Bestimmung der L?slichkeit von Salzen

Ohne Zusammenfassung     

Zum Nachweis von Schwefel, Stickstoff und Halogenen in organischen Substanzen

Ohne Zusammenfassung     

Ein Minimalgasgebl?se

Ohne Zusammenfassung     

Zum Nachweis des Furfurols

Ohne Zusammenfassung     

Superelements for the finite element solution of two-dimensional elliptic problems with boundary singularities

A novel singular superelement (SSE) formulation has been developed to overcome the loss of accuracy encountered when applying the standard finite element schemes to two-dimensional elliptic problems possessing a singularity on the boundary arising from an abrupt change of boundary conditions or a reentrant corner. The SSE consists of an inner region over which the known analytic form of the solution in the vicinity of the singular point is utilized, and a transition region in which blending functions are used to provide a smooth transition to the usual linear or quadratic isoparametric elements used over the remainder of the domain. Solution of the finite element equations yield directly the coefficients of the asymptotic series, known as the flux/stress intensity factors in linear heat transfer or elasticity theories, respectively. Numerical examples using the SSE for the Laplace equation and for computing the stress intensity factors in the linear theory of elasticity are given, demonstrating that accurate results can be attained for a moderate computational effort.     

Commuting extensions and cubature formulae

Based on a novel point of view on 1-dimensional Gaussian quadrature, we present a new approach to d-dimensional cubature formulae. It is well known that the nodes of 1-dimensional Gaussian quadrature can be computed as eigenvalues of the so-called Jacobi matrix. The d-dimensional analog is that cubature nodes can be obtained from the eigenvalues of certain mutually commuting matrices. These are obtained by extending (adding rows and columns to) certain noncommuting matrices A₁,...,A_d, related to the coordinate operators x₁,...,x_d, in R^d. We prove a correspondence between cubature formulae and “commuting extensions” of A₁,...,A_d, satisfying a compatibility condition which, in appropriate coordinates, constrains certain blocks in the extended matrices to be zero. Thus, the problem of finding cubature formulae can be transformed to the problem of computing (and then simultaneously diagonalizing) commuting extensions. We give a general discussion of existence and of the expected size of commuting extensions and briefly describe our attempts at computing them.     

REGULATION OF PROTOCHLOROPHYLL(IDE) LEVELS IN DARK-GROWN NON-DIVIDING Euglena—II. INFLUENCE OF UTILIZABLE SUBSTRATES AND INHIBITORS OF PROTEIN SYNTHESIS*

Dark-grown cells of Euglena gracilis var. bacillaris incubated on resting medium for 7 days lose half of their extractable and phototransformable protochlorophyll(ide) [Pchl(ide)]. The readily-utilized substrates glutamate and malate bring about a regeneration of both pools of Pchl(ide) to the levels found in growing cells, without causing cell division during the period of regeneration. Light does not cause a regeneration of total extractable Pchl(ide) to the levels found in growing cells, and the complete regeneration of phototransformable Pchl(ide) seen probably results from conversion of non-transformable Pchl(ide) to transformable Pchl(ide). Optimal glutamate, malate, and light in any combination are no better in causing phototransformable Pchl(ide) regeneration than any one treatment alone, indicating that the Pchl(ide) pool size is limited by other factors. The regeneration of phototransformable Pchl(ide) induced by light or substrates is insensitive to inhibitors of protein synthesis on 80 S cytoplasmic ribosomes (cycloheximide) or on 70 S chloroplast ribosomes (streptomycin). Cycloheximide, however, induces the regeneration of phototransformable Pchl(ide) in darkness in the absencc of externally-added substrates. Since cycloheximide is known to induce paramylum breakdown under the same conditions, it is likely that this process can provide internal substrates and/or reducing power for phototransformable Pchl(ide) regeneration. Possible mechanisms of regulation of formation of Pchl(ide)₆₃₅ in Euglena are discussed and compared with regulation of Pchl(ide)₆₅₀ in higher plants.