Limiting size index distributions for ball-bin models with Zipf-type frequencies

We consider a random ball-bin model where balls are thrown randomly and sequentially into a set of bins. The frequency of choices of bins follows the Zipf-type (power-law) distribution; that is, the probability with which a ball enters the ith most popular bin is asymptotically proportional to 1/i ^α , α > 0. In this model, we derive the limiting size index distributions to which the empirical distributions of size indices converge almost surely, where the size index of degree k at time t represents the number of bins containing exactly k balls at t. While earlier studies have only treated the case where the power α of the Zipf-type distribution is greater than unity, we here consider the case of α ≤ 1 as well as α > 1. We first investigate the limiting size index distributions for the independent throw models and then extend the derived results to a case where bins are chosen dependently. Simulation experiments demonstrate not only that our analysis is valid but also that the derived limiting distributions well approximate the empirical size index distributions in a relatively short period.     

Asymmetric alkynylation of aldehydes with propiolates without high reagent loading and any additives

The asymmetric alkynylation of aliphatic and aromatic aldehydes with propiolates was mediated by dialkylzinc and a novel prolinol catalyst without high reagent loading and any additives, such as Ti(Oi-Pr)(4), to give the corresponding γ-hydroxy-α,β-acetylenic esters with high enantiomeric excess of up to 95%.     

Total synthesis of broussonetine F: the orthoamide Overman rearrangement of an allylic diol

A first total synthesis of broussonetine F from diethyl L-tartrate was achieved. The cornerstone of our synthesis was an orthoamide Overman rearrangement, which provided an allylic amino alcohol with complete diastereoselectivity.     

Auger recombination dynamics in hybrid silica-coated CdTe nanocrystals

CdTe quantum dots coated with a silica layer containing CdS-like clusters exhibit intense photoluminescence and a spectral red-shift. Biexciton Auger recombination of these particles is examined by transient absorption spectroscopy. A lengthening of the Auger recombination lifetime by a factor of ～3.5 in the presence of the CdS-like clusters is observed and may contribute to the good PL properties of these nanostructures.     

Nanocrystallization of oligosilanes by a reprecipitation method: easy fabrication of H-aggregates of linear-chain oligosilane molecules

Nanocrystals of several oligosilanes have been fabricated easily by using a reprecipitation method. The nanocrystals reveal an intense absorption band at the UVB region (280 to 320 nm) and a fluorescence band with large Stokes shift. These photophysical properties show that the nanocrystals exhibit an excitonic interaction of the H-aggregate type.     

Synthesis and physical properties of high birefringence phenylacetylene liquid crystals containing a cyclohexyl group

We have synthesized new phenylacetylene-based liquid crystals containing a cyclohexyl or cyclohexylethyl group and evaluated their physical properties in order to develop a range of materials having high value of birefringence. The cyclohexyl-containing compounds exhibited nematic behaviour near room temperature and moderate values of δn of around 0.3. The cyclohexylethyl-containing compounds had a very wide nematic range with a high T_NI and very high values of δn of over 0.4. They also exhibited low viscosities. The order parameter was not affected by introducing either a cyclohexyl or a cyclohexylethyl group and the values of δn based on calculated polarizabilities were obtained experimentally.     

Inclusion Properties and Crystal Structure of Clathrates Constructed Based on “π-sandwich”

Abstract

Inclusion behavior of structurally similar host compounds, 1,4-bis[1-(9-anthryl)-3-propen-1-on-3-yl]benzene (1) and 1,4-bis[3-(9-anthryl)-3-propen-1-on-1-yl]benzene (2), has been studied. Both hosts preferred cyclic, non-branched small molecules as a guest component, to yield 1:2 clathrates specifically. X-ray powder diffraction studies revealed that those 1:2 clathrates of 1 and 2 were respectively isostructural. X-ray analyses of (1)(THF)₂ (P 1, a = 10.910(2), b = 19.656(5), c = 9.172(4) Å, α = 95.58(3), β = 93.67(2), γ = 103.30(2)°, D _calc = 1.195 g cm^?3, Z = 2, and R = 0.067 for 8644 observed reflections) and (2)(1,4-dioxane)₂, (P2₁/n, a = 5.661(1), b = 17.971(3), c = 18.619(3) Å, β = 91.37(2)°, D _calc = 1.254 g cm^?3, Z = 2, and R = 0.097 for 4353 observed reflections) illuminated that their guest preference should be ascribed to the commonly observed π-sandwich” structure, in which guest molecules are enclathrated between two anthracene planes of the host molecules.     

Enhanced performance of photorefractive poly(N‐vinyl carbazole) composites

We present the enhanced photorefractive performance of high molecular weight poly(N‐vinyl carbazole) (PVCz)‐based composites. Higher diffraction efficiency with faster speed of grating build‐up was obtained by optimizing the composition of the PVCz composites. At relatively low applied electric field of E = 45 V μm^?1, diffraction efficiency of 26% for p‐polarized probe beam and corresponding that of 5.1% for s‐polarized probe beam were measured with faster grating build‐up speed of 48.3 s^?1 for the composite with 2,4,7‐trinitrofluorenone (TNF) as a sensitizer. Fastest speed of grating build‐up of 100 s^?1 and large optical gain up to 110 cm^?1 were measured at E = 80 V μm^?1 for the composite with fullerene derivative of PCBM as a sensitizer. These improved performances are due to a large orientational enhancement effect with faster response speed in addition to Pockels effect for the samples with appropriate glass transition temperature. © 2011 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys, 2011