Factorization algorithm based on the periodicity measurement of a continuous truncated exponential sum

2010 ◽  
Author(s):  
Vincenzo Tamma ◽  
Heyi Zhang ◽  
Xuehua He ◽  
Augusto Garuccio ◽  
Yanhua Shih
Keyword(s):  
Exponential Sum ◽  
Factorization Algorithm ◽  
Periodicity Measurement

Factorization algorithm based on the periodicity measurement of a CTES

2010 ◽  
Vol T140 ◽  
pp. 014036
Author(s):  
Vincenzo Tamma ◽  
Heyi Zhang ◽  
Xuehua He ◽  
Augusto Garuccio
Keyword(s):  
Factorization Algorithm ◽  
Periodicity Measurement

scholarly journals A note on two-term exponential sum and the reciprocal of the quartic Gauss sums

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Wenpeng Zhang ◽  
Xingxing Lv
Keyword(s):  
Exponential Sums ◽  
Exponential Sum ◽  
Gauss Sums ◽  
Power Mean ◽  
Hybrid Power ◽  
Analytic Methods ◽  
Hybrid Power Mean

AbstractThe main purpose of this article is by using the properties of the fourth character modulo a prime p and the analytic methods to study the calculating problem of a certain hybrid power mean involving the two-term exponential sums and the reciprocal of quartic Gauss sums, and to give some interesting calculating formulae of them.

scholarly journals Analysis of a simple factorization algorithm

1976 ◽  
Vol 3 (3) ◽  
pp. 321-348 ◽  
Author(s):  
Donald E. Knuth ◽  
Luis Trabb Pardo
Keyword(s):  
Factorization Algorithm

Scheduling Jobs with Truncated Exponential Sum-of-Logarithm-Processing-Times Based and Position-based Learning Effects

2015 ◽  
Vol 32 (04) ◽  
pp. 1550026 ◽  
Author(s):  
Yuan-Yuan Lu ◽  
Fei Teng ◽  
Zhi-Xin Feng
Keyword(s):  
Single Machine ◽  
Minimization Problem ◽  
Completion Time ◽  
Heuristic Algorithms ◽  
Exponential Sum ◽  
Total Weighted Completion Time ◽  
Learning Effects ◽  
Processing Times ◽  
Time Minimization ◽  
Weighted Completion Time

In this study, we consider a scheduling problem with truncated exponential sum-of-logarithm-processing-times based and position-based learning effects on a single machine. We prove that the shortest processing time (SPT) rule is optimal for the makespan minimization problem, the sum of the θth power of job completion times minimization problem, and the total lateness minimization problem, respectively. For the total weighted completion time minimization problem, the discounted total weighted completion time minimization problem, the maximum lateness minimization problem, we present heuristic algorithms (the worst-case bound of these heuristic algorithms are also given) according to the corresponding single machine scheduling problems without learning considerations. It also shows that the problems of minimizing the total tardiness, the total weighted completion time and the discounted total weighted completion time are polynomially solvable under some agreeable conditions on the problem parameters.

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