Abstract: In this article a single machine time-dependent scheduling problem with total completion time criterion is considered. There are n given jobs, j1, . . . , jn, and the processing time pi of the i-th job is given by pi = 1 + bisi, where si is the starting time of the i-th job, i = 1, . . . n. If all jobs have different and non-zero deterioration rates and bi > bj ⇒ bi ≥ bmin+1 bmin bj+ ...

In this article a single machine time-dependent scheduling problem with total completion time criterion is considered. There are n given jobs j1, . . . , jn and the processing time pi of the i-th job is given by pi = 1 + bisi, where si is the starting time of the i-th job, i = 1, . . . n. If all jobs have different and non-zero deterioration rates and bi > bj ⇒ bi ≥ bmin+1 bmin bj + 1 bmin , wh...

In crisp transportation, trying to fuzzify the amount of supply of the ith origin ai and the amount of demand of the jth destination bj, we use level l fuzzy numbers and level (l, r) interval-valued fuzzy numbers to fuzzify ai and bj in the constraints. We get transportation problem in the fuzzy sense. We also cooperate some statistical concepts and corresponding to (1 α) × 100% statistical con...

Abstract In this note we study the controllability of the Generalized BenjaminBona-Mahony equation (BBM) with homogeneous Dirichlet boundary conditions. Under some conditions we shall prove the system is approximately controllable on [0, t1] if and only if the following algebraic condition holds Rank[Bj ] = γj , where Bj acts from IR m to R(Ej), λj ’ s are the eigenvalues of −∆ with Dirichlet b...

We review both the counting rule and the influence of the evolution in Q2 for the large xBj behaviour of the valance quark distribution functions. Based on a factorization procedure we present a more general perturbative treatment to compute this behaviour. A complete analysis is performed in the scalar φ[6]-theory for the parton distribution function of the “meson”, which shows that logarithmi...

Single-molecule junctions (SMJs) have been fabricated using layers generated by diazonium electroreduction. This process creates a C–Au covalent bond between the molecule and electrode. Rigid oligomers of variable length, based on porphyrin derivatives in their free base or cobalt complex forms, grafted surface. The conductance has studied scanning tunneling microscopy break junction (STM-bj) t...

congenital heart disease. Am J Cardiol 2012;109:1657–63. [3] Geyer S, Norozi K, Buchhorn R, Wessel A. Chances of employment in women and men after surgery of congenital heart disease: comparisons between patients and the general population. Congenit Heart Dis 2009;4:25–33. [4] Kamphuis M, Vogels T, Ottenkamp J, Van Der Wall EE, Verloove-Vanhorick SP, Vliegen HW. Employment in adults with congen...

1.16. Again, I’ll only do the triangle inequality. Let x = (a1, . . . , an), y = (b1, . . . , bn), z = (c1, . . . , cn) be three points in Rn, then there is some integer j, 1 ≤ j ≤ n where the max occurs, so that d∞(x, y) = |aj − bj |. Hence, d∞(x, y) = |(aj−cj)+(cj−bj)| ≤ |aj−cj |+|cj−bj | But, |aj−cj | ≤ max{|a1− c1|, . . . , |an − cn|} = d∞(x, z), since it is one of the terms occurring in th...