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...

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...

This paper is devoted to the study of discrete fractional calculus; the particular goal is to define and solve well-defined discrete fractional difference equations. For this purpose we first carefully develop the commutativity properties of the fractional sum and the fractional difference operators. Then a ν-th (0 < ν ≤ 1) order fractional difference equation is defined. A nonlinear problem wi...

We extend the results of hep-th/0310137 to show that a general classical action for D = 2, N = 2 sigma models on a non(anti)commutative superspace is not standard and contains infinite number of terms, which depend on the determinant of the non(anti)commutativity parameter, C αβ. We show that using Kähler normal coordinates the action can be written in a manifestly covariant manner. We introduc...

We extend the results of hep-th/0310137 to show that a general classical action for D = 2, N = 2 sigma models on a non(anti)commutative superspace is not standard and contains infinite number of terms, which depend on the determinant of the non(anti)commutativity parameter, C αβ. We show that using Kähler normal coordinates the action can be written in a manifestly covariant manner. We introduc...

In this paper, it is pointed out that the Berry’s phase is a good index of degree of no-commutativity of the quantum statistical model. Intrinsic relations between the ‘complex structure’ of the Hilbert space and Berry’s phase is also discussed.

Although the explicit commutativitiy conditions for second-order linear time-varying systems have been appeared in some literature, these are all for initially relaxed systems. This paper presents explicit necessary and sufficient commutativity conditions for commutativity of second-order linear time-varying systems with non-zero initial conditions. It has appeared interesting that the second r...