A New Sigma Approach to Multi-summation
نویسندگان
چکیده
We present a general algorithmic framework that allows not only to deal with summation problems over summands being rational expressions in indefinite nested sums and products (Karr 1981), but also over ∂-finite and holonomic summand expressions that are given by a linear recurrence. This approach implies new computer algebra tools implemented in Sigma to solve multi-summation problems efficiently. For instance, the extended Sigma package has been applied successively to provide a computer-assisted proof of Stembridge’s TSPP theorem.
منابع مشابه
Cascaded Feedforward Sigma-delta Modulator for Wide Bandwidth Applications
A new sigma-delta modulator architecture for wide bandwidth application called cascaded feedforward sigma-delta modulator is proposed in this paper. This sigma-delta modulator is similar to the conventional feedforward summation sigma-delta modulator. The conventional feedforward summation sigma-delta modulator uses multi-bit feedback and therefore a multi-bit digital-to-analog converter (DAC) ...
متن کاملA Comparison of Four Multi-Objective Meta-Heuristics for a Capacitated Location-Routing Problem
In this paper, we study an integrated logistic system where the optimal location of depots and vehicles routing are considered simultaneously. This paper presents a new mathematical model for a multi-objective capacitated location-routing problem with a new set of objectives consisting of the summation of economic costs, summation of social risks and demand satisfaction score. A new multi-objec...
متن کاملEfficacy of fuzzy MADM approach in Six Sigma analysis phase in automotive sector
Six Sigma is a strategy for achieving process improvement and operational excellence within an organization. Decisions on critical parameter selection in analysis phase are always very crucial; it plays a primary role in successful execution of Six Sigma project and for productivity improvement in manufacturing environment and involves the imprecise, vague and uncertain information. Using a cas...
متن کاملModern Summation Methods for Loop Integrals in Quantum Field Theory: The Packages Sigma, EvaluateMultiSums and SumProduction
Abstract. A large class of Feynman integrals, like e.g., two-point parameter integrals with at most one mass and containing local operator insertions, can be transformed to multi-sums over hypergeometric expressions. In this survey article we present a difference field approach for symbolic summation that enables one to simplify such definite nested sums to indefinite nested sums. In particular...
متن کاملA New Fuzzy Method for Assessing Six Sigma Measures
Six-Sigma has some measures which measure performance characteristics related to a process. In most of the traditional methods, exact estimation is used to assess these measures and to utilize them in practice. In this paper, to estimate some of these measures, including Defects per Million Opportunities (DPMO), Defects per Opportunity (DPO), Defects per unit (DPU) and Yield, a new algorithm ba...
متن کامل