Spirodionic acid, a novel metabolite from Streptomyces sp., part 1: structure elucidation and Diels-Alder-type biosynthesis

Spirodionic acid (1), a novel microbial metabolite with a spiro[4.5]decene skeleton, the 6-ethyl-2H-pyrone 5, dihydrosarkomycin (6), and other metabolites were isolated from the strain Streptomyces sp. Tü 6077. Structural elucidation was accomplished by NMR spectroscopic and mass-spectrometric studies, and the biosyntheses of compounds 1, 5, and 6 were investigated by feeding experiments with (13)C-labeled precursors. All results indicate a biogenetic sequence with metabolite 5 and sarkomycin (7) as precursors in the formation of spirocyclus 1 through an intermolecular Diels-Alder-type reaction.     

Sequences with equi-distributed extreme points in uniform polynomial approximation

Let E be a compact set in with connected complement and positive logarithmic capacity. For any f continuous on E and analytic in the interior of E, we consider the distribution of extreme points of the error of best uniform polynomial approximation on E. Let Λ=(n_j) be a subsequence of such that n_j+1/n_j→1. If, for nΛ, A_n( f)∂E denotes the set of extreme points of the error function, we prove that there is a subsequence Λ′ of Λ such that the distribution of any (n+2)th Fekete point set of A_n( f) tends weakly to the equilibrium distribution on E as n→∞ in Λ′. Furthermore, we prove a discrepancy result for the distribution of the point sets if the boundary of E is smooth enough.     

Elastic wave interaction with a cracked quarter-plane

Summary The elastodynamic interaction between explosively generated body and surface wave and an edge crack in a quarter-plane is investigated. Dynamic photoelasticity was employed to obtain full-field information for data analysis. Measurements of the stress distribution along the free boundaries of the quarter-plane and along the crack walls have been made. Stress intensity distributions at both, the corner and the flaw tip and surface stress distributions for the diffracted and reflected Rayleigh-waves were obtained in the region near the cracked corner.

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Sommario Si studia l’interazione elastodinamica tra onde di volume e di superficie ed una fessura su un bordo in un quarto di piano. Si è fatto uso della fotoelasticità dinamica per ottenere un’informazione completa sull’analisi dei dati. Si sono effettuate misure della distribuzione di sforzo lungo i contorni liberi del quarto di piano ed i contorni della fenditura. Si sono ottenute le distribuzioni d’intensità di sforzo sia nell’angolo che nell’estremità difettosa e le distribuzioni superficiali di sforzo per le onde di Rayleigh diffratte e riflesse nella regione dell’angolo crepato.

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Progress in cellulose shaping: 20 years industrial case studies at Fraunhofer IAP

Cellulose, the most abundant renewable organic material on earth, exhibits outstanding properties and useful applications, but also presents a tremendous challenge with regard to economical and environmentally friendly chemical processing. The viscose process, more than 100 year old is still the most widely utilized technology to manufacture regenerated cellulose fibers and films. Viscose fibers are produced today worldwide on a 5 million ton scale with various fiber types ranging from high performance tire yarn to textile filaments and staple fibers with excellent properties close to those of cotton. At Fraunhofer IAP, the technical equipment for viscose preparation, wet spinning of fibers, hollow fibers, and tube-like films is available on a min-plant scale. Research focused on raw materials testing, process optimization with regard to economic and ecological aspects, structural analysis of cellulose during processing, and structure–property relations of fibers and films. Similar to the viscose process, cellulosic fibers can be produced via cellulose carbamate as an environmentally friendly route. In a close cooperation of Fraunhofer IAP with industrial partners, a specific process based on cellulose carbamate was developed on a pilot plant scale, giving fiber properties close to those of conventional viscose fibers. In recent decades the N-methylmorpholine-N-oxide (NMMO)-technology turned out to be a nonderivatizing commercial alternative to the still dominant viscose route. From the very beginning, Fraunhofer IAP has been engaged in investigating the structure formation of cellulose fibers precipitated from NMMO-water solution, revealing structural reasons for the fibrillation tendency of these fibers and means to overcome them. Starting from fiber formation via dry-jet wet spinning, for the first time the blown film formation and the meltblown nonwovens technology were developed for cellulosics on a pilot plant scale at Fraunhofer IAP. Based on the elastic behavior of the dope at elevated temperatures, cellulose can be processed like a melt in the air-gap, offering new possibilities of shaping cellulose like meltable mass polymers. Combining cellulose carbamate with NMMO-monohydrate as a solvent, higher polymer concentrations in the dope and outstanding mechanical properties of the resulting fibers were achieved.     

Limit Laws for Symmetric k-Tensors of Regularly Varying Measures

We consider the asymptotics of certain symmetric k-tensors, the vector analogue of sample moments for i.i.d. random variables. The limiting distribution is operator stable as an element of the vector space of real symmetric k-tensors.     

Atoms, anti-atoms and complements in the lattice of quasi-uniformities

We describe the atoms of the complete lattice (q(X),⊆) of all quasi-uniformities on a given (nonempty) set X. We also characterize those anti-atoms of (q(X),⊆) that do not belong to the quasi-proximity class of the discrete uniformity on X. After presenting some further results on the adjacency relation in (q(X),⊆), we note that (q(X),⊆) is not complemented for infinite X and show how ideas about resolvability of (bi)topological spaces can be used to construct complements for some elements of (q(X),⊆).     

Uniform structures in the beginning of the third millenium

It is the aim of the present survey article to discuss briefly results published by various researchers in the area of uniform structures over the past five years.     

Curvatures and Tolerances in the Euclidean Motion Group

We investigate the action of imprecisely defined affine and Euclidean transformations and compute tolerance zones of points and subspaces. Tolerance zones in the Euclidean motion group are analyzed by means of linearization and bounding the linearization error via the curvatures of that group with respect to an appropriate metric.