Classes of plus matrices in finite dimensional indefinite scalar product spaces

We describe in terms of canonical forms various classes of plus matrices in real and complex finite dimensional spaces with indefinite scalar product and study their topological structures (such as closure and interior).Dedicated to M.G. Kreîn, one of the founding fathers of the theory of plus-operators.The work of this author was performed under the auspices of C.N.R.-G.N.F.M. and partially supported by the research project, Nonlinear problems in analysis and its physical, chemical and biological applications: Analytical, modelling and computational aspects, of the Italian Ministry of Higher Education and Research (M.U.R.S.T.)The work of this author partially supported by the NSF grant DMS 9500924.The work of all authors is partially supported by the NATO grant CGR 960700.     

Pseudo-steady-state solutions for solidification in a wedge

Polubarinova-Kochina's analytical differential equation methodis used to determine the pseudo-steady-state solution to problemsinvolving the freezing (solidification) of wedges of liquidwhich are initially at their fusion temperature. In particular,we consider four distinct problems for wedges which are: freezingwith the same constant boundary temperature, freezing with thesame constant boundary heat fluxes, freezing with distinct constantboundary temperatures and freezing with distinct constant fluxesat the boundaries. For the last two problems, a Heun's differentialequation with an unknown singularity is derived, which in bothcases admits a particularly elegant simple solution for thespecial case when the wedge angle is . The moving boundariesobtained are shown pictorially.     

Separation and quantitation of fatty acids, sterols and bile acids in feces by gas chromatography as the butyl ester-acetate derivatives

A system allowing the separation and quantitation of individual species of fecal fatty acids, sterols and bile acids in a single chromatographic step is described. The system is based on the butylation of carboxyl groups and acetylation of free hydroxyls of the compounds in fecal lipid extracts, followed by their resolution by temperature-programmed gas chromatography. As the butyl ester-acetate derivatives, fatty acids, sterols and bile acids elute separately and with no overlap on a variety of chromatographic columns, obviating the need for prior separation of each class by thin-layer or column chromatography. All common bile acids, a wide variety of sterols and keto-steroids, as well as saturated and unsaturated fatty acids may be routinely resolved. Quantitation is facilitated by the addition of the internal standards, heptadecanoic acid and nor-deoxycholic acid to each sample. With an automatic sample injector, the rapid assessment of a wide range of potential risk factors for colorectal cancer may be carried out in large numbers of samples.     

Stationary transport processes with unbounded collision operators

An abstract Hilbert space equation is studied, which models many of the stationary, one-dimensional transport equations with partial-range boundary conditions. In particular, the collision term may be unbounded and nondissipative. A complete existence and uniqueness theory is presented.     

Empirical scoring functions: I. The development of a fast empirical scoring function to estimate the binding affinity of ligands in receptor complexes

This paper describes the development of a simple empirical scoringfunction designed to estimate the free energy of binding for aprotein–ligand complex when the 3D structure of the complex is knownor can be approximated. The function uses simple contact terms to estimatelipophilic and metal–ligand binding contributions, a simple explicitform for hydrogen bonds and a term which penalises flexibility. Thecoefficients of each term are obtained using a regression based on 82ligand–receptor complexes for which the binding affinity is known. Thefunction reproduces the binding affinity of the complexes with across-validated error of 8.68 kJ/mol. Tests on internal consistency indicatethat the coefficients obtained are stable to changes in the composition ofthe training set. The function is also tested on two test sets containing afurther 20 and 10 complexes, respectively. The deficiencies of this type offunction are discussed and it is compared to approaches by other workers.     

Nonautonomous Exponential Dichotomy

In this note we generalize the strongly continuous bisemigroups generated by exponentially dichotomous operators to so-called bievolution families. These families are then related to strongly continuous bisemigroups on certain Banach spaces of continuous and measurable vector-valued functions. The research leading to this note was supported by the Italian Ministry of Education and Research (MIUR) under PRIN grant no. 2006017542-003, and by INdAM-GNCS.