Recent Submissions

  • Three Determinant Evaluations 

    Chu, Wenchang; Kılıç, Emrah (Springer, 2021)
    By means of matrix decompositions, three determinants with their entries being binomial sums are evaluated in closed forms. Ten remarkable examples are illustrated as propositions, which present determinant identities about ...
  • The Language Of The Universe: Mathematics 

    Akın, Ömer (Iğdır UniversityIğdır Üniversitesi, 2019)
    Before examining this issue, I find it necessary to summon your attention to the following fact: Human beings live in an ever-changing world filled with objects in motion and intraction. Hence, the problems we face in such ...
  • İslam Hukuku ve Dereceli Mantık İlişkisi 

    Yüksek, Ali; Akın, Ömer (Oş Devlet Üniversitesi İlahiyat Fakültesi, 2019)
    We have been making frequent and evaluations in our social and scientific life. Sometimes we encounter uncertainties due to incomplete information or technical impossibilities. In these cases we need multiple logic to ...
  • Fuzzy Modelling of Covid-19 in Turkey and Some Countries in The World 

    Baldemir, Harun; Akın, Agah; Akın, Ömer (Matematikçiler Derneği, 2020)
    Coronaviruses are a large family of viruses that are found in many different species of animals and are deadly illnesses for human. In late December 2019, China first announced the outbreak of a new coronavirus: Corona ...
  • The Irregularity Polynomials of Fibonacci and Lucas cubes 

    Eğecioğlu, Ömer; Saygı, Elif; Saygı, Zülfükar (Springer, 2021-03)
    Irregularity of a graph is an invariant measuring how much the graph differs from a regular graph. Albertson index is one measure of irregularity, defined as the sum of | deg(u) - deg(v) | over all edges uv of the graph. ...
  • Hopf bifurcations in a class of reaction-diffusion equations including two discrete time delays: An algorithm for determining Hopf bifurcation, and its applications 

    Bilazeroğlu, Ş.; Merdan, Hüseyin (Elsevier Ltd, 2021-01)
    We analyze Hopf bifurcation and its properties of a class of system of reaction-diffusion equations involving two discrete time delays. First, we discuss the existence of periodic solutions of this class under Neumann ...
  • q-binomial formulae of Dixon`s type and the Fibonomial sums 

    Chu, Wenchang; Kılıç, Emrah (University of Belgrade, School of Electrical Engineering, 2020-10)
    Cubic sums of the Gaussian q-binomial coefficients with certain weight functions will be evaluated in this paper. To realize this, we will derive two remarkable formulae by means of the Carlitz-Sears transformation on ...
  • Stability and zero-Hopf bifurcation analysis of a tumour and T-helper cells interaction model in the case of HIV infection 

    Karahisarlı, Gamzegül; Merdan, Hüseyin; Tridane, Abdessamad (University of Miskolc, 2020)
    In this paper, we present a mathematical model governing the dynamics of tumourimmune cells interaction under HIV infection. The interactions between tumour cells, helper T-cells, infected helper T-cells and virus cells ...
  • k-Fibonacci Cubes: A Family of Subgraphs of Fibonacci Cubes 

    Eğecioğlu, Ömer; Saygı, Elif; Saygı, Zülfükar (World Scientific, 2020-08)
    Hypercubes and Fibonacci cubes are classical models for interconnection networks with interesting graph theoretic properties. We consider k-Fibonacci cubes, which we obtain as subgraphs of Fibonacci cubes by eliminating ...
  • The interesting spectral interlacing property for a certain tridiagonal matrix 

    da Fonseca, Carlos M.; Kılıç, Emrah; Pereira, Antonio (International Linear Algebra Society, 2020-08)
    In this paper, a new tridiagonal matrix, whose eigenvalues are the same as the Sylvester-Kac matrix of the same order, is provided. The interest of this matrix relies also in that the spectrum of a principal submatrix is ...
  • An observation on the determinant of a Sylvester-Kac type matrix 

    da Fonseca, Carlos M.; Kılıç, Emrah (Sciendo, 2020-03)
    Based on a less-known result, we prove a recent conjecture concerning the determinant of a certain Sylvester-Kac type matrix related to some Lie Algebras. The determinant of an extension of that matrix is presented.
  • Complex Dynamics of a Discrete-Time Prey-Predator System with Leslie Type: Stability, Bifurcation Analyses and Chaos 

    Baydemir, Pınar; Merdan, Hüseyin; Karaoğlu, Esra; Sucu, Gökçe (World Scientific, 2020-08)
    Dynamic behavior of a discrete-Time prey-predator system with Leslie type is analyzed. The discrete mathematical model was obtained by applying the forward Euler scheme to its continuous-Time counterpart. First, the local ...
  • On the chromatic polynomial and the domination number of k-Fibonacci cubes 

    Eğecioğlu, Ömer; Saygı, Elif; Saygı, Zülfükar (TÜBİTAK, 2020)
    Fibonacci cubes are defined as subgraphs of hypercubes, where the vertices are those without two consecutive 1's in their binary string representation. k -Fibonacci cubes are in turn special subgraphs of Fibonacci cubes ...
  • Characterization of Absolute and Uniform Continuity 

    Aslan, İsmail; Duman, Oktay (Hacettepe UniversityHacettepe Üniversitesi, 2020)
    In the present paper, by considering nonlinear integral operators and using their approximations via regular summability methods, we obtain characterizations for some function spaces including the space of absolutely ...
  • Results on the domination number and the total domination number of Lucas cubes 

    Saygı, Zülfükar (Society of Mathematicians, Physicists and Astronomers of Slovenia, 2020)
    Lucas cubes are special subgraphs of Fibonacci cubes. For small dimensions, their domination numbers are obtained by direct search or integer linear programming. For larger dimensions some bounds on these numbers are given. ...
  • A new type of Sylvester–Kac matrix and its spectrum 

    Kılıç, Emrah; da Fonseca, C.M. (Taylor and Francis Ltd., 2021)
    The Sylvester–Kac matrix, sometimes known as Clement matrix, has many extensions and applications throughout more than a century of its existence. The computation of the eigenvalues or even the determinant have always been ...
  • On Binomial Double Sums With Fibonacci And Lucas Numbers-II 

    Kılıç, Emrah; Taşdemir, Funda (Charles Babbage Research Centre, 2019-04)
    In this paper, we compute various binomial-double-sums involving the Fibonacci numbers as well as their alternating analogous. It would be interesting that all sums we shall compute are evaluated in nice multiplication ...
  • Evaluation of sums of products of Gaussian q-binomial coefficients with rational weight functions 

    Arıkan, Talha; Kılıç, Emrah; Prodinger, Helmut (TÜBİTAK, 2020)
    Generalizing earlier results, sums over the products of the Gaussian q-binomial coefficients are computed. Some applications of the results for special choices of q are emphasized. The results are obtained by the elementary ...
  • Cubic sums of q-binomial coefficients and the Fibonomial coefficients 

    Chu, Wenchang; Kılıç, Emrah (Rocky Mountain Mathematics Consortium, 2019)
    Triple product sums on the generalized Fibonomial and Lucanomial coefficients are evaluated in closed forms by means of Bailey’s summation formulae for two terminating well-poised 3?2-series.
  • New reciprocal sums involving finite products of second order recursions 

    Kılıç, Emrah; Ersanli, Didem (University of Miskolc, 2019)
    In this paper, we present new kinds of reciprocal sums of finite products of general second order linear recurrences. In order to evaluate explicitly them by $q$-calculus, first we convert them into their $q$-notation and ...

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