An Improved Model for Predicting Proton NMR Shielding by Alkenes Based on Ab Initio GIAO Calculations

In a strong magnetic field, nuclei located over a carbon-carbon double bond experience NMR shielding effects that are the net result of the magnetic anisotropy of the nearby double bond and various other intramolecular shielding effects. We have used GIAO, a subroutine in Gaussian 4, to calculate isotropic shielding values and to predict the proton NMR shielding increment for a simple model system: methane held in various orientations and positions over ethene. The average proton NMR shielding increments of several orientations of methane have been plotted versus the Cartesian coordinates of the methane protons relative to the center of ethene. A single empirical equation for predicting the NMR shielding experienced by protons over a carbon-carbon double bond has been developed from these data. The predictive capability of this equation has been validated by comparing the shielding increments for several alkenes calculated using our equation to the experimentally observed shielding increments. This equation predicts the NMR shielding effects more accurately than a previous model that was based on only one orientation of methane over ethene. Deshielding is predicted by this equation for protons over the center and within about 3 Å of a carbon-carbon double bond. This result is in contrast to predictions made by the long-held shielding cone model based on the McConnell equation found in nearly every textbook on NMR, but is consistent with experimental observations.     

Crystal and molecular structure of aN(2)-benzyl-1,3-disubstituted-1,2,3,4-tetrahydro-β-carboline

(1R,3S)-2-Benzyl-3-methoxycarbonyl-1-methylcarboxymethyl-1,2,3,4-tetrahydro-9H-pyrido [3,4-b] indole, C₂₃H₂₄N₂O₄, was synthesized by a modified Pictet-Spengler reaction, and its crystal and molecular structure determined by single crystal X-ray diffraction methods. The crystals are monoclinic:P2₁ (No. 4),a=11.336(1),b=8.919(1),c=10.314(1)Å,=100.81(1)°,Z=2. The structure has been solved by direct methods, and refined toR=0.041 for 2203 observed reflections. The six-membered heterocyclic ring is in a half-chair conformation, and the substituents at C(3) and C(5) occupy axial and equatorial positions respectively. The CH₂Ph group attached to N(4) is in the generally less favoured axial position. The nitrogen atom of the indole system forms an intermolecular hydrogen bond with the carbonyl oxygen of the CH₂CO₂ Me group, the NO distance being 2.995(3)Å.     

Measurement of the flux of ultrahigh energy cosmic rays from monocular observations by the High Resolution Fly's Eye experiment

We have measured the cosmic ray spectrum above 10(17.2) eV using the two air-fluorescence detectors of the High Resolution Fly's Eye observatory operating in monocular mode. We describe the detector, phototube, and atmospheric calibrations, as well as the analysis techniques for the two detectors. We fit the spectrum to a model consisting of galactic and extragalactic sources.     

The asymptotic number of integer stochastic matrices

Let Hⁿ_r be the number of n × n matrices, with nonnegative integer elements, all of whose row and column sums are equal to some prescribed integer r. Similarly, let Aⁿ_r be the number of n × n (0.1) matrices with common row and column sum r. An asymptotic formula for Hⁿ_r is stated and proved, the method of proof being essentially elementary. A simple modification of the proof yields an analogous asymptotic formula for Aⁿ_r. The latter agrees with a result of O'Neil, obtained by a completely different method.     

Deux groupes finis distincts ayant la même algèbre de groupe sur tout corps

Sans résumé     

Author index to volume 44B

Evidence is presented to show that the gross features of the pion distributions in $\text{p}$p and $\text{e}$e annihilation are essentially the same.     

A mathematical model for nonlinear analysis of flow pulses utilizing an integral technique

An existing one-dimensional mathematical model, for the arterial tree was extended to include the effects of radial variation of axial fluid velocity by the application of an integral technique. The resulting formulation reduced to a system of characteristics equations similar, in form to the equations for the onedimensional model and the computer program was modified to accommodate the integral formulation. The need for a kinematic boundary condition on the axial component of wall velocity was demonstrated. Results were obtained for a variety of velocity profiles. It was found that the slope of the front and back of the waves as well as the wave, amplitude are sensitive to changes in the velocity profile and the axial component of wall velocity. The velocity of the waves is also effected but not significantly.

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Zusammenfassung Die eindimensionale Theorie von Anliker et al. (ZAMP22, 217 (1971)) wird in dieser Arbeit dahingehend erweitert, dass der Einfluss des Geschwindigkeitsprofiles mitberücksichtigt wird. Die Navier-Stokes-Gleichungen und die Kontinuitätsgleichung werden mit Hilfe einer Integraltechnik auf ähnliche, für die Rechnung mit dem Computer geeignete Gleichungen zurückgeführt, wie sie von Anliker et al. verwendet wurden. Die charakteristischen Grössen des Geschwindigkeitsprofiles sowie die Geschwindigkeit der Gefässwand gehen als Parameter in die Theorie ein, so dass parametrische Studien durchgeführt werden können.

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Nomenclature a local internal radius of the vessel - a _f , A _f constants in the cosine profile - b defined by equation (22) - local normal and tangential unit vectors (see Figure 1) - f(r/a), g (z,t) defined by equation (9) - f _R friction factor - local mass flux into the vessel - p local pressure - p _c capillary pressure - p _o pressure at the terminal end - r, z radial and axial coordinates - S local cross sectional area - t time - flow velocity at the wall interface - u, v, w radial, circumferential and axial components of flow velocity - u _w , v _w , w _w radial, circumferential and axial components of flow velocity at the wall interface - wall velocity at the interface - U _w , W _w radial and axial components of wall velocity at the interface - W mass average flow velocity defined by equation (13) - w _o maximum flow velocity - ₀, ₁, ₂, ₃ parameters defined by equation (10) - ₄ W _w /w _w - _A , _B , _C parameters defined by equation (18) - outflow parameter - wave length - _L Lagrangian multiplier - viscosity coefficient for the fluid - density of the fluid - kinematic viscosity - ()' nondimensional quantity of order one - ()₊, ()_– values of () associated with roots of equation (23) This analysis was initiated during the authors appointment as a NASA-ASEE Summer Faculty Fellow to the Stanford-Ames Program and completed through the facilities of the Computer Science Center at the University of Maryland.