We consider the on-line problem of scheduling jobs with precedence constraints on m machines. We concentrate in two models, the model of uniformly related machines and the model of restricted assignment. For the related machines model, we show a lower bound of (p m) for the competitive ratio of deterministic and randomized on-line algorithms, with or without preemptions even for known running t...

Pattern avoiding machines were introduced recently by Claesson, Cerbai and Ferrari as a particular case of the two-stacks in series sorting device. They consist two restricted stacks series, ruled right-greedy procedure avoid some specified patterns. Some obtained results have been further generalized to Cayley permutations Cerbai, specialized patterns Defant Zheng, or considered context functi...

the study of stability problems of functional equations was motivated by a question of s.m. ulam asked in 1940. the first result giving answer to this question is due to d.h. hyers. subsequently, his result was extended and generalized in several ways.we prove some hyperstability results for the equation g(ax+by)+g(cx+dy)=ag(x)+bg(y)on restricted domain. namely, we show, under some weak natural...

In this paper, we establish some new results related to distributive properties of AND ( )  and OR ( )  -operations with respect to operations of union, restricted union restricted intersection, extended intersection and restricted difference on soft sets, and provide some illustrative examples.

Minimizing Energy consumption is considered as one of the most important principles in the development of routing protocols for Wireless Sensor Networks (WSN). In this study, we propose a Location based Energy-Aware Reliable routing protocol (LEAR) for WSN based on sensor position and clustering. Geographical routing protocols are efficient and convenient for optimum energy consumption and band...