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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 …
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.
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.
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 …
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.
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.
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.
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.
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.
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.
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 …
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.
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.
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.
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].
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, …
Existence And Nonexistence Of Permutation Trinomials And Quadrinomials, Zhiguo Ding, Michael Zieve
Existence And Nonexistence Of Permutation Trinomials And Quadrinomials, Zhiguo Ding, Michael Zieve
Turkish Journal of Mathematics
For each q of the form 4k , we determine all a ∈ Fq for which X + Xq + X2q−1 + aXq2−q+1 permutes Fq2 . We also construct a class of permutation trinomials over Fq2 in case q ≡ 1 (mod 3) .
Topogenous Orders And Closure Operators On Posets, Josef Slapal, Tom Richmond, Minani Iragi
Topogenous Orders And Closure Operators On Posets, Josef Slapal, Tom Richmond, Minani Iragi
Turkish Journal of Mathematics
We introduce the notion of topogenous orders on a poset X to be certain endomaps on X. We build on a Galois connection between endomaps and binary relations on X and study relationships between endomap properties and corresponding relational properties. In particular, we determine the topogenous orders that are in a one-to-one correspondence with (idempotent) closure operators.
Ranks Of Certain Semigroups Of Transformations With Idempotent Complement Whose Restrictions Belong To A Given Semigroup, Leyla Bugay, Ruki̇ye Sönmez, Hayrullah Ayik
Ranks Of Certain Semigroups Of Transformations With Idempotent Complement Whose Restrictions Belong To A Given Semigroup, Leyla Bugay, Ruki̇ye Sönmez, Hayrullah Ayik
Turkish Journal of Mathematics
For n ≥ 2, let Pn , In , Tn , and Sn be the partial transformation semigroup, symmetric inverse semigroup, (full) transformation semigroup, and symmetric group on the set Xn = {1, . . . , n}, respectively. In this paper, we find the ranks of certain subsemigroups of Pn , In , and Tn consisting of transformations with idempotent complement whose restrictions to the set Xm belong to the (possible) semigroup Sm, Im, Tm, or Pm for 1 ≤ m ≤ n − 1.
Approximation By Operators Involving Δh -Gould-Hopper Appell Polynomials, Bi̇lge Zehra Sergi̇ Yilmaz, Gürhan İçöz
Approximation By Operators Involving Δh -Gould-Hopper Appell Polynomials, Bi̇lge Zehra Sergi̇ Yilmaz, Gürhan İçöz
Turkish Journal of Mathematics
The present paper deals with the approximation properties of the linear positive operators, including Δh -Gould-Hopper Appell polynomials. We investigate some theorems for convergence of the operators and their approximation degrees with the help of the classical approach, Peetre’s K-functional, Lipschitz class and Voronovskajatype theorem. In the last section of the paper, we introduce the Kantorovich form of the operators and examine the approximation degree.
Elastic Strips Along Isotropic Curves In Complex 3-Spaces, Dae Won Yoon, Zühal Küçükarslan Yüzbaşi
Elastic Strips Along Isotropic Curves In Complex 3-Spaces, Dae Won Yoon, Zühal Küçükarslan Yüzbaşi
Turkish Journal of Mathematics
In this paper, we define the ruled surface in terms of the Darboux vector field of an isotropic curve in a complex 3-space, and we study the ruled surface as an elastic strip along the isotropic curve. First of all, we show that elastic strips along isotropic curves that serve critical points of the modified Sadowsky functional are characterized by three Euler-Lagrange equations. As a result, we give two conservation laws to characterize elastic strips of isotropic curves in complex 3-space and explain an isotropic helix in terms of the force vector. Finally, we give some examples to illustrate elastic …
Gradient Almost Yamabe Solitons Immersed Into A Riemannian Warped Productmanifold, Willian Tokura, Levi Adriano, Elismar Batista, Adriano Bezerra
Gradient Almost Yamabe Solitons Immersed Into A Riemannian Warped Productmanifold, Willian Tokura, Levi Adriano, Elismar Batista, Adriano Bezerra
Turkish Journal of Mathematics
The purpose of this article is to study the geometry of gradient almost Yamabe solitons immersed in warped product manifolds I ×f Mn whose potential is given by the height function from the immersion. First, we present some geometric rigidity on compact solitons due to a curvature condition on the warped product manifold. In the sequel, we investigate conditions for the existence of totally geodesic, totally umbilical, and minimal solitons. Furthermore, in the scope of constant angle immersions, a classification of rotational gradient almost Yamabe solitons immersed in R ×f Rn is also made.
A Note On Hybrid Hyper Leonardo Numbers, Elen Viviani Pereira Spreafico, Paula Maria Machado Cruz Catarino
A Note On Hybrid Hyper Leonardo Numbers, Elen Viviani Pereira Spreafico, Paula Maria Machado Cruz Catarino
Turkish Journal of Mathematics
Recently, many studies have been devoted to extending particular sets of integers to other special sets, such as complex, dual, hyperbolic, and hybrid numbers. In this study, we define a new generalization of the Leonardo sequence consisting of the hybrid hyper-Leonardo numbers. This sequence of numbers is an extension of the hyper Leonardo numbers in the hybrid set. We investigate some algebraic properties of this sequence, the generating function, and the Binet formula related to this type of sequence.
Generalizations Of Zassenhaus Lemma And Jordan-Hölder Theorem For 2−Crossed Modules, Seli̇m Çeti̇n
Generalizations Of Zassenhaus Lemma And Jordan-Hölder Theorem For 2−Crossed Modules, Seli̇m Çeti̇n
Turkish Journal of Mathematics
We present a comprehensive generalization of the Zassenhaus Lemma, the Scherier Refinement Theorem, and the Jordan-Hölder Theorem, extending their applicability to both crossed modules and 2−crossed modules. It is discovered that the previously established normality conditions are insufficient for forming quotient objects of 2−subcrossed modules, as demonstrated through an illustrative example, and these conditions are rigorously revised to allow these generalizations. These new conditions now yield results that are categorically accurate. Additionally, the study has led to the derivation of several supplementary results, including isomorphism theorems for 2−crossed modules.
Some New Results On Generalized Hyers-Ulam Stability In Modular Function Spaces, Mozhgan Taliman, Mahdi Azhini, Shahram Rezapour
Some New Results On Generalized Hyers-Ulam Stability In Modular Function Spaces, Mozhgan Taliman, Mahdi Azhini, Shahram Rezapour
Turkish Journal of Mathematics
In this work, we present a new weighted method for proving the generalized Hyers-Ulam stability for nonlinear Volterra integral equations in modular spaces. Using the same technique, we also prove the generalized Hyers- Ulam stability for nonlinear functional equations under Δ2 conditions. Fixed-point theorems in modular spaces form the foundation of our main conclusions.
On The Dual Pseudo-Spherical Elastic Curves, Gözde Özkan Tükel, Ahmet Yücesan
On The Dual Pseudo-Spherical Elastic Curves, Gözde Özkan Tükel, Ahmet Yücesan
Turkish Journal of Mathematics
We investigate a dual bending energy functional that operates on the dual pseudo-sphere in dual Lorentzian space. For a nonnull dual curve on the dual pseudo-sphere to be considered elastic, it must satisfy the conditions of a dual Euler-Lagrange equation. To solve this problem, we use Jacobi elliptic functions to approach the real part and the integral factors method to solve the dual part. Using E. Study mapping, we examine situations where every timelike or spacelike dual elastic curve on the dual pseudo-sphere matches an elastic strip with a suitable base curve in Minkowski 3-space.