Sub-nanosecond lifetimes in Te

The half-lives of the 1776.8 keV 6⁺ level and the 2497.3 keV 7^? level in ¹²⁶Te are measured by registering β-γ coincidences in the decay of ¹²⁶Sb. The results are $\text{T}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext><mtext>(1776.8)\; =\; 66\pm 3</mtext><mtext>ps</mtext>}}$ and $\text{T}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext><mtext>(2497.3)\; =\; 152\pm 5\; </mtext><mtext>ps</mtext>}}$. The collective strength of the 6⁺ → 4⁺ transition depopulating the 1776.8 keV state is estimated. An additional half-life of 0.36±0.06 ns is found but not definitely assigned in the level scheme.     

A functional limit theorem for random graphs with applications to subgraph count statistics

We consider a random graph that evolves in time by adding new edges at random times (different edges being added at independent and identically distributed times). A functional limit theorem is proved for a class of statistics of the random graph, considered as stochastic processes. the proof is based on a martingale convergence theorem. the evolving random graph allows us to study both the random graph model K_{n, p}, by fixing attention to a fixed time, and the model K_{n, N}, by studying it at the random time it contains exactly N edges. in particular, we obtain the asymptotic distribution as n → ∞ of the number of subgraphs isomorphic to a given graph G, both for K_{n, p} (p fixed) and K_{n, N} (N/(ⁿ₂)→ p). the results are strikingly different; both models yield asymptotically normal distributions, but the variances grow as different powers of n (the variance grows slower for K_n, N; the powers of n usually differ by 1, but sometimes by 3). We also study the number of induced subgraphs of a given type and obtain similar, but more complicated, results. in some exceptional cases, the limit distribution is not normal.     

Data analysis of pyrolysis—chromatograms by means of simca pattern recognition

The variability between repetitive pyrolysis—chromatograms of the same type of samples is not totally random, but can in part be modelled by a principal components (PC) model. This makes it possible to use efficiently repetitive pyrolysis-chromatograms of samples of known types to obtain separate PC models for each type. Samples of unknown origin can then be classified according to which of the PC models their pyrolysis-chromatograms are most similar.The methodology is illustrated using pyrolysis—gas chromatograms of two species of the fungal genus Penicillium.     

Large-pT protons from constituent diquark scattering

Recent data from the CERN ISR on the fractional proton yield in pp collisions are explained within the Stockholm diquark model. Describing the proton as a u(ud)₀ system, the observed high magnitude and fall-off _pT, θ and $\text{s}$ of the proton yield are natural consequences of constituent diquark elastic scattering. The _pT and θ dependence favour a value of around 10 GeV²/c² for the size parameter in the diquark form factor, corresponding to a diquark rms radius of around 0.2 fm. This is consistent with earlier results of the model applied to deep inelastic lepton-nucleon scattering and e⁺e^? annihilation.     

Vertical phase separation in spin-coated films of a low bandgap polyfluorene/PCBM blend—Effects of specific substrate interaction

We report on the effect of the substrate on the vertical phase separation in spin-coated thin films of poly[(9,9-dioctylfluorenyl-2,7-diyl)-co-5,5-4′,7′-di-2-thienyl-2′,1′,3′-benzothiadiazole] (APFO-3) blended with [6,6]-phenyl-C₆₁-butyric acid methyl ester (PCBM). Compositional depth profiles of the films are measured by dynamic secondary ion mass spectrometry (SIMS). We found that changing the substrate from silicon to gold affects the composition profile near the substrate interface. This is caused by a specific interaction between the polymer (APFO-3) and the gold surface, as confirmed by X-ray photoelectron spectroscopy (XPS). The composition profile in the area away from the substrate interface, as well as the enrichment of the free surface with APFO-3, remain however unaffected by the choice of substrate. The vertical composition was also analysed for APFO-3:PCBM films spin-coated on indium tin oxide (ITO) coated with a thin layer of (3,4-ethylenedioxythiophene) poly(styrenesulfonate) (PEDOT:PSS).     

Micellar induced regioselectivity in the two-step consecutive reaction of SO3(2-) with Br-(CH2CH2)n-Br (n=2-5)

High field (800 MHz) (1)H NMR was used to monitor the two-step consecutive reaction of excess SO(3)(2-) with symmetrical bifunctional alpha,omega-dibromoalkanes with butane (DBB), hexane (DBH), octane (DBO), and decane (DBD) chains in CTAB micelles at 25 degrees C. The first-order rate constant for the first substitution step for DBB and DBH is about 5 times faster than for the second, but the kinetics for DBO and DBD were not cleanly first-order. After 40 min, the solution contained about 80% of the intermediate bromoalkanesulfonate from DBB and DBH and the remainder is alkanedisulfonate and unreacted starting material. The same reactions were carried out in homogeneous MeOH/D(2)O solutions at 50 degrees C. The rate constants for all four alpha,omega-dibromoalkanes were first-order throughout the time course of the reaction and the same within +/-10%. However, because micellar solutions are organized on the nanoscale and bring together lipophilic and hydrophilic reactants into a small reaction volume at the micellar interface, they speed this substitution reaction considerably compared to reaction in MeOH/D(2)O. The CTAB micelles also induce a significant regioselectivity in product formation by speeding the first step of the consecutive reaction more than the second. The results are consistent with the bromoalkanesulfonate intermediates having a radial orientation within the micelles with the -CH(2)SO(3)(-) group in the interfacial region and the -CH(2)Br group directed into the micellar core such that the concentration of -CH(2)Br groups in the reactive zone, i.e., the micellar interface, is significantly reduced. These results provide the first example of self-assembled surfactant system altering the relative rates of the reaction steps of a consecutive reaction and, in doing so, enhancing monosubstitution of a symmetrically disubstituted species.     

Cationic ester-containing gemini surfactants: chemical hydrolysis and biodegradation

Two cationic gemini surfactants having ester bonds between the hydrophobic tail and the cationic moiety have been synthesized. The ester bonds were either with the ester carbonyl group away from the positive charge (esterquat type arrangement) or facing the positive charge (betaine ester type arrangement). The chemical hydrolysis of the surfactants was investigated and compared with the hydrolysis of the corresponding monomeric surfactants. The betaine ester type of surfactants was found to hydrolyze much faster than the esterquat surfactants. It was also seen that above the critical micelle concentration the gemini surfactants were much more susceptible to alkaline hydrolysis than the corresponding monomeric surfactants. The biodegradation of the geminis and the monomeric surfactants were also studied. It was found that whereas the monomeric surfactants were rapidly degraded, the two gemini surfactants were more resistant to biodegradation and could not be classified as readily biodegradable. The 60% biodegradation was reached after 35-40 days. Thus, there was no correlation between rate of chemical hydrolysis and rate of biodegradation.     

Distances between pairs of vertices and vertical profile in conditioned Galton–Watson trees

We consider a conditioned Galton–Watson tree and prove an estimate of the number of pairs of vertices with a given distance, or, equivalently, the number of paths of a given length. We give two proofs of this result, one probabilistic and the other using generating functions and singularity analysis. Moreover, the latter proof yields a more general estimate for generating functions, which is used to prove a conjecture by Bousquet–Mélou and Janson (Bousquet‐Mélou and Janson, Ann Appl Probab 16 (2006) 1597–1632), saying that the vertical profile of a randomly labelled conditioned Galton–Watson tree converges in distribution, after suitable normalization, to the density of ISE (Integrated Superbrownian Excursion). © 2011 Wiley Periodicals, Inc. Random Struct. Alg., 38, 381–395, 2011