The real and the symmetric nonnegative inverse eigenvalue problems are different

We show that there exist real numbers that occur as the eigenvalues of an entry-wise nonnegative -by- matrix but do not occur as the eigenvalues of a symmetric nonnegative -by- matrix. This solves a problem posed by Boyle and Handelman, Hershkowitz, and others. In the process, recent work by Boyle and Handelman that solves the nonnegative inverse eigenvalue problem by appending 0's to given spectral data is refined.

     

Distributive multiplication rings

A ringR is said to be a left (right)n-distributive multiplication ring, n>1 a positive integer, if aa₁a₂...a_n=aa₁aa₂...aa_n (a₁a₂...a_na=a₁aa₂a...a_na) for all a, a₁,...,a_n R. It will be shown that the semi-primitive left (right)n-distributive rings are precisely the generalized boolean ringsA satisfying aⁿ=a for all a A. An arbitrary left (right)n-distributive multiplication ring will be seen to be an extension of a nilpotent ringN satisfyingN ⁿ⁺¹=0 by a generalized boolean ring described above. Under certain circumstances it will be shown that this extension splits.     

Efficient cellulose solubilization by a combined cellulosome-β-glucosidase system

The cellulosome, the multienzyme complex of the cellulase system ofClostridium thermocellum, that mediates the solubilization of insoluble cellulose, is strongly inhibited by the major end product, cellobiose. By combining a purified β-glucosidase fromAspergillus niger with the cellulosome, accumulated cellobiose was hydrolyzed thereby resulting in a dramatic enhancement (up to 10-fold) of cellulose degradation. The observed enhancement was expressed both in the rate and degree of solubilization of microcrystalline cellulose, compared with that observed for the unsupplemented cellulosome. Near-complete conversion of cellulose to glucose could be obtained from dense substrate suspensions (up to at least 200 g/L).     

Verdoppelungen von Biokolloiden

Ohne Zusammenfassung     

Spiralenbildung bei Niederschlägen in Gallerten

Zusammenfassung Gelegentlich tritt eine Niederschlagsbildung in Gallerten als Spirale auf statt der Ringe oder der parallelen Scheiben. Da die Spirale auch dann als solche weiter wächst, wenn die Kontinuität der Keimwirkung unterbrochen war, wird angenommen, daß die Ursachen für beide Bildungsformen die gleichen seien.     

Kolloid-Symbiose

Ohne Zusammenfassung     

Ueber die Formung von Gelatine durch Salzniederschläge und Kristalle

Ohne Zusammenfassung     

Über die Adjunktion von Integralen linearer homogener Differentialgleichungen

Ohne Zusammenfassung     

The analysis of cylindrical shell roofs with post tensioned edge beams

A new characteristic equation for cylindrical shell roofs is developed, together with a method for obtaining the solution and its derivatives. Post tension is introduced into the edge beam by shearing forces varying linearly from a maximum at the transverse to zero at the quarter points. The Fourier series for this converges rapidly. An end correction is then made to restore the post tension to the end of the edge beam and obtain compatibility of strain with the shell edge. The method is compared with experimental results on a model shell and with the results of a finite element program.