Browsing Matematik Bölümü / Department of Mathematics by Title
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Decompositions of the Cauchy and FerrersJackson polynomials
(Udruga Matematicara Osijek, 2016)Recently, Witula and Slota have given decompositions of the Cauchy and FerrersJackson polynomials [Cauchy, FerrersJackson and Chebyshev polynomials and identities for the powers of elements of some conjugate recurrence ... 
The discreteness of the spectrum of the Schrödinger operator equation and some properties of the snumbers of the inverse Schrödinger operator
(John Wiley and Sons Ltd, 201905)In this article, we investigate the discreteness and some other properties of the spectrum for the Schrödinger operator L defined by the formula LY=d 2 y/dx 2 +A(A+I)/x 2 y+Q(x)y on the space L 2 (H, [0, ?)), where H is ... 
Distribution of maximum loss of fractional Brownian motion with drift
(Elsevier Science Bv, 201312)In this paper, we find bounds on the distribution of the maximum loss of fractional Brownian motion with H >= 1/2 and derive estimates on its tail probability. Asymptotically, the tail of the distribution of maximum loss ... 
Double binomial sums and double sums related with certain linear recurrences of various order
(Chiang Mai University, 20180501)In this paper, we derive new double binomial sums families related with generalized second, third and certain higher order linear recurrences. We also present various parametric generalizations of some results of [1, 2]. ... 
Error Estimation for Approximate Solutions of Delay Volterra Integral Equations
(Springer Nature Switzerland, 201911)This work is related to inequalities in the approximation theory. Mainly, we study numerical solutions of delay Volterra integral equations by using a collocation method based on sigmoidal function approximation. Error ... 
Estimation of the Hurst parameter for fractional Brownian motion using the CMARS method
(Elsevier Science Bv, 201403)In this study, we develop an alternative method for estimating the Hurst parameter using the conic multivariate adaptive regression splines (CMARS) method. We concentrate on the strong solutions of stochastic differential ... 
Evaluation of Hessenberg Determinants via Generating Function Approach
(University of Nis, 2017)In this paper, we will present various results on computing of wide classes of Hessenberg matrices whose entries are the terms of any sequence. We present many new results on the subject as well as our results will cover ... 
Evaluation of spectrum of 2periodic tridiagonalSylvester matrix
(Scientific Technical Research Council TurkeyTürkiye bilimsel ve teknolojik araştırma kurumu, 2016)The Sylvester matrix was first defined by JJ Sylvester. Some authors have studied the relationships between certain orthogonal polynomials and the determinant of the Sylvester matrix. Chu studied a generalization of the ... 
Evaluation of sums involving Gaussian qbinomial coefficients with rational weight functions
(World Scientific Publishing Co. Pte Ltd, 201603)We consider sums of the Gaussian qbinomial coefficients with a parametric rational weight function. We use the partial fraction decomposition technique to prove the claimed results. We also give some interesting applications ... 
Evaluation of sums involving products of Gaussian qbinomial coefficients with applications
(De Gruyter, 201904)Sums of products of two Gaussian qbinomial coefficients, are investigated, one of which includes two additional parameters, with a parametric rational weight function. By means of partial fraction decomposition, first the ... 
Evaluation of sums involving products of Gaussian qbinomial coefficients with applications to Fibonomial sums
(Scientific Technical Research Council TurkeyTürkiye bilimsel ve teknolojik araştırma kurumu, 2017)Sums of products of two Gaussian qbinomial coefficients with a parametric rational weight function are considered. The partial fraction decomposition technique is used to evaluate the sums in closed form. Interesting ... 
Evaluation of sums of products of Gaussian qbinomial coefficients with rational weight functions
(TÜBİTAK, 2020)Generalizing earlier results, sums over the products of the Gaussian qbinomial coefficients are computed. Some applications of the results for special choices of q are emphasized. The results are obtained by the elementary ... 
Evaluation of various partial sums of Gaussian qbinomial sums
(Springer Berlin Heidelberg, 20180601)We present three new sets of weighted partial sums of the Gaussian qbinomial coefficients. To prove the claimed results, we will use qanalysis, Rothe's formula and a qversion of the celebrated algorithm of Zeilberger. ... 
Evaluation of sums containing triple aerated generalized Fibonomial coefficients
(De Gruyter Open Ltd, 201704)We evaluate a class of sums of triple aerated Fibonomial coefficients with a generalized Fibonacci number as coefficient. The technique is to rewrite everything in terms of a variable q and then to use Rothe's identity ... 
Explicit maximal and minimal curves over finite fields of odd characteristics
(Academic Press Inc Elsevier Science, 201611)In this work we present explicit classes of maximal and minimal ArtinSchreier type curves over finite fields having odd characteristics. Our results include the proof of Conjecture 5.9 given in [1] as a very special ... 
Explicit spectrum of a circulanttridiagonal matrix with applications
(American Institute of Physics Inc., 201907)We consider a circulanttridiagonal matrix and compute its determinant by using generating function method. Then we explicitly determine its spectrum. Finally we present applications of our results for trigonometric ... 
Formulae for two weighted binomial identities with the falling factorials
(Charles Babbage Research Centre, 201804)In this paper, we will give closed formulae for weighted and alternating weighted binomial sums with the generalized Fibonacci and Lucas numbers including both falling factorials and powers of indices. Furthermore we will ... 
Formulas for binomial sums including powers of fibonacci and lucas numbers
(Politechnica University of Bucharest, 2015)Recently Prodinger [2] proved general expansion formulas for sums of powers of Fibonacci and Lucas numbers. In this paper, we will prove general expansion formulas for binomial sums of powers of Fibonacci and Lucas numbers. 
Formulæ for multiparameter Gaussian qbinomial sums with applications
(Springer Nature, 202006)Some Gaussian qbinomial sum identities from KAO are further generalized, introducing two additional parameters. We prove the claimed results by qcalculus. Finally we present applications to the generalized Fibonomial ... 
Formulæ related to the qDixon formula with applications to Fibonomial sums
(Kluwer Academic Publishers, 201506)The analogue of Dixon's identity involves three binomial coefficients as summands. We find many variations of it that have beautiful corollories in terms of Fibonomial sums. Proofs involve either several instances of the ...