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Recent documents in Turkish Journal of Mathematicsen-usFri, 21 Jun 2024 09:17:51 PDT3600On the dual pseudo-spherical elastic curves
https://journals.tubitak.gov.tr/math/vol48/iss3/18
https://journals.tubitak.gov.tr/math/vol48/iss3/18Wed, 15 May 2024 07:26:14 PDT
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.
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GÖZDE ÖZKAN TÜKEL et al.A Study of the scattering analysis of the multiplicative Sturm-Liouville problem
https://journals.tubitak.gov.tr/math/vol48/iss3/17
https://journals.tubitak.gov.tr/math/vol48/iss3/17Wed, 15 May 2024 07:26:13 PDT
The main purpose of this study is to examine the scattering analysis of a multiplicative Sturm-Liouville boundary value problem. Firstly, we find the Jost solution of this problem and give the Jost function to construct the scattering function of the problem. Secondly, we obtain asymptotic equations for Jost solution and investigate some properties of the Jost function. Moreover, we present other solutions of the problem by giving the relations between these solutions and Jost solution. Finally, we define the scattering function of this problem by using the Jost function and examine the basic properties of the scattering function.
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Güler Başak Öznur et al.Generalizations of Zassenhaus lemma and Jordan-Hölder theorem
for 2−crossed modules
https://journals.tubitak.gov.tr/math/vol48/iss3/15
https://journals.tubitak.gov.tr/math/vol48/iss3/15Wed, 15 May 2024 07:26:12 PDT
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.
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SELİM ÇETİNExistence and uniqueness of continuous solutions for iterative functional
differential equations in Banach algebras
https://journals.tubitak.gov.tr/math/vol48/iss3/16
https://journals.tubitak.gov.tr/math/vol48/iss3/16Wed, 15 May 2024 07:26:12 PDT
This paper is devoted to studying the existence and uniqueness of continuous solutions of the following iterative functional differential equation d dt x(t) − h ( t, x[1](t), . . . , x[n](t) ) f (t, x[1](t), . . . , x[n](t)) = g ( t, x[1](t), . . . , x[n](t) ) , t ∈ J, x(0) = x0. By using of Boyd-Wong’s fixed point theorem and under suitable conditions, we establish the existence and uniqueness of a continuous solution.
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KHALED BEN AMARAA note on hybrid hyper Leonardo numbers
https://journals.tubitak.gov.tr/math/vol48/iss3/14
https://journals.tubitak.gov.tr/math/vol48/iss3/14Wed, 15 May 2024 07:26:11 PDT
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.
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ELEN VIVIANI PEREIRA SPREAFICO et al.Gradient almost Yamabe solitons immersed into a Riemannian warped productmanifold
https://journals.tubitak.gov.tr/math/vol48/iss3/13
https://journals.tubitak.gov.tr/math/vol48/iss3/13Wed, 15 May 2024 07:26:10 PDT
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.
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WILLIAN TOKURA et al.Elastic strips along isotropic curves in complex 3-spaces
https://journals.tubitak.gov.tr/math/vol48/iss3/11
https://journals.tubitak.gov.tr/math/vol48/iss3/11Wed, 15 May 2024 07:26:09 PDT
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 strips with isotropic curves in a complex 3-space.
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DAE WON YOON et al.Alternative solution to the fractional differential equation with recurrence
relationship
https://journals.tubitak.gov.tr/math/vol48/iss3/12
https://journals.tubitak.gov.tr/math/vol48/iss3/12Wed, 15 May 2024 07:26:09 PDT
A different solution from the one already known for sequential fractional differential equations with recurrence relation is proposed. This solution involves a Mittag-Leffler type function, which satisfies a recurrence property compatible with the behavior of sequential fractional differential equations with recurrence relation.
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LUCIANO L. LUQUE et al.Some new results on generalized Hyers-Ulam stability in modular function spaces
https://journals.tubitak.gov.tr/math/vol48/iss3/10
https://journals.tubitak.gov.tr/math/vol48/iss3/10Wed, 15 May 2024 07:26:08 PDT
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.
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MOZHGAN TALIMAN et al.Warped product pointwise hemislant submanifolds whose ambient spaces arenearly para-Kaehler manifolds
https://journals.tubitak.gov.tr/math/vol48/iss3/9
https://journals.tubitak.gov.tr/math/vol48/iss3/9Wed, 15 May 2024 07:26:07 PDT
In this article, we explain pointwise slant, pointwise hemislant, and warped product pointwise hemislant submanifolds whose ambient spaces are nearly para-Kaehler manifolds. Also, we obtain several theorems and examples. Subsequently, we get some results concerning the inequality.
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SEDAT AYAZ et al.Topogenous orders and closure operators on posets
https://journals.tubitak.gov.tr/math/vol48/iss3/8
https://journals.tubitak.gov.tr/math/vol48/iss3/8Wed, 15 May 2024 07:26:06 PDT
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.
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JOSEF SLAPAL et al.Approximation by operators Involving Δh -Gould-Hopper Appell polynomials
https://journals.tubitak.gov.tr/math/vol48/iss3/6
https://journals.tubitak.gov.tr/math/vol48/iss3/6Wed, 15 May 2024 07:26:05 PDT
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.
