A note on random coin tossing

Harris and Keane [Probab. Theory Related Fields 109 (1997) 27-37] studied absolute continuity/singularity of two probabilities on the coin-tossing space, one representing independent tosses of a fair coin, while in the other a biased coin is tossed at renewal times of an independent renewal process and a fair coin is tossed at all other times. We extend their results by allowing possibly different biases at the different renewal times. We also investigate the contiguity and asymptotic separation properties in this kind of set-up and obtain some sufficient conditions.Keywords:renewal process, absolute continuity, singularity, contiguity, asymptotic separation, martingale convergence theorem     

Capacity and entry issues in online exchanges

With the advent of open standards and Internet technologies, the number of sellers who can participate in online exchanges is greatly increased. We model the competition between identical sellers vying for the same business, and find that there exists a mixed-strategy equilibrium in prices. The results help us understand the dynamics between a seller’s capacity and his motivation to participate in an auction.     

Inseparability of Quantum Parameters

In this work, we show that ‘splitting of quantum information’ (Zhou, D., et al. in quant-ph/0503168) is an impossible task from three different but consistent principles namely unitarity of Quantum Mechanics, no-signaling condition and non-increase of entanglement under Local Operation and Classical Communication.     

Direct observation of the ... 4+-to-2+ ... [corrected] gamma transition in 8Be

Electromagnetic transition rates provide an important test for nuclear structure models. The nucleus 8Be exhibits a pronounced alpha-cluster structure and is a building block for more complex cluster nuclei. Here we report on the first observation of the gamma transition between the 4(+) and 2(+) states of 8Be in the 4He+4He reaction. The measured on-resonance cross section of 165+/-54 nb leads to a B(E2) of25+/-8e(2) fm(4), in good agreement with alpha-cluster models and sophisticated ab initio structure calculations.     

Carbon-13 NMR signals of some natural coumarins and their derivatives

The ¹³C NMR spectra of the natural coumarins ostruthin, osthol, aegelinol (enantiomer of decursinol), luvangetin, seselin, anomalin, oxypeucedanin (and its enantiomer prangolarin) and oxypeucedanin hydrate and some of their derivatives have been studied. Self-consistent resonance assignments have been made following chemical shift theory and using simple models. Carbon-hydrogen coupling constants of some compounds are also reported. The alkoxy group/s at C-5 and/or C-8 in linear furocoumarins, as well as in linear pyranocoumarins, have unusually small shielding effects on the ortho- and para-carbons. This study also indicates that the C-4a and C-8 resonance assignments of osthol, made earlier, should be reversed.     

A generalized VMD mechanism for radiative decays of cc mesons

A generalized VMD mechanism, implemented through the OPC model, is proposed for E1 and M1 decays of $\text{c}\text{c}$ mesons wherein the photon couples to two infinite sequences of radial excitations of ³S₁ and ³D₁$\text{c}\text{c}$ states. The results reveal good accord with data under the conventional assignments, with a parameter signifying a reduced magnetic coupling of ψ-ions with c quarks.     

4‐Methyl‐N‐[2‐(p‐tolylsulfanyl)phenyl]benzene­sulfonamide

The title compound, C₂₀H₁₉NO₂S₂, is formed by a palladium–copper‐catalyzed reaction between 4‐methyl‐N‐[2‐(prop‐2‐ynyl­sul­fanyl)­phenyl]­benzene­sul­fon­amide and p‐iodo­toluene. The mol­ecules contain three essentially planar parts, namely an amino­thio­phenol moiety (A), a toluene­sulfone moiety excluding the oxo ligands (B) and a tolyl group (C), approximately orthogonal to each other; the dihedral angles A/B, A/C and B/C are 111.6 (1), 89.3 (1) and 101.4 (1)°, respectively. Intermolecular N—H?O hydrogen bonds link the mol­ecules into infinite one‐dimensional chains.     

Bis­[3‐(o‐methoxy­phenyl)‐1‐methyl­triazene 1‐oxidato‐O,N3,O′]­zinc(II)

In the title compound, [Zn(C₈H₁₀N₃O₂)₂], the Zn atom displays a highly distorted octahedral coordination involving O and N atoms of two bidentate planar ligands approximately orthogonal to each other; the dihedral angle between the ligand planes is 84.95 (4)°. The ligand mol­ecules show great asymmetry in their bonding to the Zn²⁺ ion, with Zn—O bond distances ranging between 2.056 (2) and 2.534 (2) Å. The planar phenyl ring and the trigonal–planar geometry about the triazene N atom bonded to the phenyl ring suggest a resonance interaction extending over adjacent atoms.