It is investigated how much information of a random set can be preserved if one splits the random set into two halves or, more generally, cuts out an infinite portion with an infinite recursive set. The two main results are the following ones: 1. Every high Turing degree contains a Schnorr random set Z such that Z ≡T Z ∩ R for every infinite recursive set R. 2. For each set X there is a Martin-...

A local ring R is called Z-local if J(R) = Z(R) and J(R) = 0. In this paper the structures of a class of Z-local rings are determined.

This chapter gives an overview of our ongoing experimental research in the MeMoSpace project, concerning the cognitive processes underlying human spatial reasoning. Our theoretical background is mental model theory, which conceives reasoning as a process in which mental models of the given information are constructed and inspected to solve a reasoning task. We first report some findings of our ...

Let k be an algebraically closed field of characteristic p > 0, and let R be a complete discrete valuation ring dominating the ring of Witt vectors W (k). Let π denote a uniformizing parameter of R, and let R be the integral closure in a fixed algebraic closure of K := Fr(R). Throughout the paper we shall assume that R contains a prescribed primitive p-th root of unity, which we denote by ζ. In...

We introduce the notions of T-dual Rickart and strongly T-dual Rickart modules. We provide several characterizations and investigate properties of each of these concepts. It is shown that every free (resp. finitely generated free) $R$-module is T-dual Rickart if and only if $overline{Z}^2(R)$ is a  direct summand of $R$ and End$(overline{Z}^2(R))$ is a semisimple (resp. regular) ring. It is sho...

Given a commutative ring R with identity 1?0, let the set Z(R) denote of zero-divisors and Z*(R)=Z(R)?{0} be non-zero R. The zero-divisor graph R, denoted by ?(R), is simple whose vertex Z*(R) each pair vertices in are adjacent when their product 0. In this article, we find structure Laplacian spectrum graphs ?(Zn) for n=pN1qN2, where p<q primes N1,N2 positive integers.

Dual-polarization radar rainfall estimation relationships have been extensively tested in continental and subtropical coastal rain regimes, with little testing over tropical oceans where the majority of rain on Earth occurs. A 1.5-yr Indo-Pacific warm pool disdrometer dataset was used to quantify the impacts of tropical oceanic drop-size distribution (DSD) variability on dual-polarization radar...