An atomless probability space (Ω,A, P ) is said to have the saturation property for a probability measure μ on a product of Polish spaces X×Y if for every random element f of X whose law is margX(μ), there is a random element g of Y such that the law of (f, g) is μ. (Ω,A, P ) is said to be saturated if it has the saturation property for every such μ. We show each of a number of desirable proper...

We study the dependence of entropy solutions in the large for hyperbolic systems of conservation laws whose flux functions depend on a parameter vector μ. We first formulate an effective approach for establishing the L-estimate pointwise in time between entropy solutions for μ 6= 0 and μ = 0, respectively, with respect to the flux parameter vector μ. Then we employ this approach and successfull...

Abstract In this paper, a Lie symmetry method is used for the nonlinear generalized Camassa–Holm equation and as result reduction of order computing conservation laws are presented. Furthermore, μ -symmetry -conservation obtained.

In non-commutative probability theory, cumulants and their appropriate generating function are defined when a notion of independence is given [17, 18, 19]. They are useful especially in the central limit theorem and Poisson’s law of small numbers. We denote by any one of classical, free and boolean convolutions. We denote by Dλ the dilation operator defined by (Dλμ)(B) = μ(λ B) for any Borel se...

Particles in turbulence live complicated lives. It is nonetheless sometimes possible to find order in this complexity. It was proposed in Falkovich et al. [Phys. Rev. Lett. 110, 214502 (2013)] that pairs of Lagrangian tracers at small scales, in an incompressible isotropic turbulent flow, have a statistical conservation law. More specifically, in a d-dimensional flow the distance R(t) between t...

Dembski’s “Law of Conservation of Information” is investigated using a more formal approach than is provided in his latest book “No Free Lunch”. It is concluded that the Law of Conservation of Information is mathematically unsubstantiated.

We develop a conservation law for a multi-class GI/GI/1 queue operating under a general work-conserving scheduling discipline. For single-class single-server queues, conservation laws have been obtained for both nonanticipating and anticipating disciplines with general service time distributions. For multi-class single-server queues, conservation laws have been obtained for (i) nonanticipating ...

Plant Genetic Resources (PGRs) are one of the most valuable natural resources of anycountry. Biotechnology through genetic engineering of plants and the creation of new plantvarieties can increase the value of these resources. Different technical and legalmechanisms such as ex situ/in situ collection of PGRs, and Intellectual Property Rights(IPRs...