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BİLGE ZEHRA SERGİ YILMAZ et al.Conformal-projective transformations on statistical
and semi-Weyl manifolds with torsion
https://journals.tubitak.gov.tr/math/vol48/iss3/7
https://journals.tubitak.gov.tr/math/vol48/iss3/7Wed, 15 May 2024 07:26:05 PDT
We show that statistical and semi-Weyl structures with torsion are invariant under conformal-projective transformations. We prove that a nondegenerate submanifold of a semi-Weyl (respectively, statistical) manifold with torsion is also a semi-Weyl (respectively, statistical) manifold with torsion, and that the induced structures of two conformal-projective equivalent semi-Weyl (respectively, statistical) structures with torsion on a manifold to a nondegenerate submanifold, are conformal-projective equivalent, too. Also, we prove that the umbilical points of a nondegenerate hypersurface in a semi-Weyl manifold with torsion are preserved by conformal-projective changes. Then we consider lightlike hypersurfaces of semi-Weyl manifolds with torsion and we describe similarities and differences with respect to the nondegenerate hypersurfaces. Finally, we show that a semi-Weyl manifold with torsion can be realized by a nondegenerate affine distribution.
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ADARA M. BLAGA et al.Ranks of certain semigroups of transformations with idempotent complement
whose restrictions belong to a given semigroup
https://journals.tubitak.gov.tr/math/vol48/iss3/5
https://journals.tubitak.gov.tr/math/vol48/iss3/5Wed, 15 May 2024 07:26:04 PDT
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.
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LEYLA BUGAY et al.Existence and nonexistence of permutation trinomials and quadrinomials
https://journals.tubitak.gov.tr/math/vol48/iss3/4
https://journals.tubitak.gov.tr/math/vol48/iss3/4Wed, 15 May 2024 07:26:03 PDT
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) .
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ZHIGUO DING et al.Dynamics of compositions of some Lotka–Volterra mappings operating in a
two-dimensional simplex
https://journals.tubitak.gov.tr/math/vol48/iss3/3
https://journals.tubitak.gov.tr/math/vol48/iss3/3Wed, 15 May 2024 07:26:02 PDT
In a number of applied problems (immunology, epidemiology, virology, etc.), there is a need to study the dynamics of the trajectories of the compositions of the Lotka–Volterra mappings. In this paper, some variants of these compositions are considered, in particular, the dynamics of the trajectories of the compositions of the Lotka–Volterra mappings acting in a two-dimensional simplex, with transitive tournaments, which can be applied in the study of these processes. Cards of fixed points are constructed for compositions and the characters of fixed points are studied.
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DILFUZA ESHMAMATOVA et al.Cover and Contents
https://journals.tubitak.gov.tr/math/vol48/iss3/1
https://journals.tubitak.gov.tr/math/vol48/iss3/1Wed, 15 May 2024 07:26:01 PDTInteger representations of classical Weyl groups
https://journals.tubitak.gov.tr/math/vol48/iss3/2
https://journals.tubitak.gov.tr/math/vol48/iss3/2Wed, 15 May 2024 07:26:01 PDT
In this paper, we define a mixed-base number system over a Weyl group Dn , the group of even-signed permutations. We introduce one-to-one correspondence between the positive integers of the set {1, · · · , 2n−1n!} and elements of this group, after constructing the subexceedant function associated with the group. Thus, the integer representations of all the classical Weyl groups are now completed. Furthermore, we present an inversion statistic on the group Dn by using a decomposition of a positive root system of this reflection group. This inversion statistic is compatible with the length function on the group Dn . Then we derive some combinatorial properties for the inversion statistic. In addition, we prove that the D-major index is equi-distributed with this inversion statistic on Dn . Finally, we propose a public-key cryptosystem based on both the generalized hidden discrete logarithm problem and the integer representation over the group Dn .
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Hasan Arslan et al.Laguerre type twice-iterated Appell polynomials
https://journals.tubitak.gov.tr/math/vol48/iss2/17
https://journals.tubitak.gov.tr/math/vol48/iss2/17Sun, 17 Mar 2024 06:28:42 PDT
In this study, we use discrete Appell convolution to define the sequence of Laguerre type twice-iterated Appell polynomials. We obtain explicit representation, recurrence relation, determinantal representation, lowering operator, integro-partial raising operator and integro-partial differential equation. In addition, the special cases of this new family are investigated using Euler and Bernoulli numbers. We also state their corresponding characteristic properties.
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NESLİHAN BİRİCİK et al.Special subdiagrams of Young diagrams and numerical semigroups
https://journals.tubitak.gov.tr/math/vol48/iss2/16
https://journals.tubitak.gov.tr/math/vol48/iss2/16Sun, 17 Mar 2024 06:28:41 PDT
In this study, Young diagrams and their corresponding numerical sets are considered, and a new notion called special subdiagrams is described. Characterizations of special subdiagrams and their corresponding numerical sets, as well as the conditions when they are numerical semigroups, are provided. Young diagrams of symmetric, almost symmetric and Arf numerical semigroups are also considered and properties of their special subdiagrams are given.
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MERAL SÜER et al.