On the solution of singular linear systems of algebraic equations by semiiterative methods

Summary For a square matrixT ^n,n , where (I–T) is possibly singular, we investigate the solution of the linear fixed point problemx=T x+c by applying semiiterative methods (SIM's) to the basic iterationx ₀ ⁿ ,x _k T c _k–1+c(k1). Such problems arise if one splits the coefficient matrix of a linear systemA x=b of algebraic equations according toA=M–N (M nonsingular) which leads tox=M ^–1 N x+M ^–1 bT x+c. Even ifx=T x+c is consistent there are cases where the basic iteration fails to converge, namely ifT possesses eigenvalues 1 with ||1, or if =1 is an eigenvalue ofT with nonlinear elementary divisors. In these cases — and also ifx=T x+c is incompatible — we derive necessary and sufficient conditions implying that a SIM tends to a vector which can be described in terms of the Drazin inverse of (I–T). We further give conditions under which is a solution or a least squares solution of (I–T)x=c.Research supported in part by the Alexander von Humboldt-Stiftung     

N-(17-Phosphonooxylinolenoyl)glutamine and N-(17-phosphonooxylinoleoyl)glutamine from insect gut: the first backbone-phosphorylated fatty acid derivatives in nature

N-(17-Phosphonooxylinolenoyl)glutamine (1) and N-(17-phosphonooxylinoleoyl)glutamine (2) were isolated from the regurgitate of Spodoptora exigua and identified as the first natural alkyl chain-phosphorylated fatty acid derivatives. The compounds were characterized by HPLC-MS/MS and the assigned structures confirmed by synthesis via a dissymmetric bis-Wittig approach as the key reaction. Rearing of the larvae on a diet enriched with inorganic phosphate increased the amount of the phosphorylated N-acyl glutamines in the regurgitate.     

Impact of electron-electron interaction on the electron energy distribution function in molecular plasmas under rf field action

Calculations of the electron energy distribution and of relevant macroscopic quantities of collision-dominated, weakly ionized plasmas under rf field action have been performed with increasing degrees of ionization, and the impact of the electron-electron interaction on these quantities was determined. The investigations were performed for the gas plasmas in CO and H₂ as representatives of molecular plasmas The energy distribution and macroscopic quantities are obtained by solving the nonstationary Bolizmann equation for a given rf field and degree of ionization taking into accoung and additional Fokker-Planck term besides the collision integrals for the elastic and the main inelastic collision processes. In these molecular plasmas a remarkable impact of the electron-electron interaction connected with increasing Maxwellization is observed for degrees of ionization greater than 10.     

3,7-Dioxaazelaamides as Ionophores for Lithium Ion Selective Liquid Membrane Electrodes

Lipophilic neutral carriers were synthesized which show Li⁺/Na⁺ selectivities of up to ca. 80 in highly lipophilic liquid membranes. The sensor membranes exhibit improved response times and increased lifetimes as compared to systems described earlier. They allow reliable measurements of Li⁺ in blood serum within the clinical concentration range. A 1:1 Li⁺/ionophore complex of one representative (N,N,N′,N′-tetracyclohexyl-5,5-dimethyl-3,7-dioxaazelaamide) has been prepared, and its structure was elucidated by X-ray analysis.     

Dynamic Fourier transform infrared spectroscopy in polymer research

The rapid-scanning capability of FTIR instrumentation has revitalized the field of vibrational spectroscopy in polymer research and will be discussed with reference to the study of polyurethane kinetics, the temperature dependence of hydrogen bonding in polyamide 6 and strain-induced crystallization in a polydimethylsiloxane elastomer.     

Solubility of gases in liquids. 18. High-precision determination of Henry fugacities for argon in liquid water at 2 to 40°C

The solubility of argon in pure liquid water was measured at ca. 100 kPa and from 2 to 40°C using an analytical method characterized by an imprecision of about ±0.05%. From the experimental results, Henry fugacities H _2,1 (T,P _s,1 ) (also known as Henry's Law constants or Henry coefficients) at the vapor pressure P _s,1 of water as well as Ostwald coefficients L _2,1 at infinite dilution were obtained. Measurements were made at roughly 0.5°C and/or 1° intervals between 2 and 8°C (region I), and at 5°C intervals above 10°C (region II). A difference plot lnH _2,1 /T suggests an unusual temperature dependence in region I, i.e., between 2 and 8°C. Because of this, the data were treated separately in two parts corresponding to these two regions. Our results are compared with the recent high-precision data of Krause and Benson (Henry fugacities), and with calorimetrically determined quantities (enthalpies and heat capacities of solution). Finally, experimental results are compared with values calculated via scaled particle theory.Communicated in part at the 2^nd International Symposium on Solubility Phenomena in Newark, New Jersey, August 12–15, 1986, and at the 4^th ISSP in Troy, New York, July 20–August 3, 1990.     

Biosynthesis of cis-Jasmone: a pathway for the inactivation and the disposal of the plant stress hormone jasmonic acid to the gas phase?

Flowers of Jasminum rincospernum convert deuterium-labeled jasmonic acid [²H₅]- 4a and methyl 1,2-didehy-drojasmonate [²H₄]- 8 into labeled cis-jasmone [²H₄]- 1. The labeling pattern of the resulting cis-jasmone ( 1 ) is consistent with a Grob fragmentation of the didehydrojasmonic acid 8a by decarboxylation after protonation of the keto group. The pathway is also operative in leaves of several higher plants, including mono- and dicotyledonous specimens. In Lima beans besides cis-jasmone ( 1 ) an equimolar mixture of trans- and cis-isomers of methyl jasmonate ( 4 ) and epi- 4 , is emitted after treatment with Jasmonic acid ( 4a ). The relative ratio of 1 and 4 /epi- 4 is critically dependent on the concentration of the administered jasmonic acid ( 4a ) and the ambient temperature of the plant. Unlike 4a , the 1,2-didehydrojasmonic acid ( 8a ) is not able to induce volatile biosynthesis. Therefore, the transformation of 4a via 8 a into 1 appears to have a special importance for the irreversible inactivation and disposal of the plant stress hormone jasmonic acid to the gas phase and may serve, besides other modes of inactivation, as a shunt in case of high internal of the stress hormone 4a. The conversion of the biologically active jasmonic acid ( 4a ) into the inactive and volatile cis-jasmone (1) is the first example of a disposal of an inactive metabolite of a phytohormone to the gas phase as an infinite sink.