A sensitivity analysis for linear systems involving M-matrices and its application to the Leontif model

A sensitivity analysis is made for solutions to linear equation systems involving M-matrices. We present a theorem which tells about relative changes of elements of the solution vector when the coefficients of a given M-matrix shift. The Metzler theorem and the Morishima theorem are generalized, and applied to the Leontief model.     

Deposition of coatings on long-period fiber gratings: tunnel effect analogy

The sensitivity of Long-period fiber gratings (LPFGs), coated with high-refractive-index thin film overlays, to the refractive index and the thickness of the overlay, and to the ambient refractive index, can be enhanced with a design based on a two-overlay coating of an LPFG. The first overlay of lower refractive index than the cladding affects the guidance of a cladding mode in the second overlay of higher refractive index than the cladding. This causes a more abrupt cladding modal redistribution than with the deposition of a unique high-refractive-index overlay. The phenomenon is analyzed with a method based on a vectorial analysis of modes and the application of coupled mode theory.     

Atom based parametrization for a conformationally dependent hydrophobic index

An atomic parametrization for the determination of a hydrophobicity index that depends on the molecular conformation is presented. The hydrophobicity parameter was calculated in four alternative ways based on charge densities and atomic contributions to the total molecular surface area and depending on the approach, the molecular dipole moment. The geometries required for the computations were calculated using quantum mechanical semiempirical methods as well as molecular mechanics. The charges were computed using semiempirical methods as well as the Gasteiger method.     

Calculations of heat of solvation by a simple electrostatic approach to molecular interactions

An extremely simple formula to estimate the heat of formation of complexes between anion and a polar molecule or between highly polar systems is presented.The formula is entirelyelectrostatic and the expression used is verified by means of perturbation theory.This formula is test-ed for several ion-molecule and molecule-molecule pairs.It is also applied to estimate the heat ofhydration of simple salts.     

Highly stereoselective radical cyclization of haloacetals controlled by the acetal center

A systematic investigation of radical haloacetal cyclizations (Ueno-Stork reaction) where the acetal center is the unique stereogenic element is reported. This highly diastereoselective reaction can be used for the preparation of polysubstituted tetrahydrofurans and gamma-lactones. We report herein the full experimental details of reactions where up to three new chiral centers are created. To demonstrate the potential of this approach, short syntheses of (+)-eldanolide and of tricyclic acetals related to biologically active lignans have been achieved.