The diamagnetic Kepler problem

It has turned out that the analysis ofclassical periodic orbits is the key to understanding the modulations in thequantal spectra of hydrogen Rydberg atoms in magnetic fields. Inspired by this quantum chaological connection, we analyse some fundamental periodic orbits of the diamagnetic Kepler problem, abandoning the condition of vanishing azimuthal angular momentuml _z used in the literature so far. We report the bifurcation and confluence schemes of the orbits in their dependence onl _z and discuss the structural changes in terms of catastrophe theory.     

An unprecedented N-transacylation reaction on 2-acetamido-2-deoxy-α-d-glucopyranosides

An unprecedented N-transacylation reaction on 2-acetamido-2-deoxy-α-d-glucopyranosides was disclosed in the presence of acyl chloride and DMAP under reflux in pyridine.     

Process improvement in acetone-butanol production from hardwood by simultaneous saccharification and extractive fermentation

The acetone-butanol production by simultaneous saccharification and extractive fermentation (SSEF) was investigated. In the SSEF employing cellulase enzymes andClostridium acetobutylicum, both glucan and xylan fractions of pretreated aspen are concurrently converted into acetone and butanol. Continuous removal of the fermentation products from the bioreactor by extraction was an important factor that allowed long-term fed-batch operation. The use of membrane extraction prevented the problems of phase separation and extractant loss. Increase in substrate feeding as well as reduction of nutrient supply was found to be beneficial in suppressing the acid production, thereby improving the solvent yield. Because of prolonged low growth conditions prevalent in the fed-batch operation, the butanol-to-acetone ratio in the product was significantly higher at 2.6–2.8 compared to the typical value of two.     

Optically active polymers containing side-chain photochromic moieties: Synthesis and chiroptical properties of copolymers of trans-4-(phenylazo)-1-naphthyl acrylate and trans-4-(1-naphthylazo)-phenyl acrylate with (?)-menthyl acrylate

The synthesis of photochromic optically active copolymers from trans-4-(phenylazo)-1-naphthyl acrylate (PANA), or trans-4-(1-naphthylazo)-phenyl acrylate (NAPA), and (?)-menthyl acrylate (MtA) is described. The copolymers prepared, having different contents of trans-phenylazonaphthalene moieties, have been characterized by IR, ¹H-NMR, UV, and GPC techniques. The chiroptical properties have been investigated by circular dichroism (CD) and the induced optical activity on the side-chain trans-phenylazonaphthalene chromophores discussed in terms of different conformational situations of the macromolecules in both the copolymer series. © 1994 John Wiley & Sons, Inc.     

Development of xylose-fermenting yeasts for ethanol production at high acetic acid concentrations

Mutants resistant to comparatively high levels of acetic acid were isolated from the xylose-fermenting yeastsCandida shehatae andPichia stipitis by adapting these cultures to increasing concentrations of acetic acid grown in shake-flask cultures. These mutants were tested for their ability to ferment xylose in presence of high acetic acid concentrations, in acid hydrolysates of wood, and in hardwood spent sulfite liquor, and compared with their wild-type counterparts and between themselves. TheP. stipitis mutant exhibited faster fermentation times, better tolerance to acid hydrolysates, and tolerance to lower pH.     

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

Degree of approximation of analytic functions by “near-best” polynomial approximants

We study the rate of approximation of a functionfA(K) in the interior of the compact setK by polynomials, that are close to best polynomial approximants on the whole setK. Lower and upper estimates of possible improvement of convergence (depending on the geometry ofK) are obtained.Communicated by Vilmos Totik.