We investigated the effect of noise on propagation of two interacting particles pairs in a quasi one–dimensional random potential. It is shown that pair diffusion is strongly enhanced by short range interaction comparing with the non–interacting case.

We study a class of strongly solvable modes, called differential modes. We characterize abelian algebras in this class and prove that all of them are quasi-affine, i.e., they are subreducts of modules over commutative rings.

2 Regimes of 1D gases 2 2.1 Strongly versus weakly interacting regimes . . . . . . . . . . . . . . . . . . . . 4 2.2 Nearly ideal gas regime . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 2.3 Quasi-condensate regime . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 2.3.1 Density fluctuations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 2.3.2 Phase fluc...

An R-module M is called strongly noncosingular if it has no nonzero Rad-small (cosingular) homomorphic image in the sense of Harada. It is proven that (1) an R-module M is strongly noncosingular if and only if M is coatomic and noncosingular; (2) a right perfect ring R is Artinian hereditary serial if and only if the class of injective modules coincides with the class of (strongly) noncosingula...

This paper generalizes the idea of strongly associative hyperoperation introduced in [7]  to the class of hyperrings. We introduce and investigate hyperrings of type 1, type 2 and SDIS. Moreover, we study some examples of these hyperrings and give a new kind of hyperrings called  totally hyperrings. Totally hyperrings give us a characterization of Krasner hyperrings. Also, we investigate these ...

Numerical simulation of the high order derivatives based on the sampling data is an important and basic problem in numerical approximation, especially for solving the differential equations numerically. The classical method is the divided difference method. However, it has been shown strongly unstable in practice. Actually, it can only be used to simulate the lower order derivatives in applicat...

In this paper, the concepts of minimal and maximal left hyperideals in ordered semihypergroups are introduced, and several related properties are investigated. Furthermore, we introduce the concepts of weakly prime, quasi-prime, quasi-semiprime and weakly quasiprime left hyperideals of an ordered semihypergroup, and establish the relationship among the four classes of left hyperideals. Moreover...

Quasi-Newton methods are widely used in practise for convex loss minimization problems. These methods exhibit good empirical performance on a wide variety of tasks and enjoy super-linear convergence to the optimal solution. For largescale learning problems, stochastic Quasi-Newton methods have been recently proposed. However, these typically only achieve sub-linear convergence rates and have no...

Classical structure of rough set theory was first formulated by Z. Pawlak in [6]. The foundation of its object classification is an equivalence binary relation and equivalence classes. The upper and lower approximation operations are two core notions in rough set theory. They can also be seenas a closure operator and an interior operator of the topology induced by an equivalence relation on a u...