WoS İndeksli Yayınlar Koleksiyonu / WoS Indexed Publications Collection

Permanent URI for this collectionhttps://hdl.handle.net/11147/7150

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Department: search.filters.department.İzmir Institute of Technology. MathematicsScopus Q: search.filters.scopusQuartile.Q4

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Now showing 1 - 10 of 30
  • Article
    Citation - WoS: 1
    Citation - Scopus: 1
    Euler-Zagier Sums Via Trigonometric Series
    (Publishing House of the Romanian Academy, 2023) Çam Çelik, Şermin; Göral, Haydar
    In this note, we study the evaluations of Euler sums via trigonometric series. It is a commonly believed conjecture that for an even weight greater than seven, Euler sums cannot be evaluated in terms of the special values of the Riemann zeta function. For an even weight, we reduce the evaluations of Euler sums into the evaluations of double series and integrals of products of Clausen functions. We also re-evaluate Euler sums of odd weight using a new method based on trigonometric series.
  • Article
    Citation - Scopus: 2
    Analysis of the Logistic Growth Model With Taylor Matrix and Collocation Method
    (Etamaths Publishing, 2023) Çelik, Elçin; Uçar, Deniz
    Early analysis of infectious diseases is very important in the spread of the disease. The main aim of this study is to make important predictions and inferences for Covid 19, which is the current epidemic disease, with mathematical modeling and numerical solution methods. So we deal with the logistic growth model. We obtain carrying capacity and growth rate with Turkey epidemic data. The obtained growth rate and carrying capacity is used in the Taylor collocation method. With this method, we estimate and making predictions close to reality with Maple. We also show the estimates made with the help of graphics and tables. © 2023 the author(s).
  • Article
    Citation - WoS: 1
    Citation - Scopus: 1
    Irreducibility and Primality in Differentiability Classes
    (Michigan State University Press, 2023) Batal, Ahmet; Eyidoğan, S.; Göral, Haydar
    In this note, we give criteria for the irreducibility of functions in Cm [0, 1], where m ∈ {1, 2, 3, ...} ∪ {∞} ∪ {ω}. We also discuss irreducibility in multivariable differentiability classes. Moreover, we characterize irreducible functions and maximal ideals in C∞ [0, 1]. In fact, irreducible and prime smooth functions are the same, and every maximal ideal of C∞ [0, 1] is principal. © 2023 Michigan State University Press. All rights reserved.
  • Article
    Class Number and the Special Values of L-Functions
    (Romanian Academy, 2022) Göral, Haydar
    We give infinitely many explicit new representations of the class number of imag inary quadratic fields in terms of certain trigonometric series. Our result relies on a hybrid between power series and trigonometric series. Furthermore, in some cases we prove that the special values of Dirichlet L-functions can be evaluated as certain finite sums.
  • Article
    Citation - WoS: 2
    Citation - Scopus: 3
    The Green-Tao Theorem and the Infinitude of Primes in Domains
    (Taylor & Francis, 2022) Göral, Haydar; Özcan, Hikmet Burak; Sertbaş, Doğa Can
    We first prove an elementary analogue of the Green-Tao Theorem. The celebrated Green-Tao Theorem states that there are arbitrarily long arithmetic progressions in the set of prime numbers. In fact, we show the Green-Tao Theorem for polynomial rings over integral domains with several variables. Using the Generalized Polynomial van der Waerden Theorem, we also prove that in an infinite unique factorization domain, if the cardinality of the set of units is strictly less than that of the domain, then there are infinitely many prime elements. Moreover, we deduce the infinitude of prime numbers in the positive integers using polynomial progressions of length three. In addition, using unit equations, we provide two more proofs of the infinitude of prime numbers. Finally, we give a new proof of the divergence of the sum of reciprocals of all prime numbers.
  • Article
    Citation - WoS: 7
    Citation - Scopus: 9
    Parity, Virtual Closure and Minimality of Knotoids
    (World Scientific Publishing, 2021) Güğümcü, Neslihan; Kauffman, Louis H.
    In this paper, we study parity in planar and spherical knotoids in relation to virtual knots. We introduce a planar version of the parity bracket polynomial for planar knotoids. We show that the virtual closure map (a map from the set of knotoids in S-2 to the set of virtual knots of genus at most one) is not surjective, by utilizing the surface bracket polynomial of virtual knots. We give specific examples of virtual knots that are not in the image of the virtual closure map. Turaev conjectured that minimal diagrams of knot-type knotoids have zero height. We prove this conjecture by using the results of Nikonov and Manturov induced by parities of virtual knots.
