We present families of unital algebras obtained through a doubling process from a cyclic central simple algebra D = (K/F, σ, c), employing a K-automorphism τ and an element d ∈ D. These algebras appear in the construction of iterated spacetime block codes. We give conditions when these iterated algebras are division which can be used to construct fully diverse iterated codes. We also briefly lo...

The conditional in conditional Kolmogorov complexity commonly is taken to be a finite binary string. The Coding Theorem of L.A. Levin connects unconditional prefix Kolmogorov complexity with the discrete universal distribution. The least upper semicomputable code-length is up to a constant equal to the negative logarithm of the greatest lower semicomputable probability mass function. We investi...

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...

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...

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...

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...

The economic situation in Indonesia has suffered a major hit various sectors since the end of 2019. This study aims to analyze Valuation Technology Company Shares listed on Stock Exchange using Dividend Discount Model and Free Cash Flow Equity. uses sample 8 companies from 35 technology Exchange. research data compares stock valuations 2019, 2020 2021 before, during after Covid 19. Statistical ...

June 4, 2010 Xiaofeng Shao and Xianyang Zhang University of Illinois at Urbana-Champaign Abstract: This article considers the CUSUM-based (cumulative sum) test for a change point in a time series. In the case of testing for a mean shift, the traditional KolmogorovSmirnov test statistic involves a consistent long run variance estimator, which is needed to make the limiting null distribution free...