Weak law of large numbers for iterates of random-valued functions

Aequationes mathematicae - Given a probability space $$ (\Omega , {\mathcal {A}}, P) $$ , a complete and separable metric space X with the $$ \sigma $$ -algebra $$ {\mathcal {B}} $$ of all its...     

From biased coin to any discrete distribution

Periodica Mathematica Hungarica - In this note we construct an algorithm generating any discrete distribution with an arbitrary coin (and, as a result, with arbitrary initial distribution). The...     

A Comparison of the Experimental and ab Initio Values of theO NMR Chemical Shifts in the Carbonyl Group

New experimental and theoretical results are presented for the NMR shielding of oxygen in the carbonyl group. The experimental values clearly demonstrate that the solvent effects are very significant. The new results for the chemical shifts are in better agreement than the previous literature data with the corresponding ab initio values calculated for isolated molecules.     

An investigation of the reliability of the Galerkin-Petrov method

The Galerkin-Petrov method is applied to the determination of the ground state energy of the beryllium atom. The basis set of the coordinate subspace consists of correlated wavefunctions of the combined configuration-interaction-Hylleraas type. The basis set of the projective subspace is of the configuration-interaction type. The usefulness of a previously proposed way of characterization of pairs of subspaces has been further confirmed. Experience in constructing close pairs of subspaces gathered in the case of two-electron systems is used for the larger system. Two methods for constructing pairs of subspaces are used in the calculations.     

Studies towards the total synthesis of di- and sesterterpenes with dicyclopenta[a,d]cyclooctane skeletons. Three-component approach to the A/B rings building block

Sesqui- and sesterterpenes of ophiobolin and fusicoccin families are important synthetic targets because of complexity of structure and potentially useful physiological activities, including anti-tumor activity. A synthesis of versatile building blocks for these terpenoids is described. Cyclopenta[8]annulene rings system with properly dislocated substituents was constructed using as key steps ring closing metathesis reaction and Wagner - Meerwein rearrangement. Ring closing metathesis reaction leading to cyclopenta[8]annulene was studied in detail.     

A complex impedance study of Pt∣NaCl and C∣NaCl interfaces

The a.c. impedance of Pt∣NaCl∣Pt and C∣NaCl∣C cells was measured in the frequency range from 10^?3 to 10³ Hz. Two contributions to the interface impedance could be distinguished, hindered charge transfer and an adsorption/desorption or slow reaction contribution, the latter being the rate determining step in the frequency range studied. An approximately symmetric nonlinear dependence of both the capacitance and the conductance on overvoltage was found at the lowest frequencies, indicating that the crystal/electrode interface is in a state which can be characterized as close to equilibrium. It should be ensured by two electrochemical reactions of approximately equal rates. The concept of a temporarily reversible electrode is introduced. It is a result of the ability of ions to discharge at the interface and to produce a finite reservoir of adsorbed or absorbed reaction products. An external voltage increases or reduces this reservoir, and therefore only a transient electric current may be carried by a backward reaction.     

Quantum key distribution based on arbitrarily weak distillable entangled states

States with private correlations but little or no distillable entanglement were recently reported. Here, we consider the secure distribution of such states, i.e., the situation when an adversary gives two parties such states and they have to verify privacy. We present a protocol which enables the parties to extract from such untrusted states an arbitrarily long and secure key, even though the amount of distillable entanglement of the untrusted states can be arbitrarily small.     

A simple and practical phase-separation approach to the recycling of a homogeneous metathesis catalyst

The air stable asarone-derived Ru carbene 16, a robust olefin metathesis catalyst, can be easily separated after reaction by deposition on silica gel and reused up to nine times. This procedure provides products of excellent purity with low Ru content.     

Aspects of multistation quantum information broadcasting

We study quantum information transmission over multiparty quantum channel. In particular, we show an equivalence of different capacity notions and provide a multiletter characterization of a capacity region for a general quantum channel with k senders and m receivers. We point out natural generalizations to the case of two-way classical communication capacity.