustafayev
Individual Stability Of Representations Of Abelian Semigroups, Heybetkulu Mustafayev
Turkish Journal of Mathematics
Let S be a suitable subsemigroup of a locally compact abelian group and let T={T(s)}s(-S be a bounded and strongly continuous trepresentation of S on a Banach space X. In this note, we study the spectral conditions on T and the ergodic conditios on x in X which will imply that T(s)x-->0 strongly as s--> infinity through S.
A Non-Newtonian Conics In Multiplicative Analytic Geometry, Aykut Has, Beyhan Yilmaz
A Non-Newtonian Conics In Multiplicative Analytic Geometry, Aykut Has, Beyhan Yilmaz
Turkish Journal of Mathematics
In this study, conics (circle, ellipse, hyperbola) are characterized by taking into account basic multiplicationoperations in multiplicative space. For this purpose, firstly multiplicative axes and regions are introduced. Additionally,the multiplicative cone definition is given and visualized on the figure. General definitions and theorems of non-Newtonianconics are given. Additionally, examples were given and drawings were made to make the resulting characterizations andtheorems more memorable.
On The Connection Between Σϵ(A1 ⊗ A2) And Σϵ(A1), Σϵ(A2) For Certain Specialoperators, Fati̇h Yilmaz
On The Connection Between Σϵ(A1 ⊗ A2) And Σϵ(A1), Σϵ(A2) For Certain Specialoperators, Fati̇h Yilmaz
Turkish Journal of Mathematics
In this paper, the connection between the ϵ -pseudospectrum of the tensor product operator A1 ⊗ A2 andthe ϵ -pseudospectrums of operators A1 and A2 has been investigated and some results are given about this connectionunder certain conditions.
Rings And Finite Fields Whose Elements Are Sums Or Differences Of Tripotents And Potents, Adel Abyzov, Stephen Cohen, Peter Danchev, Daniel Tapkin
Rings And Finite Fields Whose Elements Are Sums Or Differences Of Tripotents And Potents, Adel Abyzov, Stephen Cohen, Peter Danchev, Daniel Tapkin
Turkish Journal of Mathematics
We significantly strengthen results on the structure of matrix rings over finite fields and applythem to describe the structure of the so-called weakly n-torsion clean rings. Specifically, we establish that, forany field F with either exactly seven or strictly more than nine elements, each matrix over F is presentableas a sum of of a tripotent matrix and a q-potent matrix if and only if each element in F is presentable as asum of a tripotent and a q-potent, whenever q > 1 is an odd integer. In addition, if Q is a power of an oddprime and F is a field …
Spherical Product Hypersurfaces In Euclidean Spaces, Sezgi̇n Büyükkütük, Günay Öztürk
Spherical Product Hypersurfaces In Euclidean Spaces, Sezgi̇n Büyükkütük, Günay Öztürk
Turkish Journal of Mathematics
Spherical product surfaces are obtained with the help of a special product by considering two curves inn−dimensional space. One of their special cases is rotational surface. The reason why the present study is significantthat the spherical product is used to construct hypersurfaces. (n−1)−curves are needed during this construction. Firstly,the spherical product hypersurfaces are defined in E4 , Gaussian and mean curvature are yielded and then conditionsbeing flat or minimal are examined. Moreover, superquadrics, which are associated with spherical product, are handledfor the first time in hypersurface form and give some examples. Finally, spherical product hypersurfaces are generalizedto n−dimensional Euclidean space …
A Sufficient Condition For The Wildness Of An Automorphism Of A Free Leibnizalgebra, Zeynep Özkurt
A Sufficient Condition For The Wildness Of An Automorphism Of A Free Leibnizalgebra, Zeynep Özkurt
Turkish Journal of Mathematics
In this paper, we apply the criterion of Mikhalev and Umirbaev for the invertibility of an endomorphismof a finitely generated free Leibniz algebra via its Jacobian matrix to determine whether a given endomorphism is anautomorphism. Moreover, it is shown that the invertibility of the determinant of the Jacobian matrix of an automorphismimplies its wildness.
