A new class of long-tailed pausing time densities for the CTRW

We present some asymptotic results for the family of pausing time densities having the asymptotic (t) property(t) [t ln¹⁺(t/T)]^–1. In particular, we show that for this class of pausing time densities the mean-squared displacement r ²(t) is asymptotically proportional to ln(t/T), and the asymptotic distribution of the displacement has a negative exponential form.     

Symmetric Markov chains in ℤd: How fast can they move?

Summary Consider a reversible Markov chain X _n which takes values in a subset of ^d. If the steps of the chain are uniformly bounded and the invariant measure satisfies a mild regularity condition, Varopoulos, Carne and Kesten have obtained estimates on \lambda n^{1/2} )$$ " align="middle" border="0"> which exhibit a Gaussian tail in but blow up as n. Following Kesten's approach we derive bounds which are uniform in n in some special cases. Our main result, however, is an example which shows that in general the estimates of Varopoulos, Carne and Kesten are essentially best possible.Research partially supported by an S.E.R.C. (U.K.) visiting fellowship and an operating grant from N.S.E.R.C. of Canada     

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.