Invariant integrals applied to nematic liquid crystals with small Ericksen number and topological defects

Invariant integrals are derived for nematic liquid crystals and applied to materials with small Ericksen number and topological defects. The nematic material is confined between two infinite plates located at y = -h and y = h (h is an element of R+) with a semi-infinite plate at y = 0 and x < 0. Planar and homeotropic strong anchoring boundary conditions to the director field are assumed at these two infinite and semi-infinite plates, respectively. Thus, a line disclination appears in the system which coincides with the z-axis. Analytical solutions to the director field in the neighbourhood of the singularity are obtained. However, these solutions depend on an arbitrary parameter. The nematic elastic force is thus evaluated from an invariant integral of the energy-momentum tensor around a closed surface which does not contain the singularity. This allows one to determine this parameter which is a function of the nematic cell thickness and the strength of the disclination. Analytical solutions are also deduced for the director field in the whole region using the conformal mapping method. (C) 2013 Elsevier Ltd. All rights reserved.

Unified min-max and interlacing theorems for linear operators

There exist striking analogies in the behaviour of eigenvalues of Hermitian compact operators, singular values of compact operators and invariant factors of homomorphisms of modules over principal ideal domains, namely diagonalization theorems, interlacing inequalities and Courant-Fischer type formulae. Carlson and Sa [D. Carlson and E.M. Sa, Generalized minimax and interlacing inequalities, Linear Multilinear Algebra 15 (1984) pp. 77-103.] introduced an abstract structure, the s-space, where they proved unified versions of these theorems in the finite-dimensional case. We show that this unification can be done using modular lattices with Goldie dimension, which have a natural structure of s-space in the finite-dimensional case, and extend the unification to the countable-dimensional case.

Molecular details of INH-C-10 binding to wt KatG and Its S315T mutant

Isoniazid (INH) is still one of the two most effective antitubercular drugs and is included in all recommended multitherapeutic regimens. Because of the increasing resistance of Mycobacterium tuberculosis to INH, mainly associated with mutations in the katG gene, new INH-based compounds have been proposed to circumvent this problem. In this work, we present a detailed comparative study of the molecular determinants of the interactions between wt KatG or its S315T mutant form and either INH or INH-C10, a new acylated INH derivative. MD simulations were used to explore the conformational space of both proteins, and results indicate that the S315T mutation did not have a significant impact on the average size of the access tunnel in the vicinity of these residues. Our simulations also indicate that the steric hindrance role assigned to Asp137 is transient and that electrostatic changes can be important in understanding the enzyme activity data of mutations in KatG. Additionally, molecular docking studies were used to determine the preferred modes of binding of the two substrates. Upon mutation, the apparently less favored docking solution for reaction became the most abundant, suggesting that S315T mutation favors less optimal binding modes. Moreover, the aliphatic tail in INH-C10 seems to bring the hydrazine group closer to the heme, thus favoring the apparent most reactive binding mode, regardless of the enzyme form. The ITC data is in agreement with our interpretation of the C10 alkyl chain role and helped to rationalize the significantly lower experimental MIC value observed for INH-C10. This compound seems to be able to counterbalance most of the conformational restrictions introduced by the mutation, which are thought to be responsible for the decrease in INH activity in the mutated strain. Therefore, INH-C10 appears to be a very promising lead compound for drug development.

Aroylhydrazone Cu(II) complexes in keto form: structural characterization and catalytic cctivity towards cyclohexane oxidation

The reaction of the Schiff base (3,5-di-tert-butyl-2-hydroxybenzylidene)-2-hydroxybenzohydrazide (H3L) with a copper(II) salt of a base of a strong acid, i.e., nitrate, chloride or sulphate, yielded the mononuclear complexes [Cu(H2L)(NO3)(H2O)] (1), [Cu(H2L)Cl]center dot 2MeOH (2) and the binuclear complex [{Cu(H2L)}(2)(mu-SO4)]center dot 2MeOH (3), respectively, with H2L- in the keto form. Compounds 1-3 were characterized by elemental analysis, Infrared (IR) spectroscopy, Electrospray Ionisation-Mass Spectrometry (ESI-MS) and single crystal X-ray crystallography. All compounds act as efficient catalysts towards the peroxidative oxidation of cyclohexane to cyclohexyl hydroperoxide, cyclohexanol and cyclohexanone, under mild conditions. In the presence of an acid promoter, overall yields (based on the alkane) up to 25% and a turnover number (TON) of 250 (TOF of 42 h(-1)) after 6 h, were achieved.