Department of Mathematics
Recent Submissions

Quasiequivalence of bases in some Whitney spaces
(Cambridge University Press, 20210518)If the logarithmic dimension of a Cantortype set K is smaller than 1 , then the Whitney space E(K) possesses an interpolating Faber basis. For any generalized Cantortype set K, a basis in E(K) can be presented by ... 
Lines in supersingular quartics
(Nihon Sugakkai,Mathematical Society of Japan, 20211019)We show that the number of lines contained in a supersingular quartic surface is 40 or at most 32, if the characteristic of the field equals 2, and it is 112, 58, or at most 52, if the characteristic equals 3. If the quartic ... 
Cyclicity of elliptic curves modulo primes in arithmetic progressions
(Cambridge University Press, 20210503)We consider the reduction of an elliptic curve defined over the rational numbers modulo primes in a given arithmetic progression and investigate how often the subgroup of rational points of this reduced curve is cyclic. 
“Books i used as a child were mathematically incorrect”: reasons to use children’s shaperelated books as a resource to improve mathematical knowledge for teaching
(Modestum Publishing Ltd., 20210405)Some goals of mathematics teacher education include ensuring that preservice teachers (PSTs) have strong content knowledge, the skill to anticipate and interpret student thinking, the ability to plan how to respond, and ... 
On the influence of the fixed points of an automorphism to the structure of a group
(Academic Press, 20210106)Let α be a coprime automorphism of a group G of prime order and let P be an αinvariant Sylow psubgroup of G. Assume that p∉π(CG(α)). Firstly, we prove that G is pnilpotent if and only if CNG(P)(α) centralizes P. In the ... 
Stabilization of higher order Schrödinger equations on a finite interval: part II
(AIMS Press, 202107)Backstepping based controller and observer models were designed for higher order linear and nonlinear Schrödinger equations on a finite interval in [3] where the controller was assumed to be acting from the left endpoint ... 
Correction to: Modelling personal cautiousness during the COVID19 pandemic: a case study for Turkey and Italy
(Springer, 20210614)Although policy makers recommend or impose various standard measures, such as social distancing, movement restrictions, wearing face masks and washing hands, against the spread of the SARSCoV2 pandemic, individuals follow ... 
A short note on generic initial ideals
(TÜBİTAK, 20210419)The definition of a generic initial ideal includes the assumption x1 > x2 > · · · > xn . A natural question is how generic initial ideals change when we permute the variables. In the article [1, §2], it is shown that the ... 
KelvinMöbiusinvariant harmonic function spaces on the real unit ball
(Elsevier, 20210507)We define the KelvinMöbius transform of a function harmonic on the unit ball of Rn and determine harmonic function spaces that are invariant under this transform. When n ≥ 3, in the category of Banach spaces, the minimal ... 
Shift operators on harmonic Hilbert function spaces on real balls and von Neumann inequality
(Elsevier, 20210422)On harmonic function spaces, we define shift operators using zonal harmonics and partial derivatives, and develop their basic properties. These operators turn out to be multiplications by the coordinate variables followed ... 
Dade groups for finite groups and dimension functions
(Academic Press, 20210615)Let G be a finite group and k an algebraically closed field of characteristic p > 0. We define the notion of a Dade kGmodule as a generalization of endopermutation modules for pgroups. We show that under a suitable ... 
Logarithmic dimension and bases in Whitney spaces
(Scientific and Technical Research Council of Turkey  TUBITAK,Turkiye Bilimsel ve Teknik Arastirma Kurumu, 20210727)We give a formula for the logarithmic dimension of the generalized Cantortype set K . In the case when the logarithmic dimension of K is smaller than 1, we construct a Faber basis in the space of Whitney functions E(K). 
Hilbert series of tangent cones for Gorenstein monomial curves in A4(K)
(Scientific and Technical Research Council of Turkey  TUBITAK,Turkiye Bilimsel ve Teknik Arastirma Kurumu, 20210121)In this paper, we study the Hilbert series of the tangent cone of Gorenstein monomial curves in the 4 dimensional affine space. We give an explicit formula for the reduced Hilbert series of the tangent cone of a ... 
On the extremal points of the Λpolytopes and classical simulation of quantum computation with magic states
(Rinton Press, Inc., 202111)We investigate the Λpolytopes, a convexlinear structure recently defined and applied to the classical simulation of quantum computation with magic states by sampling. There is one such polytope, Λn, for every number n ... 
Conics in sextic K3Surface in P4
(Cambridge University Press, 20211129)We prove that the maximal number of conics in a smooth sextic K3surface X ⊂ P4 is 285, whereas the maximal number of real conics in a real sextic is 261. In both extremal configurations, all conics are irreducible. 
Ricci solitons on singly warped product manifolds and applications
(Elsevier BV * NorthHolland, 202108)The purpose of this article is to study implications of a Ricci soliton warped product manifold to its base and fiber manifolds. First, it is proved that if a warped product manifold is Ricci soliton then its factors are ... 
Duo property for rings by the quasinilpotent perspective
(Vasyl Stefanyk Precarpathian National University, 20210316)In this paper, we focus on the duo ring property via quasinilpotent elements, which gives anew kind of generalizations of commutativity. We call this kind of ringsqnilduo. Firstly, someproperties of quasinilpotents in a ... 
φ (Ric)vector fields on warped product manifolds and applications
(Springer, 202111)Sufficient and necessary conditions are provided on warped product manifolds and their base and fiber manifolds for a vector field φj to be a φ(Ric)vector field , that is, ∇iφj=μRij where Rij is the Ricci tensor of M and ... 
Daylight Saving Time policy and energy consumption
(Elsevier BV, 202111)Daylight Saving Time is argued to be effective in saving energy. Turkey is one of the few countries that annulled the clock changes and remained in the summertime zone in 2016. Therefore, the country provides a unique ... 
On the discretization of Darboux integrable systems admitting the secondorder integrals
(Rossiiskaya Akademiya Nauk Ufimskii Nauchnyi Tsentr, Institut Matematiki s Vychislitel'nym Tsentrom, 2021)We consider a discretization problem for hyperbolic Darboux integrable systems. In particular, we discretize continuous systems admitting 𝑥 and 𝑦integrals of the first and second order. Such continuous systems were ...