Pythagorean euclidean four point properties

Characterizations of real inner product spaces among a class of metric spaces have been obtained based on homogeneity of metric pythagorean orthogonality, a metrization of the concept of pythagorean orthogonality as defined in normed linear spaces. In the present paper a considerable weakening of this hypothesis is shown to characterize real inner product spaces among complete, convex, externally convex metric spaces, generalizing a result of Kapoor and Prasad [9], and providing a connection with the many characterizations of such spaces using euclidean four point properties.     

Complete assignment of the 1H and 13C NMR Spectra of 11,12-Dimethoxy[1]benzothieno[3,2-a]-4,7-phenanthroline and its 8-Chloro Analogue: Concerted Use of Two-Dimensional NMR Techniques

The ¹H and ¹³C nmr spectra of 11,12-dimethoxy[1]benzothieno[3,2-a]-4,7-phenanthroline and its 8-chloro precursor were totally assigned using a combination of two-dimensional nmr techniques. After correlation of the majority of the proton signals by a COSY spectrum and one-bond heteronuclear correlation, the full assignment of the ¹H and ¹³C nmr spectra of the novel heterocyclic compounds required the application of long-range CH coupling information particularly for quaternary carbon resonance assignments and the orientations of individual spin systems relative to one another. Key long-range heteronuclear couplings in both compounds served to confirm the one-bond heteronuclear correlations. Unequivocal interpretation of the spectral data leads to the complete assignments of the resonances.     

From the Boltzmann equation to the Stokes‐Fourier system in a bounded domain

We prove that the renormalized solutions of the Boltzmann equation considered in a bounded domain with different types of (kinetic) boundary conditions converge to the Stokes‐Fourier system with different types of (fluid) boundary conditions when the main free path goes to zero. This extends the work of F. Golse and D. Levermore [9] to the case of a bounded domain. © 2003 Wiley Periodicals, Inc.     

COSMIC(90): An improved molecular mechanics treatment of hydrocarbons and conjugated systems

Summary Four modifications to the COSMIC molecular mechanics force field are described, which greatly increase both its versatility and the accuracy of calculated conformational energies. The Hill non-bonded van der Waals potential function has been replaced by a two-parameter Morse curve and a new H-H potential, similar to that in MM3, incorporated. Hydrocarbon energies in particular are much improved.A simple iterative Hückel pi-electron molecular orbital calculation allows modelling of conjugated systems. Calculated bond lengths and rotational barriers for a series of conjugated hydrocarbons and nitrogen heterocycles are shown to be as accurate as those determined by the MM2 SCF method.Explicit hydrogen-bonding potentials for H-bond acceptor-donor atom pairs have been included to give better hydrogen bond energies and lengths. The van der Waals radii of protonic hydrogens are reduced to 0.5 Å and the energy well depth is increased to 1.0 kcal mol^-1.Two new general atom types, N⁺ _sp ² and O^- _sp ³ , have been introduced which allow a wide variety of charged conjugated systems to be studied. A minimum of parameterisation is required, as the new types are easily included in the Hückel scheme which automatically adjusts bond and torsional parameters according to the defined bond-order relationships.     

The Spirit Is Willing: Nonlinearity, Bifurcations, and Mental Control

In recent years there has been considerable interest in the construction of nonlinear models of the dynamics of human behavior. In this exploratory article we argue that attempts at controlling problematic thoughts, emotions, or behaviors can lead to nonlinearity in mental/behavioral dynamics. We illustrate our model by fitting threshold autoregression models to self-recorded time series of the daily highs in intensity of anxiety and obsessive ruminations, kept by an individual in therapy for this problem. In our discussion, we raise the possibility that bifurcations that occur in this nonlinear model may offer insight into mental control paradoxes.