Computer-aided process planning (CAPP) is an essential component in linking computer-aided design (CAD) and computer-aided manufacturing (CAM). Operation sequencing in CAPP is an essential activity. Each sequence of production operations which is produced in a process plan cannot be the best possible sequence every time in a changing production environment. As the complexity of the product incr...

A helpful starting point is the paper entitled "Fibonacci Series Modulo m by D. D. Wall [3]. With Wall, we let /„ denote the n member of the sequence of integers fQ = a, f1 = b9 ..., where fn + 1 = fn + f n _ r The symbol h(m) will denote the length of the period of the sequence resulting from reducing each /„ modulo w. The basic Fibonacci sequence will be given by uQ = 0, ux = 1, ... and the L...

Let E be a real quadratic field with discriminant d 6≡ 0 (mod p) where p is an odd prime. For ρ = ±1 we determine ∏ 0<c<d, ( d c )=ρ ( p−1 bpc/dc ) modulo p2 in terms of a Lucas sequence, the fundamental unit and the class number of E.

which give the arithmetic and the geometric means of the first n values of the Euler function, respectively, are uniformly distributed modulo 1. A. Schinzel modified these questions by asking whether these sequences are dense modulo 1. This question was repeated at the meeting on Uniform Distribution in Luminy in January 2008. In this paper, we give an affirmative answer to Schinzel’s question....

This paper presents an algorithm based on multi-objective approach for network reconfiguration. Multiple objectives are considered for reduction in the system power loss, deviations of the nodes voltage and transformers loading imbalance, while subject to a radial network structure in which all the loads must be energized and no branch current constraint is violated. These three objectives are ...

In this paper, a new mathematical model for the problem of job scheduling in virtual manufacturing cells (VMC) is presented to minimizing the completion time of all jobs. Sequence dependent setup times of machines is considered and lot-streaming is possible. In Virtual manufacturing cells, each job has a different processing path and there is a set of machines for processing each operation. The...

Let q ≥ 2 be an integer and sq(n) denote the sum of the digits in base q of the positive integer n. The goal of this work is to study a problem of Gelfond concerning the repartition of the sequence (sq(P (n)))n∈N in arithmetic progressions when P ∈ Z[X] is such that P (N) ⊂ N. We answer Gelfond’s question and we show the uniform distribution modulo 1 of the sequence (αsq(P (n)))n∈N for α ∈ R \Q...