The dirac-schwinger covariance condition in classical field theory

A straightforward derivation of the Dirac-Schwinger covariance condition is given within the framework of classical field theory. The crucial role of the energy continuity equation in the derivation is pointed out. The origin of higher order derivatives of delta function is traced to the presence of higher order derivatives of canonical coordinates and momenta in the energy density functional.     

Combinatorial geometries representable over GF(3) and GF(q). II. Dowling geometries

Letq be an odd prime power not divisible by 3. In Part I of this series, it was shown that the number of points in a rank-n combinatorial geometry (or simple matroid) representable over GF(3) and GF(q) is at mostn ². In this paper, we show that, with the exception ofn = 3, a rank-n geometry that is representable over GF(3) and GF(q) and contains exactlyn ² points is isomorphic to the rank-n Dowling geometry based on the multiplicative group of GF(3).This research was partially supported by the National Science Foundation under Grants DMS-8521826 and DMS-8500494.     

Sensitivity analysis of oscillatory systems

Methods of sensitivity analysis are extended to find the parametric dependencies of systems of ordinary differential equations which exhibit limit cycle oscillations. The quantitative relations between the system parameters and the observable period, amplitude, phase and cycle shape are developed. These formulae, presented for both the first and second order, are applicable to systems of arbitrary size and complexity. The techniques are used here to develop correlations for period and amplitude in a non-isothermal oscillating stirred-tank chemical reactor, and to find and optimize a beneficial periodic operating strategy for a lumped-parameter catalytic reacting system.     

MRI of hepatic lymphoma

Thirteen patients with biopsy proven hepatic lymphoma (2 Hodgkin, 11 Non-Hodgkin) and a control group of 15 patients with hepatic metastases were analyzed quantitatively and qualitatively by MRI. Focal hepatic lymphoma was most reliably detected (eight of eight patients) and appeared hypointense relative to liver on T₁ weighted (CNR − 7.4 ± 2.3) and hyperintense on T₂ weighted (CNR + 8.4 ± 2.9) images. The mean T₁ and T₂ relaxation times of focal hepatic lymphoma (T₁ = 832 ± 234 msec, T₂ = 84 ± 16 ms) differed significantly from adjacent non-tumorous liver (T₁ = 420 ± 121 ms, T₂ = 51 ± 9 ms; p < 0.05), however CNR values and relaxation times were similar to those of hepatic metastases. Diffuse hepatic lymphoma (microscopic periportal infiltration) was undetectable by MRI in three patients by either morphologic features or quantitative criteria. A mixed pattern of hepatic lymphoma (focal lesions and diffuse infiltration) showed focal areas of slightly decreased signal intensity on T₁ weighted images (CNR = −1.7 ± 0.4) while T₂ weighted images revealed multiple regions of focal hyperintensity (CNR = +13.3 ± 8.4) superimposed on a diffusely hyperintense liver. Our experience demonstrates that either T₁ or T₂ weighted techniques are useful in detecting focal and that T₂ weighted techniques are useful in detecting mixed hepatic lymphoma. Conventional image derived relaxation time measurements and quantitative parameters were of no additional diagnostic value.     

Chemical and electrochemical doping in poly(paraphenylene vinylene) blends

Blends of poly(p-phenylene vinylene) (PPV), with other polymers were made by film-casting from an aqueous mixture of the water-soluble sulfonium salt precursor to PPV and the second polymer. The rates of chemical doping, using As F₅, and of electrochemical doping, using perchlorate counter ion, of the PPV component are strongly influenced by the nature of the added macromolecule. In all cases studied the blends appear to be phase separated under all conditions. The most versatile blend was with poly(ethylene oxide) (PEO), which could be heated to 225°C without degradation and which yielded the highest electrical conductivity when doped. The utility of blends was demonstrated using free-standing PPV/PEO blend samples as rechargeable battery electrodes.     

Mass spectrometric fragmentation patterns of isomeric 5-methyl-3-alkyl-2-alkenylpyrazines

The detailed mass spectral fragmentation pathways of a series of both naturally occurring and synthetic 5-methyl-3-alkyl-2-aIkenylpyrazines have been elucidated with the aid of deuterium labels placed specifically in the alkenyl side-chain. The influence on the fragmentation pattern of the stereochemistry of the alkenyl group as well as the relative placement of the groups on the pyrazine nucleus have also been evaluated. This provides information of some diagnostic value in the assignment of structures by mass spectrometry to new compounds within this class.     

Synthesis and reactions of 2,3-diamino-4(3H)-pyrimidinones and 3-amino-2-hydrazino-4(3H)-pyrimidinones. I

A series of new 2,3-diamino-4-pyrimidinones and 3-amino-2-hydrazino-4-pyrimidinones were synthesized by the reactions of β-ketoesters with amino or diaminoguanidines.     

The application of the sulphide contraction to the synthesis of some simple pyrrolidine alkaloids

The alkaloids (±)-hygrine, (±)-dehydrodarlinine, (±)-dehydrodarlingianine, and (±)-N-methylruspolinone have been synthesised by selective reduction of vinylogous amides formed by sulphide contraction of the salts prepared by reaction of N-methyl-2-thiopyrrolidone with the appropriate bromomethyl ketones.