Common Cause Completability of Classical and Quantum Probability Spaces

It is shown that for a given set of correlations either in a classical or in a quantumprobability space both the classical and the quantum probability spaces areextendable in such a way that the extension contains common causes of thegiven correlations, where common cause is taken in the sense of Reichenbach'sdefinition. These results strongly restrict the possible ways of disprovingReichenbach's common cause principle and indicate that EPR-type quantumcorrelations might very well have a common cause explanation.     

Pre-Super Brownian Motion

Periodica Mathematica Hungarica -     

A strong approximation of self-normalized sums

Let {X,Xn,n1} be a sequence of independent identically distributed random variables with EX=0 and assume that EX2I(|X|≤x) is slowly varying as x→∞,i.e.,X is in the domain of attraction of the normal law.In this paper a Strassen-type strong approximation is established for self-normalized sums of such random variables.     

Periodic pulses of calcium ions in a chemical system

By coupling the bromate-sulfite-ferrocyanide oscillating chemical reaction with the complexation of calcium ion by EDTA, we construct a system that generates periodic pulses of free Ca(2+) with an amplitude of 2 orders of magnitude and a period of ca. 20 min. These pulses may be observed either with a calcium ion-selective electrode or with Arsenazo(III) as an indicator. We describe the systematic design procedure and the properties of this first abiotic calcium-based chemical oscillator.     

Effects of the alternating backbone configuration on the secondary structure and self-assembly of beta-peptides

Heterochiral homo-oligomers with alternating backbone configurations were constructed by using the different enantiomers of the cis- and trans-2-aminocyclopentanecarboxylic acid (ACPC) monomers. Molecular modeling and the spectroscopic techniques (NMR, ECD, and VCD) unequivocally proved that the alternating heterochiral cis-ACPC sequences form an H10/12 helix, where extra stabilization can be achieved via the cyclic side chains. The ECD and TEM measurements, together with molecular modeling, revealed that the alternating heterochiral trans-ACPC oligomers tend to attain a polar-strand secondary structure in solution, which can self-assemble into nanostructured fibrils. The observations indicate that coverage of all the possible secondary structures (various helix types and strand-mimicking conformations) can be attained with the help of cyclic beta-amino acid diastereomers. A relationship has been established between the backbone chirality pattern and the prevailing secondary structure, which underlines the role of stereochemical control in the beta-peptide secondary structure design and may contribute to future biological applications.     

Reichenbachian Common Cause Systems of Arbitrary Finite Size Exist

A partition of a Boolean algebra Ω in a probability measure space (Ω, p) is called a Reichenbachian common cause system for the correlation between a pair A,B of events in Ω if any two elements in the partition behave like a Reichenbachian common cause and its complement; the cardinality of the index set I is called the size of the common cause system. It is shown that given any non-strict correlation in (Ω, p), and given any finite natural number n > 2, the probability space (Ω,p) can be embedded into a larger probability space in such a manner that the larger space contains a Reichenbachian common cause system of size n for the correlation.     

Partitions with k Crossings

We study the number S_k(n) of partitions of the set {1, 2,..., n} with k crossings and show that for each k, their ordinary generating function S_k(x) is a rational function of x and the ordinary generating function of the Catalan numbers. If k = 1, then we get a sequence first found by Cayley in 1890.     

Detection of ammonia released from zeolite by the quantum cascade laser based photoacoustic set-up

We report the first results obtained with a Brazilian sedimentary zeolite (hereafter called the zeolite concentrate, ZC) to reduce ammonia volatilization – loss of the nitrogen nutrient – in tropical farms. Preliminary laboratory tests were made with both ammonium sulfate and urea into ZC. The reported field tests – obtained in rose cultivations – show a significant effect of the use of urea mixed with ZC on the stem growth of the rose buds. In the laboratory tests, the observations of the retention of ammonia by ZC were done using the photoacoustic set-up described in this work. The report data were obtained at temperatures of 25 and 60°C, simulating typical tropical weather temperatures.