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 …
Properties Of Gyrogroups Induced By Groups Whose Central Quotients Being 2-Engel, Jaturon Wattanapan, Teerapong Suksumran
Properties Of Gyrogroups Induced By Groups Whose Central Quotients Being 2-Engel, Jaturon Wattanapan, Teerapong Suksumran
Turkish Journal of Mathematics
A group Γ is said to be CCII if the quotient Γ/Z(Γ) is 2-Engel or, equivalently, commutator-inversion invariant, where Z(Γ) is the center of Γ. In this article, we prove algebraic and topological properties of gyrogroups that are induced by CCII groups. Then, using a classification of non-abelian groups of order n with n < 32, we determine all finite CCII groups of order less than 32.
Positive And Decreasing Solutions For Higher Order Caputo Boundary Valueproblems With Sign-Changing Green’S Function, Rian Yan, Yige Zhao, Xuan Leng, Yabing Li
Positive And Decreasing Solutions For Higher Order Caputo Boundary Valueproblems With Sign-Changing Green’S Function, Rian Yan, Yige Zhao, Xuan Leng, Yabing Li
Turkish Journal of Mathematics
In this paper, Caputo boundary value problems of order 3 < ζ ≤ 4 are investigated on the interval [0, 1] .By Guo-Krasnoselskii fixed point theorem, some criteria of existence and multiplicity of positive and decreasing solutionsare established. The main novelty of the paper lies in its capability to achieve positive solutions while the correspondingGreen’s function changes sign. Finally, two examples are provided to illustrate the application of these results.
On Vietoris’ Hybrid Number Sequence, Nurten Gürses, Gülsüm Yeli̇z Saçli, Sali̇m Yüce
On Vietoris’ Hybrid Number Sequence, Nurten Gürses, Gülsüm Yeli̇z Saçli, Sali̇m Yüce
Turkish Journal of Mathematics
This work is intended to establish a relation between Vietoris’ sequence, which is a rational sequence, andhybrid numbers. Then it provides some characteristic properties of the hybrid numbers with Vietoris’ number coefficients.Some relations between this hybrid number and its norm, the recurrence relations, the generating function, Binet-likeformula and Catalan-like identities are also indicated. Furthermore, a determinantal approach is presented to obtainelements of Vietoris’ hybrid number sequence.
Stacks In Einstein Gravity, Kadri̇ İlker Berktav
Stacks In Einstein Gravity, Kadri̇ İlker Berktav
Turkish Journal of Mathematics
In this paper, we examine stacky structures in certain Einstein gravity theories. In brief, using the classicalformulation of (vacuum) gravity, with vanishing cosmological constant, we first construct the stack of solutions to Einsteinfield equations on any given fixed manifold. Using a similar approach and setup, we also study Einstein’s gravity onfamilies of manifolds and define another stack encoding this situation. Later on, we focus on the gauge theoreticalinterpretation of 3D gravity and provide a natural stack associated with that interpretation. Finally, in a particularsetup, we give a natural morphism between the two stacks arising from different descriptions of 3D gravity.
The Flow-Geodesic Curvature And The Flow-Evolute Of Spherical Curves, Mircea Crasmareanu
The Flow-Geodesic Curvature And The Flow-Evolute Of Spherical Curves, Mircea Crasmareanu
Turkish Journal of Mathematics
We introduce and study a deformation of the geodesic curvature for a given spherical curve γ . Also, wedefine a new type of evolute and two Fermi-Walker type derivatives for γ . Some concrete examples are detailed with aspecial attention towards space curves with a constant torsion.
Some Qualitative Results For Nonlocal Dynamic Boundary Value Problem Of Thermistor Type, Svetlin G. Georgiev, Mahammad Khuddush, Sanket Tikare
Some Qualitative Results For Nonlocal Dynamic Boundary Value Problem Of Thermistor Type, Svetlin G. Georgiev, Mahammad Khuddush, Sanket Tikare
Turkish Journal of Mathematics
This paper is concerned with second-order nonlocal dynamic thermistor problem with two-point boundary conditions on time scales. By utilizing the fixed point theorems due to Schaefer and Rus, we establish some sufficient conditions for the existence and uniqueness of solutions. Further, we discuss the continuous dependence of solutions and four types of Ulam stability. We provide examples to support the applicability of our results.
