We study multiplicities of jumping numbers multiplier ideals in a smooth variety arbitrary dimension. prove that the multiplicity function is quasi-polynomial, hence proving Poincar\'e series rational function. further when various components quasi-polynomial have highest possible degree and relate it to contributed by Rees valuations. Finally, we special case monomial ideals.

We consider the problem of finding optimal “jumping” patterns from 1 to N where there is a cost associated with each jump. This will be done for two cost functions, in the first case the cost of jumping from a to b will be (1 − q)/a for 0 < q < 1, while the second cost function will be b/a. For the first cost function we will show that all the jump lengths, except possibly the last jump, are be...

In this paper, we propose an extension of the JAsCo aspectoriented programming language for declaratively specifying a protocol fragment pointcut. The proposed pointcut language is equivalent to a finite state machine. Advices are attached to every transition specified in the pointcut protocol. We claim that stateful aspects benefit from run-time weaving and therefore introduce the JAsCo run-ti...