The stability of the exponential equation

We generalize the well-known Baker's superstability result for exponential mappings with values in the field of complex numbers to the case of an arbitrary commutative complex semisimple Banach algebra. It was shown by Ger that the superstability phenomenon disappears if we formulate the stability question for exponential complex-valued functions in a more natural way. We improve his result by showing that the maximal possible distance of an -approximately exponential function to the set of all exponential functions tends to zero as tends to zero. In order to get this result we have to prove a stability theorem for real-valued functions additive modulo the set of all integers .

     

Separation techniques for biotechnology in the 1990s.

Scientists are constantly looking for better and cheaper separation techniques to replace or complement the current technology. Over the past few decades, and in particular the last 10 years, new separation techniques or modifications of existing techniques have become available for separating compounds from complex sample matrices. There are many areas, however, where the separation technology is not sufficient to achieve high purity and yield while remaining cost effective. In the area of biotechnology, separation techniques are urgently needed to meet demands for ultra-high purity and yield. Thus, a variety of techniques are being developed to address these needs. Generally, biological compounds for the pharmaceutical and biotechnology industries must be obtained at greater than 99.9% purity (sometimes greater than 99.99%) while maintaining high yield. In any area of chemistry this degree of purity would cause problems; in biotechnology it is even more difficult to achieve because of the complex sample matrices. In addition, the compounds of interest may be very similar to impurities or contaminants in the sample matrix, and the compounds could be denatured (or even destroyed) by certain solvents and/or high temperature. In particular, three areas of biotechnology have presented scientists with problems in separations: cell separations, DNA-RNA separations, and protein-peptide separations. The current technology available and possible future trends in these areas are discussed, and also problems to be solved in the future.     

Calculs de complexité relatifs à une méthode de dissection emboîtée

Résumé Nous présentons une numérotation de type Nested Dissection des inconnues d'un système linéaireAX=B pour des ensembles de matricescreuses symétriques définies positives correspondant à des famille de graphes non orientés,à degré borné, et admettant un -thérème de séparation. Comparativement aux méthodes et résultats de Rose [9], l'algorithme présenté est plus simple, mais les théorèmes de complexité moins généraux, en raison de l'hypothèse restrictive de degré borné. En outre, les démonstrations font appel en permanence à la structure d'arbre sur la famille des séparateurs qui constitue, par ailleurs, une partition de l'ensemble des sommets du graphe initial. Nous présentons ensuite le schéma général d'implémentation dans le cadre du code d'éléments finis MODULEF pourdes problèmes plans d'éléments finis, et nous donnons quelques mesures comparatives avec la numérotation plus classique qui tend à minimiser le profil de la matrice.

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Complexity bounds for a nested dissection method

Summary A nested dissection ordering is given for solving any system of linear equationsAX=B, for the family ofsparse symmetric positive definite matrices corresponding to the class of undirected graphs withbounded degree, and satisfyinga -separator theorem. If we compare the methods and results presented by Rose [9], our algorithm is more simple, but the complexity results are less general because of the restriction of bounded degree. Besides, our proofs use continually the arborescent structure on the family of separators, which is, by another way, a partition of the set of vertices for the initial graph. Then, the general implementation scheme in the finite element package MODULEF, fortwo-dimensional finite element problems, is presented, and numerical comparisons between our ordering and the standard envelope method are given.

     

Arylselenenation of conjugated dienes by arylselenenamides in the presence of phosphorus(V) oxyhalides

Arylselenenation of conjugated and non-conjugated dienes by arylselenenamides in the presence of phosphorus(V) oxyhalides has been studied. Reactions with conjugated dienes lead to 1,4-adducts whilst only addition to double bonds takes place in reactions with non-conjugated dienes.     

Neue Macrolide und einige Sesquiterpen-Derivate aus dem Galbanum-Harz

New Macrolides and Some Sesquiterpenoid Derivatives Occurring in Galbanum Absolute Analytical investigations of a Galbanum absolute have revealed for the first time the presence of four macrolides 1 – 4 derived from the corresponding hydroxylated C₁₃–C₁₆ fatty acids by lactonization of a secondary alcoholic group with the carboxylic group. The musky odor strengthens with increasing number of members in the macrocycle, whereas the woody note is predominant in the smaller rings. Isolation, identification and synthesis of the new naturally occurring substances are described. Shyobunol ( 24 ) epishyobunol ( 25 ) as well as their acetates 26 and 27 were identified - together with 10-epijunenyl acetate ( 28 ) - in the same substrate, thus indicating 25 and 26 to be natural products. The corresponding known and already naturally occurring ketones 23 and 24 are trace components in the investigated material derived from the so-called Galbanum oleo-gum-resin.     

Monolayer metal coverage of fullerenes: the optical response

A first-principles investigation of the photoabsorption cross section of the specially stable cluster Li₁₂C₆₀ is carried out, including the icosahedral symmetry of the cluster and treating the ions via ab initio pseudopotentials. The role of the coating metal is assessed by computing the same quantity for the fullerene “seed”. It is found that the main absorption features are determined by the carbon molecule, both at low and high excitation energies, in spite of a reduction of 60% for the ionization threshold of Li₁₂C₆₀ as compared to C₆₀. Nonetheless the lithium coating is responsible for small yet clearly observable effects throughout the spectrum, in particular for a more structured and broad strength distribution at excitation energies below the ionization threshold of C₆₀, and a double peak structure in the Mie resonance at ≈20 eV.     

Oxygen equilibrium pressure as a measure of oxygen binding energy in the V2O5−x system

Using the redox mechanism of vanadia catalyst action as a starting point, oxygen binding energy and its measurement have been discussed. Experimental results on the equilibrium oxygen pressure are presented and two types of equilibrium are distinguished: chemisorbed and redox. It has been shown that univariant redox equilibrium is appropriate for characterizing vanadia catalysts.     

Thermal Analysis of the System Na3AlF6–NaVO3

Summary. The phase diagram of the system Na₃AlF₆–NaVO₃ was determined by means of thermal analysis. The system is a simple binary eutectic one. The eutectic point was estimated at x(NaVO₃) = 0.975 and t _eut = 617°C. The XRD patterns of samples after thermal analysis revealed the presence of cryolite and NaVO₃ only supporting the above assumption of a simple eutectic binary system.