A proof of Freud's conjecture for exponential weights

LetW (x) be a function nonnegative inR, positive on a set of positive measure, and such that all power moments ofW ²(x) are finite. Let {p _n (W ²;x)} ₀ denote the sequence of orthonormal polynomials with respect to the weightW ²(x), and let {A _n } ₁ and {B _n } ₁ denote the coefficients in the recurrence relation

Synthesis of a biotinated amphiphile

The synthesis of a biotinated amphiphile assembled from d-(+)-biotin, ethylene diamine as spacer, galactaric acid and 1-dodecylamine was achieved in six steps. The key step was the synthesis of a bisacetonide protected galactaric ester, the structure of which was determined by X-ray analysis. Aminolysis, spacer attachment, coupling with biotin and deprotection led to the amphiphilic galactaramide.     

Degradation of ²-O-4 lignin model and related compounds by the ascomyceteChrysonilia sitophila (TFB 27441 strain)

Growth of the ascomyceteChrysonilia sitophila during degradation of lignin model dimers and monomers was compared to a glucose control. An inhibition of growth by Cα-carbonyl monomers and stimulation by β-O-4 lignin model and vanillyl alcohol were observed. A comparison of the degradation by this ascomycete with the basidiomycetePhanerochaete chrysosoporium showed similarities in relation to the type of degradation caused.     

Classical theory of vibration energy transfer in collinear collisions

Classical theory of collisions is cast in a form which also includes the uncertainty principle. This theory is used for analyzing the vibration energy transfer in the collinear collision which approximates the He-H₂ system. The results are compared with the quantum calculations and several classical and semiclassical approaches. Very good agreement with quantum theory is found, for all the parameters investigated.     

Photobioreactor culture of photosynthetic soybean cells

Photosynthetic suspension cultures of higher plants offer an alternative approach to biomass production, potentially yielding cellulosic material and protein on a continuous year-round basis. A bench-top hybrid photobioreactor was developed to study photomixotrophic and photoautotrophic growth of Glycine max as a model system. Maximum biomass doubling times for photomixotrophic and photoautotrophic growth were 1.87 and 3.92 d, respectively. The presence of exogenous sugars resulted in photomixotrophic growth, reduced chlorophyll levels, and a reduction in photosynthetically-evolved oxygen. Depletion of carbohydrates from the medium coincided with the beginning of stationary phase and an increase in oxygen evolution by the cells. A second growth phase, prolonging cell viability, could be initiated by increasing the carbon dioxide from 2 to 5%, just before the onset of stationary phase. Biomass from bioreactor cultured cells proved resistant to enzymatic attack without pretreatment. Composition of the biomass was 7.8% lignin, 20.7% α-cellulose, 23% hemicellulose, 5.5% starch, 14.5% protein and 6.5% nucleic acids.     

Cyclotomic units over finite fields

Let ζ be a primitivesp-th root of unity for a primep>2, and consider the group Ω(ζ) of cyclotomic units in the ringR(ζ)=ℒ[ζ+ζ^-1]. This paper deals with the image of Ω(ζ) in the unit group ofR(ζ)/qR(ζ), whereq is a prime ≠p. In particular, it obtains criteria for this image to be essentially everything, and a lower bound on the density of primesp (withq fixed) for which it cannot be. These results have a direct bearing on previous work about units in integral group rings for cyclic groups of orderpq. Work supported in part by an operating grant from NSERC (Canada).     

Wilson's functional equations on groups

We study properties of solutionsf, g, h C(G) of the functional equation

On translation planes of orderq 3 that admit a collineation group of orderq 3, II

Let II be a translation plane of orderq ³ with kernel GF(q) that admits a collineation groupG of orderq ³ in the linear translation complement such thatG fixes a point at infinity and acts transitively on the remaining points at infinity.In this paper, we show that any such translation plane II is one of the following types of planes:     

Large deviations for martingales with some applications

Let(X _i ) be a martingale difference sequence. LetY be a standard normal random variable. We investigate the rate of uniform convergence