A chaos hypothesis for some large systems of random equations

Summary This paper is about the behavior of solutions to large systems of linear algebraic and differential equations when the coefficients are random variables. We will prove a law of large numbers and a central limit theorem for the solutions of certain algebraic systems, and the weak convergence to a Gaussian process for the solution of a system of differential equations. Some of the results were surprisingly difficult to prove, but they are all easily anticipated from a chaos hypothesis: i.e. an assumption of near independence for the components of the solutions of large systems of weakly coupled equations.Supported by the National Science Foundation under grant MCS76-80762, by the U.S. Air Force under grant AFOSR 78-3514 and the U.S. Army under grant DAAG 2980-K-0006     

Head-to-head coiled arrangement of the subunits of the animal fatty acid synthase

The role of the beta-ketoacyl synthase domains in dimerization of the 2505 residue subunits of the multifunctional animal FAS has been evaluated by a combination of crosslinking and characterization of several truncated forms of the protein. Polypeptides containing only the N-terminal 971 residues can form dimers, but polypeptides lacking only the N-terminal 422 residue beta-ketoacyl synthase domain cannot. FAS subunits can be crosslinked with spacer lengths as short as 6 A, via cysteine residues engineered near the N terminus of the full-length polypeptides. The proximity of the N-terminal beta-ketoacyl synthase domains and their essential role in dimerization is consistent with a revised model for the FAS in which a head-to-head arrangement of two coiled subunits facilitates functional interactions between the dimeric beta-ketoacyl synthase and the acyl carrier protein domains of either subunit.     

Synthesis and coordination chemistry of perfluoroalkylated dithiophosphate ligands

Dithiophosphoric acids [HS₂P(OC₂H₄C_nF_2n+1)₂] (n = 4, 6) have been prepared in high yields. Deprotonation and reaction with transition metal substrates affords fluorous metal complexes which have been characterised by elemental analysis, mass spectrometry, IR and NMR spectroscopies. The structures of [Cu{S₂P(OC₂H₄C_nF_2n+1)₂}(PPh₃)₂] (n = 4, 6) and [Cu{-S₂P(OC₂H₄C₄F₉)₂}(PPh₃)]₂ have been determined by single crystal X-ray diffraction.     

A new configuration for coupling purge-and-trap/cryogenic focusing/capillary column gas chromatography with splitless injection mode

A new configuration for coupling a purge-and-trap unit to a capillary column gas chromatograph via a cryogenic focusing interface has been developed. In this configuration, the precolumn of the cryogenic focusing interface was inserted through the septum of a split/splitless injection port where it served as both sample transfer and carrier gas supply lines. The injection port of the gas chromatograph was modified by plugging the carrier gas and the septum purge lines. This configuration allowed for the desorption of analytes at high flow rates while maintaining low, analytical-column flow rates which are necessary for optimum capillary column operation. The capillary column flow rate is still controlled by the column backpressure regulator. Chromatograms of purgeable aromatics exhibited improved resolution, especially for early eluting components compared to those obtained by direct liquid injection using the normal splitless injection mode. Quantitative sample transfer to the analytical column afforded excellent linearity and reproducibility of compounds studied.     

Chelating diphos ligands with inorganic backbones. Crystal structure of [PtCl2{(PPh2O)2SiPh2}]

The metallo-phosphaalkenes (η⁵-C₅Me₅)(CO)₂FeP=C(R)(SiMe₃) (Ia: R = SiMe₃, Ib: R = Ph) and MeO₂C---CC---CO₂Me undergo a dipolar [3+2]-cycloaddition to afford the metallo-heterocycles [(η⁵-C₅Me₅)(CO)

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=C(R)SiMe₃] (IIIa,b) with exocyclic P=C double bonds.     

Thermochemistry of polyhalides. II. Caesium and rubidium dibromoiodides

Using a solution-reaction calorimeter the standard enthalpies of formation of crystalline caesium and rubidium dibromoiodides have been determined as ?445.5±4.1 and ?428.3±4.2 kJ mol^?1, respectively. Thermodynamic parameters, including lattice energies, are calculated and the thermal stability of polyhalides discussed. Thermometric titrations have been used to investigate the mechanism of reaction of caesium dibromoiodide with aqueous silver nitrate.     

Antiresonances in the Rydberg spectrum of naphthalene. A new analysis

The Rydberg “antiresonances” in the spectra of large molecules are reexamined under the assumption that Rydberg level-valence vibronic level mixing is of primary importance in determining the interference phenomenon. The line shape calculated using this point of view fits very well the observed “antiresonance” line shape in the naphthalene spectrum. The formalism also provides a satisfying rationalization for the absence of antiresonances in the Rydberg spectra of most large molecules.     

Sunfish cationic amphiphiles: toward an adaptative lipoplex morphology

A detailed physicochemical study is presented on a new class of cationic amphiphiles, Sunfish amphiphiles, recently designed, synthesized, and tested for gene delivery. These materials have two hydrophobic tails, connected to the cationic pyridinium headgroup at the 1- and 4-positions. Two extreme morphologies can be visualized, i.e. one by back-folding involving association of both tails at one side of the pyridinium ring and one by independent unfolding of the tails, the two molecular geometries leading to considerable differences in the aggregate morphology. The behavior of six members of the Sunfish family in mixtures with DOPE, applying different conditions relevant for transfection, has been studied by a combination of techniques (DLS, DSC, NMR, SAXS, Cryo-TEM, fluorescence, etc.). The effects of structural parameters such as the presence of unsaturation in the tails and length of the alkyl chains on the properties of the aggregates have been assessed. A correlation of these structural data with cellular transfection efficiencies reveals that the highest transfection efficiency is obtained with those amphiphiles that are easily hydrated, form fluid aggregates, and undergo a transition to the inverted hexagonal phase in the presence of plasmid DNA (p-DNA) at physiological ionic strength.     

Influence of hydrodynamic coupling on the density dependence of quasi-one-dimensional diffusion

The effect on the short time one particle diffusion coefficient of hydrodynamic interaction between pairs of colloid particles, and between colloid particles and the walls of a quasi-one-dimensional cylindrical channel, are calculated using the method of reflections. The nonzero size of the colloid particle is accounted for in the analysis, and the theoretical predictions are compared with the experimental data of Lin, Cui, Lee, and Yu for the short time one particle diffusion coefficient of colloids in a square open channel [Europhys. Lett. 57, 724 (2002)].