Approximating weak Chebyshev subspaces by Chebyshev subspaces

We examine to what extent finite-dimensional spaces defined on locally compact subsets of the line and possessing various weak Chebyshev properties (involving sign changes, zeros, alternation of best approximations, and peak points) can be uniformly approximated by a sequence of spaces having related properties.     

FLUORESCENCE SPECTRAL CHANGES OF HEMATOPORPHYRIN DERIVATIVE UPON BINDING TO LIPID VESICLES, Staphylococcus aureus AND Escherichia coli CELLS

Abstract— The binding of hematoporphyrin derivated (Hpd) to lipid vesicles and bacterial membranes was determined by fluorescence spectroscopy. The fluorescence measurements of Hpd in aqueous solutions showed two bands at 613 and 677 nm. In lipid environments of lecithin vesicles the fluorescence spectrum was shifted to 631 and 692 nm, respectively. Hpd was rapidly bound to the cell membrane of Staphylococcus aureus while much less binding occurred in the presence of Escherichia coli. At the same time, spheroplasts of both bacteria were shown to bind Hpd to a similar extent. These results are well correlated with the photoinactivation of the gram positive bacteria with Hpd while the gram negative cells were shown to be resistant. The pH dependence of both Hpd binding to S. aureus as well as the photodynamic inhibitory effect of the same bacteria are similar. It is concluded that the segregation of Hpd to the cell membrane is a prerequisite for its photodynamic effect.     

Gas-phase acidities of disubstituted methanes and of enols of carboxamides substituted by electron-withdrawing groups

The gas-phase acidities DeltaG degrees (acid) of some 20 amides/enols of amides RNHCOCHYY'/RNHC(OH)=CYY' [R = Ph, i-Pr; Y, Y' = CO(2)R', CO(2)R' ', or CN, CO(2)R', R', R' ' = Me, CH(2)CF(3), CH(CF(3))(2)], the N-Ph and N-Pr-i amides of Meldrum's acid, 1,3-cyclopentanedione, dimedone, and 1,3-indanedione, and some N-p-BrC(6)H(4) derivatives and of nine CH(2)YY' (Y, Y' = CN, CO(2)R', CO(2)R' '), including the cyclic carbon acids listed above, were determined by ICR. The acidities were calculated at the B3LYP/6-31+G//B3LYP/6-31+G level for both the enol and the amide species or for the carbon acid and the enol on the CO in the CH(2)YY' series. For 12 of the compounds, calculations were also conducted with the larger base sets 6-311+G and G-311+G. The DeltaG degrees (acid) values changed from 341.3 kcal/mol for CH(2)(CO(2)Me)(2) to 301.0 kcal/mol for PhNHC(OH)=C(CN)CH(CF(3))(2). The acidities increased for combinations of Y and Y' based on the order CO(2)Me < CO(2)CH(2)CF(3) < CN, CO(2)CH(CF(3))(2) for a single group and reflect the increased electron-withdrawal ability of Y,Y' coupled with the ability to achieve planarity of the crowded anion. The acidities of corresponding YY'-substituted systems follow the order N-Ph enols > N-Pr-i enols > CH(2)YY'. Better linear relationships between DeltaG degrees (acid) values calculated for the enols and the observed values than those for the values calculated for the amides suggest that the ionization site is the enolic O-H of most of the noncyclic trisubstituted methanes. The experimental DeltaG degrees (acid) value for Meldrum's acid matches the recently reported calculated value. The calculated structures and natural charges of all species are given, and the changes occurring in them on ionization are discussed. Correlations between the DeltaG degrees (acid) values and the pK(enol) values, which are linear for the trisubstituted methanes, excluding YY' = (CN)(2) and nonlinear for the CH(2)YY' systems, are discussed.     

Uniform solution for uniform polyhedra

An arbitrary precision solution of uniform polyhedra and their duals is presented. The solution is uniform for all polyhedra given by their kaleidoscopic construction, with no need to examine each polyhedron separately.In memoriam of my father, Gershon Har'El, who introduced me to spatial structures.     

Photoinduced intramolecular charge transfer in 4-(dimethyl)aminobenzonitrile--a theoretical perspective

Recent advances in time-dependent density functional theory (TDDFT) have led to computational methods that can predict properties of photoexcited molecules with satisfactory accuracy at comparably moderate cost. We apply these methods to study the photophysics and photochemistry of 4-(dimethyl)aminobenzonitrile (DMABN). DMABN is considered the paradigm of photoinduced intramolecular charge transfer (ICT), leading to dual fluorescence in polar solvents. By comparison of calculated emission energies, dipole moments, and vibrational frequencies with recent results from transient spectroscopy measurements, a definitive assignment of the electronic and geometric structure of the two lowest singlet excited states of DMABN is possible for the first time. We investigate the mechanism of the ICT reaction by means of minimum energy path calculations. The results confirm existing state-crossing models of dual fluorescence. Our study suggests that analytical TDDFT derivative methods will be useful to predict and classify emissive properties of other donor-acceptor systems as well.     

PHOTOINDUCED DEGRADATION AND MODIFICATION OF PHOTOFRIN II IN CELLS in vitro

Abstract— Human cells of the line NHIK 3025 were incubated with Photofrin II (PII) and exposed to light. Fluorescence- and absorption spectra of PII in the cells were measured. Light exposure resulted in a degradation of PII in the cells and changes in the shape of the fluorescence spectra. These changes are probably partly due to a photochemical modification of PII and to a relocalization of PII in the cells. Notably, a destruction of binding sites for PII on or close to proteins was caused by the light exposure. The rate of the light-induced decay of the porphyrin fluorescence intensity was only slightly increasing with the PII concentration, indicating that each porphyrin molecule is mainly degraded by photoproducts originating from itself. On the other hand, the rate of the degradation of porphyrin binding sites on the proteins increased with increasing PII concentrations.
The excitation spectrum of PII in cells has a peak at285–290 nm attributed to energy transfer from proteins to porphyrins located close to the proteins. The intensity of this peak relative to the intensity of the Soret band increases with decreasing porphyrin concentrations. This might indicate that some of the binding sites close to proteins have a higher affinity for the porphyrin than binding sites at longer distances from the proteins.     

On approximation and computation of modified Bessel functions of complex order

Easy-to-compute approximations of modified Bessel functions for any complex order are found. The case of two second-order differential equations with polynomial coefficients is considered. For approximately solving them, a scheme based on canonical vector-polynomials introduced by the author is proposed. The functions under consideration are of significant interest in light of the introduction of a new class of Yakubovich integral transforms.     

A variational problem determined by probability measures

ABSTRACT

An optimization problem of maximizing an integral of a function over a family of probability measures is considered. The problem is a generalization of a well-studied variational problem in mathematical economics, concerning optimal allocations. The specific generalization that we examine arises also in the limit of singularly perturbed optimal control problems. We examine the mathematical problem and allude to the singular perturbation motivation.     

Twist impeded self-diffusion in a cholesteric

Molecular self-diffusion along the pitch axis of a twisted nematic is measured by its motional averaging effect on the deuterium quadrupole interaction. The diffusion constant is found to decrease as the pitch length is decreased. This result is explained by simple phenomenological considerations and is consistent with published viscosity measurements.