Curves As Slant Submanifolds Of An Almost Product Riemannian Manifold, Pablo Alegre, Alfonso Carriazo
Curves As Slant Submanifolds Of An Almost Product Riemannian Manifold, Pablo Alegre, Alfonso Carriazo
Turkish Journal of Mathematics
In this paper, we show that in an almost product manifold there exist curves that are slant submanifolds. Wecharacterize these curves and study them in two and three-dimensional locally product manifolds. Finally, we constructcurves in a hypersurface of a Kaehler manifold.
Bernstein-Nikol’Skii-Markov-Type Inequalities For Algebraic Polynomials In Aweighted Lebesgue Space In Regions With Cusps, Uğur Değer, Fahreddi̇n Abdullayev
Bernstein-Nikol’Skii-Markov-Type Inequalities For Algebraic Polynomials In Aweighted Lebesgue Space In Regions With Cusps, Uğur Değer, Fahreddi̇n Abdullayev
Turkish Journal of Mathematics
In this paper, we study Bernstein-Nikol’skii-Markov type inequalities for arbitrary algebraic polynomials withrespect to a weighted Lebesgue space, where the weight functions have some singularities on a given contour. We considercurves which can contain a finite number of exterior and interior corners with power law tangency of the boundary arcs atthose points where the weight functions have both zeros and poles of finite order. The estimates are given for the growthof the module of derivatives for algebraic polynomials on the closure of a region bounded by a given curve, dependingon the behavior of weight functions, on the property of curve, …
New Oscillation Criteria For First-Order Differential Equations With General Delay Argument, Emad R. Attia, Irena Jadlovska
New Oscillation Criteria For First-Order Differential Equations With General Delay Argument, Emad R. Attia, Irena Jadlovska
Turkish Journal of Mathematics
This paper is concerned with the oscillation of solutions to a class of first-order differential equations withvariable coefficients and a general delay argument. New oscillation criteria are established, which improve and extendmany known results reported in the literature. A couple of illustrative examples are given to show the efficiency of thenewly obtained results. In particular, it is shown that our criteria partially fulfill a remaining gap in a recent sharp resultby Pituk et al. [31].
On A Class Of Permutation Trinomials Over Finite Fields, Burcu Gülmez Temür, Buket Özkaya
On A Class Of Permutation Trinomials Over Finite Fields, Burcu Gülmez Temür, Buket Özkaya
Turkish Journal of Mathematics
In this paper, we study the permutation properties of the class of trinomials of the form f(x) = x4q+1 +λ1xq+4 +λ2x2q+3 ∈ Fq2 [x] , where λ1, λ2 ∈ Fq and they are not simultaneously zero. We find all necessary and sufficientconditions on λ1 and λ2 such that f(x) permutes Fq2 , where q is odd and q = 22k+1, k ∈ N.
Interior Schauder-Type Estimates For M − Th Order Elliptic Operators Inrearrangement-Invariant Sobolev Spaces, Emi̇nağa M. Mamedov, Şeyma Çeti̇n
Interior Schauder-Type Estimates For M − Th Order Elliptic Operators Inrearrangement-Invariant Sobolev Spaces, Emi̇nağa M. Mamedov, Şeyma Çeti̇n
Turkish Journal of Mathematics
In this study, we investigate the m-th order elliptic operators on n-dimensional bounded domain Ω ⊂ Rnwith discontinuous coefficients in the rearrangement-invariant Sobolev space WmX (Ω). In general, the consideredrearrangement-invariant spaces are not separable, so the use of classical methods in these spaces requires substantialmodification of classical methods and a lot of preparation, concerning correctness of substitution operator, problemsrelated to the extension operator in such spaces, etc. For this purpose, the corresponding separable subspaces of thesespaces, in which the set of compact supported infinitely differentiable functions is dense, are introduced based on theshift operator. We establish interior Schauder-type estimates in …
Fusion In Supersolvable Hall Subgroups, Muhammet Yasi̇r Kizmaz
Fusion In Supersolvable Hall Subgroups, Muhammet Yasi̇r Kizmaz
Turkish Journal of Mathematics
Let H be a supersolvable Hall π -subgroup of a finite group G. We prove that G has a normal π -complement if and only if H controls G-fusion in H.
