scholarly journals Binomial symmetries inspired by Bruckman's problem

Filomat ◽  
2010 ◽  
Vol 24 (1) ◽  
pp. 41-46 ◽  
Author(s):  
Wenchang Chu ◽  
Ying You
Keyword(s):  
Decomposition Method ◽  
Partial Fraction ◽  
Subject Classifications ◽  
Special Cases ◽  
Secondary 05A30 ◽  
Primary 05A10 ◽  
Partial Fraction Decomposition ◽  
Mathematics Subject Classifications ◽  
Binomial Identities

The partial fraction decomposition method is employed to establish two general algebraic identities, which contain consequently several binomial identities and their q-analogues as special cases. 2010 Mathematics Subject Classifications. Primary 05A10; Secondary 05A30. .

scholarly journals Global approximation properties of modified SMK operators

Filomat ◽  
2010 ◽  
Vol 24 (1) ◽  
pp. 47-61 ◽  
Author(s):  
Ali Özarslan ◽  
Oktay Duman
Keyword(s):  
Approximation Properties ◽  
Global Approximation ◽  
Subject Classifications ◽  
Special Cases ◽  
Mathematics Subject Classifications

In this paper, introducing a general modification of the classical Sz?sz-Mirakjan-Kantorovich (SMK) operators, we study their global approximation behavior. Some special cases are also presented. 2010 Mathematics Subject Classifications. 41A25, 41A36. .

scholarly journals Binomial Coefficient – Harmonic Sum Identities Associated to Supercongruences

Integers ◽  
2011 ◽  
Vol 11 (6) ◽  
Author(s):  
Dermot McCarthy
Keyword(s):  
Decomposition Method ◽  
Binomial Coefficient ◽  
Partial Fraction ◽  
Partial Fraction Decomposition

AbstractWe establish two binomial coefficient-generalized harmonic sum identities using the partial fraction decomposition method. These identities are a key ingredient in the proofs of numerous supercongruences. In particular, in other works of the author, they are used to establish modulo

Evaluation of sums involving products of Gaussian q-binomial coefficients with applications

2019 ◽  
Vol 69 (2) ◽  
pp. 327-338 ◽  
Author(s):  
Emrah Kiliç ◽  
Helmut Prodinger
Keyword(s):  
Weight Function ◽  
Binomial Coefficients ◽  
Partial Fraction ◽  
Partial Fraction Decomposition ◽  
Sums Of Products ◽  
Binomial Identities

Abstract Sums of products of two Gaussian q-binomial coefficients, are investigated, one of which includes two additional parameters, with a parametric rational weight function. By means of partial fraction decomposition, first the main theorems are proved and then some corollaries of them are derived. Then these q-binomial identities will be transformed into Fibonomial sums as consequences.

scholarly journals A new identity via partial fraction decomposition

Filomat ◽  
2016 ◽  
Vol 30 (7) ◽  
pp. 1957-1967
Author(s):  
Ji-Ke Ge ◽  
Tao-Tao Liu ◽  
Qiu-Ming Luo
Keyword(s):  
Partial Fraction ◽  
Partial Fraction Decomposition ◽  
Binomial Identities

In this paper, we obtain a new identity using the partial fraction decomposition. As applications, some interesting binomial identities are also derived.

scholarly journals Two-loop leading colour QCD corrections to $$ q\overline{q} $$ → γγg and qg → γγq

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
Bakul Agarwal ◽  
Federico Buccioni ◽  
Andreas von Manteuffel ◽  
Lorenzo Tancredi
Keyword(s):  
Numerical Code ◽  
Tree Level ◽  
Partial Fraction ◽  
Integration By Parts ◽  
Analytic Expressions ◽  
Partial Fraction Decomposition ◽  
Loop Amplitudes

Abstract We present the leading colour and light fermionic planar two-loop corrections for the production of two photons and a jet in the quark-antiquark and quark-gluon channels. In particular, we compute the interference of the two-loop amplitudes with the corresponding tree level ones, summed over colours and polarisations. Our calculation uses the latest advancements in the algorithms for integration-by-parts reduction and multivariate partial fraction decomposition to produce compact and easy-to-use results. We have implemented our results in an efficient C++ numerical code. We also provide their analytic expressions in Mathematica format.

scholarly journals A New Approach for Analyzing the Reliability of the Repair Facility in a Series System with Vacations

2012 ◽  
Vol 2012 ◽  
pp. 1-16
Author(s):  
Renbin Liu ◽  
Yong Wu
Keyword(s):  
Renewal Process ◽  
Decomposition Method ◽  
Process Theory ◽  
Series System ◽  
New Approach ◽  
Numerical Examples ◽  
Special Cases ◽  
The Mean ◽  
Repair Facility

Based on the renewal process theory we develop a decomposition method to analyze the reliability of the repair facility in ann-unit series system with vacations. Using this approach, we study the unavailability and the mean replacement number during(0,t]of the repair facility. The method proposed in this work is novel and concise, which can make us see clearly the structures of the facility indices of a series system with an unreliable repair facility, two convolution relations. Special cases and numerical examples are given to show the validity of our method.

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