The equivalence of universal measure, a priori probability and the negative exponential of Kolmogorov complexity is a well known result with signiicance both to the theory of Kolmogorov complexity and many of its applications. In this paper we consider deenitions for the time-bounded setting where similar equivalences hold. Unlike the unbounded case, time-bounded universal distributions give ri...

A model of laminated weak turbulence (WT) is presented. This model consists of two co-existing layers one with continuous spectra, covered by Kolmogorov ́s theory and KAM tori, and one with discrete spectra, covered by discrete classes of waves and Clipping method. Some known laboratory experiments and numerical simulations are explained in the frame of this model. A few problems which might app...

The purpose of this thesis is to give a formal definition of quantum Kolmogorov complexity and rigorous mathematical proofs of its basic properties. Classical Kolmogorov complexity is a well-known and useful measure of randomness for binary strings. In recent years, several different quantum generalizations of Kolmogorov complexity have been proposed. The most natural generalization is due to B...

In this article, we prove that the Kolmogorov operator associated to the Burgers equation driven by a space-time white noise is m-dissipative. This implies several properties on the Kolmogorov equation. This result is obtained thanks to the introduction of a modified Kolmogorov operator. New a priori estimates on the solutions of the Burgers equation and on the invariant measure are obtained. T...

Because X is a modification of Y , the right-hand side is a union of finitely many P -null sets, hence is itself a P -null set. A and B each belong to F , so P (A4B) = 0. Because P (A4B) = 0, P (A) = P (B), i.e. P (Xt1 ∈ A1, . . . , Xtn ∈ An) = P (Yt1 ∈ A1, . . . , Ytn ∈ An). 1We have not assumed that (Ω,F , P ) is a complete measure space, so we must verify that a set is measurable before spea...

We study reals with infinitely many incompressible prefixes. Call A ∈ 2 Kolmogorov random if (∃∞n) C(A n) > n − O(1), where C denotes plain Kolmogorov complexity. This property was suggested by Loveland and studied by Martin-Löf, Schnorr and Solovay. We prove that 2-random reals are Kolmogorov random.1 Together with the converse—proved by Nies, Stephan and Terwijn [11]—this provides a natural c...

We extend and solve the classical Kolmogorov problem of finding general classes of Kolmogorov equations that can be transformed to the backward heat equation. These new classes include Kolmogorov equations with time-independent and time-dependent coefficients. Our main idea is to include nonlocal transformations. We describe a step-by-step algorithm for determining such transformations. We also...

construction industry is the second most contributor of gross domestic product and the high rates of accidents /fatalities have tarnished the image of construction industry in india. the importance of safety at site cannot be underscored and it needs the combined attention of all stakeholders to address the issue of safety in construction industry in india. although the construction industry pl...