An element x of the ring R is called periodic if there exist distinct positive integers m, n such that xm = xn; and x is potent if there exists n > 1 for which xn = x. We denote the set of potent elements by P or P(R), the set of nilpotent elements by N or N(R), the center by Z or Z(R), and the Jacobson radical by J or J(R). The ring R is called periodic if each of its elements is periodic, and...

Traditional analysis and usage of operation commutativity relies on pairwise commutativity relationships. In contrast, this paper presentsmethod group commutativity, which specifies the conditions under which operations in amethod group will commute. Method group commutativity can be practically applied to efficiently support distributed object caching and concurrency control. A formal definiti...

We prove that for a generic hypersurface in P of degree at least 2 + 2/n, the n-th Picard number is one. The proof is algebraic in nature and follows from certain coherent cohomology vanishing.

We study supersymmetric Sp(N) gauge theories with an antisymmetric tensor and degree n+1 tree level superpotential. The generalized Konishi anomaly equations derived in hep-th/0304119 and hep-th/0304138 are used to compute the low energy superpotential of the theory. This is done by imposing a certain integrality condition on the periods of a meromorphic one form. Explicit computations for Sp(2...

We construct a differential graded algebra to compute the cohomology of ordered configuration spaces on an algebraic variety with vanishing Euler characteristic. show that k-th Betti number $$\mathrm{Conf}(C,n)$$ (C is elliptic curve) grows as polynomial degree exactly $$2k-2$$ . also for $$k< 6$$ and arbitrary n.

Atomic objects have suitable properties to realize reliable distributed computing. Using semantic information of atomic objects can make reliable distributed computing highly concurrent. This paper describes a commutativity based concurrency control algorithm in a multiversion object for highly concurrent distributed computing. Weihl proposed two concurrency control algorithms based on a commut...