Tangential chow forms — rank 1 hypersurfaces in a Grassmannian

Let X ⁿ P ^N be an n-dimensional projective variety, and N–n–1kN–1. The closure in the Grassmannian G(k+1, N+1) of the set of k-planes meeting the smooth locus of X nontransversally is a tangential Chow form (TCF) of X.TCF's are generally hypersurfaces. We show that a hypersurface is a TCF iff its conormal form has rank 1, and that a TCF is a hypersurface iff some quadric in the second fundamental form of X has rank n+k+1–N.     

Properties of noninteger moments in a first passage time problem

We calculate the moments t ^q , whereq is not necessarily an integer, of the first passage time to trapping for a simple diffusion problem in one dimension. If a characteristic length of the system isL and t _q ~L (q) asL, then we show that there is a phase transition atq=q _c such that whenq<q _c ,(g)=0, and forq>q _c , (q) is a linear function ofq. These analytical results can be used to explain results for large moments for diffusion on a hierarchic structure. We also show how to calculate noninteger moments in terms of characteristic functions.     

Necessity of aromatic carboxylate anions to be planar to induce growth of cationic micelles

It is well-known that some aromatic anions have the ability to induce viscoelastic transformation in aqueous solutions of cationic surfactants even at added salt concentrations as low as 10-20 mM. This behavior is associated with the formation of an entangled network of elongated micelles. However, the effect of aromatic ring substituents on the anion's ability to promote rapid micelle growth is not well-understood. We have performed ab initio calculations of the carbonyl group rotation barriers in a series of substituted benzoate and naphthoate anions at the MP2/STO-3G level of theory. It was found that aromatic carboxylates, known to be particularly effective in causing sphere-rod transition in cationic micelles, preferably adopt conformations with the COO(-) group in the same plane as the ring(s). This structural preference can be attributed to either intramolecular hydrogen bonding (o-hydroxyl derivatives) or pi-conjugation effects (m- and p-halogenated derivatives). In the former case the barrier to rotation is 40-50 kcal/mol, whereas in the latter case the threshold value is around 3.0 kcal/mol. Propensity for the planar conformation correlates with a greater depth of counterion penetration into the micelle surface, as inferred from NMR experiments, compared to the anions with less hindered carbonyl rotation. This points to favorable hydrophobic interactions between the surfactant methylene groups and the aromatic ring(s) of the anion as a possible explanation for the rapid growth of cationic micelles observed upon addition of certain aromatic carboxylates.     

Production of cellulase in solid-state fermentation withTrichoderma reesei MCG 80 on wheat straw

Applied Biochemistry and Biotechnology - It is an accepted fact that ethanol production from lignocellulosic materials is not economical as yet because of the high cost of cellulase production. To...     

Observation of a quadrupole plasmon mode for a colloidal solution of gold nanoprisms

The synthesis and optical properties of single crystalline gold nanoprisms have been investigated. A three-step mediated seed growth process in an aqueous solution generated gold nanoprisms with a relatively homogeneous size distribution. The purity of these nanostructures has allowed us to observe a weak quadrupole resonance in addition to a strong dipole resonance associated with these novel structures. The experimental optical spectra agree with discrete dipole approximation calculations that have been modeled from the dimensions of gold nanoprisms produced in this synthesis.     

Structure-activity relationships of pyrethroid insecticides. Part 2. The use of molecular dynamics for conformation searching and average parameter calculation

Summary Molecular dynamics simulations have been performed on a number of conformationally flexible pyrethroid insecticides. The results indicate that molecular dynamics is a suitable tool for conformational searching of small molecules given suitable simulation parameters. The structures derived from the simulations are compared with the static conformation used in a previous study. Various physicochemical parameters have been calculated for a set of conformations selected from the simulations using multivariate analysis. The averaged values of the parameters over the selected set (and the factors derived from them) are compared with the single conformation values used in the previous study.     

The vibrational spectra of some 1,3-dimethyl-1,3-diaza-2-boracyclopentanes

A detailed vibrational assignment is proposed for 1,3-dimethyl-1,3-diaza-2-boracyclopentanes:

where X = Cl, Br or NMe₂. The assignments are generally in accord with C_2v symmetry, but there is some evidence for a slight breakdown, as some A₂ modes appear in the IR. The BN₂ stretches are near 1500 cm^?1, (antisymmetric) and 1300 cm^?1 (symmetric), consistent with a large degree of π-bonding.     

Deuterium exchange of 4-pyrimidones and 4-pyrimidthiones

The hydrogen-deuterium exchange of H-2 in 4-pyrimidone, a number of 1- and 3-alkyl-4-pyrimidones and several of their thione analogs in deuterium oxide at moderate temperatures is reported. This reaction is apparently not susceptible to acid or base catalysis. Cations of the 4-pyrimidones were found not to exchange H-2 at all in acid media. Catalytic amounts of bases do not alter the exchange rates whereas more concentrated alkali decompose the pyrimidone. However, 1,4(3,4)-dihydro-1,3-dimethyl-4-oxopyrimidinium iodide (and its 6-methyl analog) exchange H-2 quite rapidly in neutral deuterium oxide, almost instantly when triethylamine is added as a catalyst, and very slowly in dilute solutions of deuterium chloride in deuterium oxide. Mechanisms are proposed to account for these phenomena.     

Lars Onsager (1903–1976), Chemist-Physicist, on the Silver Anniversary of His Death

The Norwegian-born theoretical chemist-physicist Lars Onsager (1903–1976) received the 1968 Nobel Prize for Chemistry for the discovery of the reciprocal relations bearing his name, which are fundamental for the thermodynamics of irreversible processes. A recipient of numerous awards and honorary degrees, which he did not receive until relatively late in life, he taught at the Johns Hopkins and Brown universities, but spent most of his academic career at Yale University (1933–1972). He spent his post-retirement years (1972–1976) as Distinguished University Professor at the University of Miamis Center for Theoretical Studies, where he continued his work with several postdoctoral research fellows.