  • Article
    Citation - WoS: 1
    Citation - Scopus: 1
    Rings Whose Nonsingular Right Modules Are R-Projective
    (Mathematical Institute of Charles University, 2021) Alagöz, Yusuf; Benli Göral, Sinem; Büyükaşık, Engin
    A right R-module M is called R-projective provided that it is projective relative to the right R-module R-R. This paper deals with the rings whose all nonsingular right modules are R-projective. For a right nonsingular ring R, we prove that R-R is of finite Goldie rank and all nonsingular right R-modules are R-projective if and only if R is right finitely Sigma-CS and fiat right R-modules are R-projective. Then, R-projectivity of the class of nonsingular injective right modules is also considered. Over right nonsingular rings of finite right Goldie rank, it is shown that R-projectivity of nonsingular injective right modules is equivalent to R-projectivity of the injective hull E(R-R). In this case, the injective hull E(R-R) has the decomposition E(R-R) = U-R circle plus V-R, where U is projective and Hom(V, R/I) = 0 for each right ideal I of R. Finally, we focus on the right orthogonal class N-perpendicular to of the class IV of nonsingular right modules.
  • Article
    Citation - WoS: 2
    Citation - Scopus: 3
    Biquandle Brackets and Knotoids
    (World Scientific Publishing, 2021) Güğümcü, Neslihan; Nelson, Sam; Oyamaguchi, Natsumi
    Biquandle brackets are a type of quantum enhancement of the biquandle counting invariant for oriented knots and links, defined by a set of skein relations with coefficients which are functions of biquandle colors at a crossing. In this paper, we use biquandle brackets to enhance the biquandle counting matrix invariant defined by the first two authors in (N. Gügümcü and S. Nelson, Biquandle coloring invariants of knotoids, J. Knot Theory Ramif. 28(4) (2019) 1950029). We provide examples to illustrate the method of calculation and to show that the new invariants are stronger than the previous ones. As an application we show that the trace of the biquandle bracket matrix is an invariant of the virtual closure of a knotoid.
  • Article
    Citation - WoS: 3
    Citation - Scopus: 4
    Quantum Coin Flipping, Qubit Measurement, and Generalized Fibonacci Numbers
    (Pleiades Publishing, 2021) Pashaev, Oktay
    The problem of Hadamard quantum coin measurement in n trials, with an arbitrary number of repeated consecutive last states, is formulated in terms of Fibonacci sequences for duplicated states, Tribonacci numbers for triplicated states, and N-Bonacci numbers for arbitrary N-plicated states. The probability formulas for arbitrary positions of repeated states are derived in terms of the Lucas and Fibonacci numbers. For a generic qubit coin, the formulas are expressed by the Fibonacci and more general, N-Bonacci polynomials in qubit probabilities. The generating function for probabilities, the Golden Ratio limit of these probabilities, and the Shannon entropy for corresponding states are determined. Using a generalized Born rule and the universality of the n-qubit measurement gate, we formulate the problem in terms of generic n- qubit states and construct projection operators in a Hilbert space, constrained on the Fibonacci tree of the states. The results are generalized to qutrit and qudit coins described by generalized FibonacciN-Bonacci sequences.
  • Article
    Citation - WoS: 17
    Citation - Scopus: 17
    Quantum Calculus of Fibonacci Divisors and Infinite Hierarchy of Bosonic-Fermionic Golden Quantum Oscillators
    (World Scientific Publishing, 2021) Pashaev, Oktay
    Starting from divisibility problem for Fibonacci numbers, we introduce Fibonacci divisors, related hierarchy of Golden derivatives in powers of the Golden Ratio and develop corresponding quantum calculus. By this calculus, the infinite hierarchy of Golden quantum oscillators with integer spectrum determined by Fibonacci divisors, the hierarchy of Golden coherent states and related Fock-Bargman representations in space of complex analytic functions are derived. It is shown that Fibonacci divisors with even and odd kappa describe Golden deformed bosonic and fermionic quantum oscillators, correspondingly. By the set of translation operators we find the hierarchy of Golden binomials and related Golden analytic functions, conjugate to Fibonacci number F-kappa. In the limit. kappa -> 0, Golden analytic functions reduce to classical holomorphic functions and quantum calculus of Fibonacci divisors to the usual one. Several applications of the calculus to quantum deformation of bosonic and fermionic oscillator algebras, R-matrices, geometry of hydrodynamic images and quantum computations are discussed.