Combinatorial Results For Semigroups Of Orientation-Preserving Transformations, Ayşegül Dağdevi̇ren, Gonca Ayik
Combinatorial Results For Semigroups Of Orientation-Preserving Transformations, Ayşegül Dağdevi̇ren, Gonca Ayik
Turkish Journal of Mathematics
Let Xn denote the chain {1, 2, . . . , n} under its natural order. We denote the semigroups consisting of all order-preserving transformations and all orientation-preserving transformations on Xn by On and OPn , respectively. We denote by E(U) the set of all idempotents of a subset U of a semigroup S . In this paper, we first determine the cardinalities of Er(On) = {α ∈ E(On) : |im(α)| = |fix(α)| = r}, E ∗ r (On) = {α ∈ Er(On) : 1, n ∈ fix(α)}, Er(OPn) = {α ∈ E(OPn) : |fix(α)| = r}, E ∗ r …
Langevin Delayed Equations With Prabhakar Derivatives Involving Two Generalized Fractional Distinct Orders, Mustafa Aydin
Langevin Delayed Equations With Prabhakar Derivatives Involving Two Generalized Fractional Distinct Orders, Mustafa Aydin
Turkish Journal of Mathematics
This paper is devoted to defining the delayed analogue of the Mittag-Leffler type function with three parameters and investigating a representation of a solution to Langevin delayed equations with Prabhakar derivatives involving two generalized fractional distinct orders, which are first introduced and investigated, by means of the Laplace integral transform. It is verified by showing the solution satisfies the introduced system. Special cases which are also novel are presented as examples. The findings are illustrated with the help of the RLC circuits.
On The Oscillation And Asymptotic Behavior Of Solutions Of Third Order Nonlineardifferential Equations With Mixed Nonlinear Neutral Terms, Shaimaa Salem, Mohamed M. A. El-Sheikh, Ahmed Mohamed Hassan
On The Oscillation And Asymptotic Behavior Of Solutions Of Third Order Nonlineardifferential Equations With Mixed Nonlinear Neutral Terms, Shaimaa Salem, Mohamed M. A. El-Sheikh, Ahmed Mohamed Hassan
Turkish Journal of Mathematics
This paper is concerned with the oscillation and asymptotic behavior of solutions of third-order nonlinear neutral differential equations with a middle term and mixed nonlinear neutral terms in the case of the canonical operator. We establish several oscillation criteria that guarantee that all solutions are oscillatory or converge to zero. The given results are obtained by applying the comparison method, the Riccati transformation and the integral averaging technique. The results improve significantly and extend existing ones in the literature. Finally, illustrative examples are given.
Duality And Norm Completeness In The Classes Of Limitedly Lwc Anddunford–Pettis Lwc Operators, Ömer Şafak Alpay, Eduard Emelyanov, Svetlana Gorokhova
Duality And Norm Completeness In The Classes Of Limitedly Lwc Anddunford–Pettis Lwc Operators, Ömer Şafak Alpay, Eduard Emelyanov, Svetlana Gorokhova
Turkish Journal of Mathematics
We study the duality and norm completeness in the new classes of limitedly L-weakly compact and Dunford–Pettis L-weakly compact operators from Banach spaces to Banach lattices.
An Extension Of The Definition On The Compositions Of The Singular Distributions, Emi̇n Özçağ
An Extension Of The Definition On The Compositions Of The Singular Distributions, Emi̇n Özçağ
Turkish Journal of Mathematics
Gelfand and Shilov give the definition of the composition δ(g(x)) for an infinitely differentiable function g(x) having any number of simple roots. In the paper, we consider their definition for an infinitely differentiable function having any number of multiple roots by using the method of the discarding of unwanted infinite quantities from asymptotic expansions and give some examples. Further, we define the compositions δ(g+) and δ(g−) for a locally summable function g(x).