This article studies an infinite dimensional analog of Milstein’s scheme for finite dimensional stochastic ordinary differential equations (SODEs). The Milstein scheme is known to be impressively efficient for SODEs which fulfill a certain commutativity type condition. This article introduces the infinite dimensional analog of this commutativity type condition and observes that a certain class ...

Partial evaluation (PE) is a powerful and general program optimization technique with many successful applications. However, it has never been investigated in the context of expressive rule-based languages like Maude, CafeOBJ, OBJ, ASF+SDF, and ELAN, which support: 1) rich type structures with sorts, subsorts and overloading; 2) equational rewriting modulo axioms such as commutativity, associat...

Field theories based on non-commutative spacetimes exhibit very distinctive non-local effects which mix the ultraviolet with the infrared in bizarre ways. In particular if the time coordinate is involved in the non-commutativity the theory seems to be seriously acausal and inconsistent with conventional hamiltonian evolution. To illustrate these effects we study the scattering of wave packets i...

Quantum discord is a manifestation of quantum correlations due to non-commutativity rather than entanglement. Two measures of quantum discord by the amount of non-commutativity via the trace norm and the Hilbert-Schmidt norm respectively are proposed in this paper. These two measures can be calculated easily for any state with arbitrary dimension. It is shown by several examples that these meas...

In this talk I review the well known relation existing between extended supersymmetry and complex geometry in the non-linear sigma-models, and then briefly discuss some recent developments related to the introduction of the nonanti-commutativity in the context of the supersymmetric non-linear sigma-models formulated in extended superspace. This contribution is suitable for both physicists and m...

In this paper, we prove common fixed point theorems in fuzzy metric spaces for weakly compatible mappings along with property (E.A.) satisfying implicit relation. Property (E.A.) buys containment of ranges without any continuity requirement besides minimizing the commutativity conditions of the maps to commutativity at their point of coincidence. Moreover, property (E.A.) allows replacing the c...

We present a scheme for constructing various Conley indices for locally deened maps. In particular we extend the shape index of Robbin and Salamon to the case of a locally deened map in a locally compact Hausdorr space. We compare the shape index with the cohomological Conley index for maps. We also prove the commutativity property of the Conley index, which is analogous to the commutativity pr...

Identified are a number of conditions on square patterns that are closely related to allowing commutativity with the full pattern. Implications and examples that show non-implications are given, along with a graph that summarizes the provided information. A complete description of commutativity with the full pattern is given in both the irreducible case and the reducible case in which there are...

We compute commutativity degrees of wreath products A o B of finite abelian groups A and B . When B is fixed of order n the asymptotic commutativity degree of such wreath products is 1/n2. This answers a generalized version of a question posed by P. Lescot. As byproducts of our formula we compute the number of conjugacy classes in such wreath products, and obtain an interesting elementary numbe...

This paper presents the semantic foundations of commutativity analysis, an analysis technique for automatically parallelizing programs written in a sequential, imperative programming language. Commutativity analysis views the computation as composed of operations on objects. It then analyzes the program at this granularity to discover when operations commute (i.e. generate the same result regar...