Zinc porphyrin tweezer in host-guest complexation: determination of absolute configurations of primary monoamines by circular dichroism

A nonempirical exciton chirality circular dichroic (CD) method for determining the absolute configurations of primary monoamines with amino group directly linked to the stereogenic center is described. Conventional exciton chirality CD method cannot be applied to these compounds since they lack the two sites for attaching the interacting chromophores. This was solved by covalently linking the monoamine to a trifunctional bidentate carrier moiety 1. Treatment of the carrier/monoamine conjugate with the porphyrin tweezer 4 consisting of two pentanediol-linked zinc porphyrins gives rise to 1:1 host-guest macrocyclic complexes that exhibit exciton-coupled CD spectra. The sign of the CD couplet can then be correlated with the absolute configuration of the monoamine as follows: a clockwise arrangement of the L, M, and S (large, medium, small) groups in the Newman projection of the monoamine with the amino group in the rear gives rise to a positive CD couplet, and vice versa; the assignments of L, M, S groups are based on conformational energies (A values). This method is applicable to cyclic and acyclic aliphatic amines, aromatic amines, amino esters, amides, and cyclic amino alcohols, and can be performed at the several microgram level.     

Computations on the growth of the first factor for prime cyclotomic fields II

It is shown by computing thath(p) — the first factor of the class number of the prime cyclotomic fieldk(exp(2i/p)) — is strictly increasing for 19p1097.     

Normal Auger spectra of Br in alkali bromide molecules

Molecular Auger electron spectra following the bromine 3d ionization in gas-phase alkali bromides and in HBr were studied both experimentally and theoretically. The AES for HBr and CsBr were measured using photoexcitation, and for LiBr, NaBr, and KBr by using electron impact. These results are compared with the theoretical spectra from nonrelativistic ab initio calculations and one-center approximation and with the spectra of Br(-), computed with the multiconfiguration Dirac-Fock method.     

A Phragmén — Lindelöf principle for subsolutions of quasi — linear equations

Quasi — linear elliptic equations of homogeneous type are studied in this paper. The equation satisfies uniform ellipticity and growth conditions. A Phragmén — Lindelöf principle is proved by a combined technique of Ladyenskaya-Ural'ceva and Moser. This technique makes it possible to estimate the growth of the maximum modulus of a subsolution in general unbounded domains.     

Chaos in the one-dimensional gravitational three-body problem

We have investigated the appearance of chaos in the one-dimensional Newtonian gravitational three-body system (three masses on a line with -1/r pairwise potential). In the center of mass coordinates this system has two degrees of freedom and can be conveniently studied using Poincare sections. We have concentrated in particular on how the behavior changes when the relative masses of the three bodies change. We consider only the physically more interesting case of negative total energy. For two mass choices we have calculated 18 000 full orbits (with initial states on a 100x180 lattice on the Poincare section) and obtained dwell time distributions. For 105 mass choices we have calculated Poincare maps for 10x18 starting points. Our results show that the Poincare section (and hence the phase space) divides into three well defined regions with orbits of different characteristics: (1) There is a region of fast scattering, with a minimum of pairwise collisions. This region consists of 'scallops' bordering the E=0 line, within a scallop the orbits vary smoothly. The number of the scallops increases as the mass of the central particle decreases. (2) In the chaotic scattering region the interaction times are longer, and both the interaction time and the final state depend sensitively on the starting point on the Poincare section. For both (1) and (2) the initial and final states consist of a binary + single particle. (3) The third region consists of quasiperiodic orbits where the three masses are bound together forever. At the center of the quasiperiodic region there is a periodic orbit discovered (numerically) by Schubart in 1956. The stability of the Schubart orbit turns out to correlate strongly with the global behavior.     

Calculations of millimeter wave depolarization due to melting layer and rain

A model for calculating the total depolarization due to the melting layer and rain is proposed under the assumption that oblate spheroidal melting particles and raindrops have the same orientation. The melting layer is composed of the melting particles which are made up from the mixture of ice, air and water. The specific attenuation and the specific phase shift both for the melting layer and for rain are given in the power lawaR ^b form for the rain rates 0R12.5 mm/h and the parameters are tabled over the frequency range of 1–100 GHz. Using the model, the numerical calculation of the depolarization is possible for three drop size distributions.     

p-Laplacian Inclusions via Fixed Points for Multifunctions in Posets

We consider the Dirichlet problem for elliptic differential inclusions involving the p-Laplacian and governed by multivalued nonlinearities bounded above and below by single-valued monotone functions not necessarily continuous. The aim of this note is to provide existence and comparison results for the problem under consideration without imposing further regularity assumptions. The main tools used in the proof of our results are existence and comparison results for extremal solutions of (single-valued) nonlinear elliptic equations, and an abstract comparison principle for fixed points of multivalued operators in partially ordered sets (posets).     

Midazolam sedation increases fluctuation and synchrony of the resting brain BOLD signal

The blood oxygen level-dependent (BOLD) magnetic resonance signal of functional brain cortices is dominated by very low frequency (VLF) fluctuations in anesthetized child patients. The temporal synchrony of the BOLD signal is also higher in anesthetized children compared with awake adults. The origin of the synchronous fluctuations can be related to maturation, pathological status or the anesthesia used in the imaging. Two of the three confounding variables (maturation and pathology) were controlled in this study. The effect of midazolam (4+/-0.8 mg) sedation on the BOLD signal was assessed in 12 healthy adults (aged 24+/-1.5 years) at 1.5 T. The VLF fluctuation power and temporal synchrony of the BOLD signal increased significantly after the sedation in the auditory and visual cortices. The fast Fourier transformation power spectral baseline fit parameters of the BOLD signal were also found to change significantly after sedation. It is concluded that the VLF fluctuation and temporal synchrony of the BOLD signal become increased after sedation in functional brain regions.