Given a system model where machines have distinct speeds and power ratings but are otherwise compatible, we consider various problems of scheduling under resource constraints on the system which place the restriction that not all machines can be run at once. These can be power, energy, or makespan constraints on the system. Given such constraints, there are problems with divisible as well as no...

The divisible load model is motivated by divisible load theory, where both communication and computation can be arbitrarily divisible into as many independent partitions as required and facilitates a good approximation for many real-world application systems such as those arising in large physics experiments. Scheduling an application with divisible load in data grid is significantly important ...

261 Davis, J.A., New constructions of divisible designs, Discrete Mathematics 120 (1993) 261-268. A construction is given for a (p2"(p+l),p,p2"+ 1(p+l),p2"+ ,p"(p+l)) (pa prime) divisible difference set in the group H x z~.+, where His any abelian group of order p+ 1. This can be used to generate a symmetric semi-regular divisible design; this is a new set of parameters for .l. 1 ;<'0, and thos...

1. In the first theorem of [3], Wiegandt incorrectly states that a semimodule is complete if and only if it is divisible. (See §2 for definitions.) In this paper we show (in §3) that his theorem should read: a semimodule is complete if and only if it is a divisible group. Divisible semimodules which are not necessarily groups are discussed in §4, in connection with Wiegandt's second theorem. It...

in this paper, we study the notion of solvable $l$-subgroup of an $l$-group and provide its level subset characterization and this justifies the suitability of this extension. throughout this work, we have used normality of an $l$-subgroup of an $l$-group in the sense of wu rather than liu.

suppose that $h$ is a subgroup of $g$‎, ‎then $h$ is said to be‎ ‎$s$-permutable in $g$‎, ‎if $h$ permutes with every sylow subgroup of‎ ‎$g$‎. ‎if $hp=ph$ hold for every sylow subgroup $p$ of $g$ with $(|p|‎, ‎|h|)=1$)‎, ‎then $h$ is called an $s$-semipermutable subgroup of $g$‎. ‎in this paper‎, ‎we say that $h$ is partially $s$-embedded in $g$ if‎ ‎$g$ has a normal subgroup $t$ such that $ht...

We introduce an axiomatic extension of Höhle’s Monoidal Logic called Semi–divisible Monoidal Logic, and prove that it is complete by showing that semi–divisibility is preserved in MacNeille completion. Moreover, we introduce Strong semi– divisible Monoidal Logic and conjecture that a predicate formula α is derivable in Strong Semi–divisible Monadic logic if, and only if its double negation ¬¬α ...

m-dependent stationary infinitely divisible sequences are characterized as a certain generalized finite moving average sequence or equivalently via the structure of their Lévy measure. This characterization is used to find necessary and sufficient conditions for the weak convergence of centered and normalized partial sums of m-dependent stationary infinitely divisible sequences. Partial sum con...

J.BSTllCT A set of examples is described which suggests that members of a certain class of Markov processes have infinitely divisible limit distributions. A counter example rilles out such a possibility and raises the question of what further restrictions are required to guarantee infinitely divisible limits. Some related examples illustrate the same occurrence of infinitely divisible limit dis...

For real numbers C, T 1 , T 2 , ... we find all solutions µ to the stochastic fixed point equation W j≥1 T j W j + C, where W, W 1 , W 2 , ... are independent real-valued random variables with distribution µ and means equality in distribution. All solutions are infinitely divisible. The set of solutions depends on the closed multiplicative subgroup of R * = R\{0} generated by the T j. If this g...