Orthogonal decomposition of Lorentz transformations

The canonical decomposition of a Lorentz algebra element into a sum of orthogonal simple (decomposable) Lorentz bivectors is defined and discussed. This decomposition on the Lie algebra level leads to a natural decomposition of a proper orthochronous Lorentz transformation into a product of commuting Lorentz transformations, each of which is the exponential of a simple bivector. While this later result is known, we present novel formulas that are independent of the form of the Lorentz metric chosen. As an application of our methods, we obtain an alternative method of deriving the formulas for the exponential and logarithm for Lorentz transformations.     

Second-generation aerosol shock tube: an improved design

An improved, second-generation aerosol shock tube (AST II) has been developed for the study of the chemical kinetics of low-vapor-pressure fuels. These improvements enable a wider range of fuel concentrations and enhanced spatial uniformity relative to our initial aerosol shock tube (AST I). In addition, the design of AST II limits the aerosol loading zone in the shock tube to a fixed region (1.2 m in length adjacent to the shock tube endwall). AST II achieves these improvements using a separate holding tank to prepare the aerosol mixture and a slightly under-pressure dump tank to carefully pull the aerosol mixture into the tube in a plug-flow. This filling method is capable of producing room temperature test gas mixtures of n-dodecane with equivalence ratios of up to 3.0 in 21 % O₂, three times the loading achievable in the earlier AST I that used a flow-through strategy. Improvements in aerosol uniformity were quantified by measuring the liquid volume concentration at multiple locations in the shock tube. The measurements made over a length of 1.1 m of shock tube indicate that the AST II method of filling produces non-uniformities in liquid volume concentration of less than 2 %, whereas in the AST I method of filling the non-uniformities reached 16 %. The improved uniformity can also be seen in measurement of gas-phase fuel concentration behind the incident shock wave after the liquid droplets have evaporated. Significant reduction in the scatter of ignition delay times measured using AST II have also been achieved, confirming the importance of uniform loading of the aerosol in making high-quality combustion measurements.     

Crystal and molecular structures of three trimethylamine-boron halide adducts: (CH3)3NBCl3, (CH3)3NBBr3, and (CH3)3NBI3

X-ray diffraction data from single crystals of the trimethylamine complexes of the three boron halides, BCl₃, BBr₃, and BI₃, lead to aP2₁/m monoclinic cell containing two molecules for each complex. The unit cell dimensions area = 6·68(1),b = 10·247(3),c = 6·502(6) Å, =116·2(1)° (chloro);a = 6·86(1),b = 10·612(4),c = 6·737(6) Å, = 115·8(1)° (bromo);a = 6·92(2),b = 10·86(1),c = 7·147(6) Å, = 93·9(1)° (iodo). The structures were solved by three-dimensional sharpened Patterson functions and show only the chloro and bromo compounds to be isomorphous. Refinement of 662,718 and 954 observed reflexions for the chloro, bromo and iodo complexes, respectively, using anisotropic thermal parameters yielded conventionalR factors of 0·045, 0·087 and 0·054.The molecules are shown to possess a B—N dative bond, a staggered conformation, and effective 3m (C _3v) symmetry. Average C—N bond lengths are 1·52(1) Å for all three complexes. Boronhalogen bond lengths average 1·864(4), 2·04(2) and 2·28(2) Å, while B—N bond distances are 1·609(6), 1·60(2) and 1·58(3) Å, respectively, for the chloro through iodo compounds. Bond angles are approximately tetrahedral with the C—N—C angle decreasing by several degrees in the Cl Br I series.Based in part on a dissertation submitted by Patty H. Clippard to the Rackham School of Graduate Studies of the University of Michigan, January 1969 in partial fulfillment of the requirements of the Ph.D. Degree.     

Mechanistic studies of the triggered release of liposomal contents by matrix metalloproteinase-9

Matrix metalloproteinases (MMPs) constitute a class of extracellular-matrix-degrading enzymes overexpressed in many cancers and contribute to the metastatic ability of the cancer cells. We have recently demonstrated that liposomal contents can be released when triggered by the enzyme MMP-9. Herein, we report the results of our mechanistic studies of the MMP-9-triggered release of liposomal contents. We synthesized peptides containing the cleavage site for MMP-9 and conjugated them with fatty acids to prepare the corresponding lipopeptides. By employing circular dichroism (CD) spectroscopy, we demonstrated that the lipopeptides, when incorporated into liposomes, are demixed in the lipid bilayers and generate triple-helical structures. MMP-9 cleaves the triple-helical peptides, leading to the release of the liposomal contents. Other MMPs, which cannot hydrolyze triple-helical peptides, fail to release the contents from the liposomes. We also observed that the rate and extent of release of the liposomal contents depend on the mismatch between the acyl chains of the synthesized lipopeptide and phospholipid components of the liposomes. CD spectroscopic studies imply that the observed differences in the release reflect the ability of the liposomal membrane to anneal the defects following the enzymatic cleavage of the liposome-incorporated lipopeptides.     

Diterpenoids

This review covers the isolation and structures of diterpenoids including labdanes, clerodanes, pimaranes, abietanes, kauranes, cembranes, taxanes and marine diterpenoids; 173 references are cited.     

Fungal terpene metabolites: biosynthetic relationships and the control of the phytopathogenic fungus Botrytis cinerea

The structures and biosynthesis of the sesquiterpenoid metabolites of Botrytis cinerea and their relationship to the presilphiperfolanes are reviewed. The development of a novel strategy for the control of this phytopathogenic fungus based on analogues of these metabolites is described. There are 75 references.     

Mid-infrared absorption measurements of liquid hydrocarbon fuels near

Quantitative absorption spectra for several hydrocarbon fuels in the liquid phase at are presented. Measurements of toluene, n-dodecane, n-decane, and three samples of gasoline were made over the spectral region 2700–3200 to support the development of mid-infrared laser-absorption diagnostics for measurements of fuel vapor in the presence of liquid films and aerosols. A procedure for quantitative Fourier transform infrared (FTIR) absorption measurements of strongly absorbing liquids is described and the resulting absorption spectra are compared with previously measured absorption spectra in the vapor phase. The measured absorption spectra for liquid gasoline are shown to scale with the volume percent of olefin, alkane, and aromatic hydrocarbons in each sample. Finally, the observed frequency shift of in the spectra of vapor and liquid hydrocarbons is discussed, including the potential for measurements of fuel vapor in the presence of liquid films.