Minimal polynomial and the rank of principal submatrices of a matrix

The following theorem is proved: If r is the degree of the minimal polynomial of a matrix A then there exists a principal submatrix of A with order r and rank at least r-1.     

Whole cell matrix-assisted laser desorption/ionization time-of-flight mass spectrometry and in situ structure analysis of streptocidins, a family of tyrocidine-like cyclic peptides

Streptocidins, a family of tyrocidine-like cyclic decapeptides, are an ideal demonstration object for the detection and in situ structure analysis of natural compounds directly in microbial cells using whole cell matrix-assisted laser desorption/ionization time-of-flight-mass spectrometry (MALDI-TOFMS), an emerging technique that can be used for rapid sensitive metabolic profiling of microorganisms. Five main members of the streptocidin family (A-E) were detected in Brevibacillus cells picked from agar plates and identified by in situ structure analysis with post-source decay MALDI-TOFMS. This efficient modern method allows the precise detection of metabolites within minutes without the need to isolate and purify the target compounds. The generated mass spectra are of similar quality to those obtained for the purified peptides. In addition, surface extracts were prepared by treating Brevibacillus cells with 70% acetonitrile in the presence of 0.1% trifluoroacetic acid and fractionated by high-resolution reversed-phase high-performance liquid chromatography (HPLC). In this way ten minor streptocidins were detected demonstrating the full biosynthetic variety of streptocidin production on the cellular level. The streptocidins differ from the well-known tyrocidines essentially in position 3 of the decapeptide chain by replacement of the aromatic amino acid (F/W) found in tyrocidines by L-leucine or L-valine.     

Townsend-Koeffizient α für Alkoholdämpfe,Luft und Argon

Measurements of the first Townsend coefficient for the vapours of CH₃OH, C₂H₅OH, C₃H₇OH(n), C₃H₇OH(iso) are described. The experimental arrangement is tested by measuring the known values of air and argon.     

Weak convergence of approximate solutions of random equations

Approximations of random operator equations are considered where the stochastic inputs and the underlying deterministic equation are approximated simultaneously. The main convergence result asserts that, under reasonable and verifiable assumptions, a sequence of weak solutions of approximate random equations converges weakly to a weak solution of the original equation. It is shown that this theorem extends and unifies results already known. We apply our theory to approximations of random differential equations involving stochastic processes with discontinuous paths and to projection methods for nonlinear random Hammerstein integral equations in spaces of integrable functions.     

Moore-penrose involutions in the classes of laplacians and simplices

The Moore-Penrose generalized inverse defines an involution in the class of real positive definite n×n matrices with rank n?1 and row-sums zero. We show that there is an analogous situation for weighted undirected graphs on n vertices and for classes (n?1)-simplices in a Euclidean (n?1)-space.     

Cellulose,Zellstoff

Analytical and Bioanalytical Chemistry -