Why define atoms in real space?

The physics of a system is determined by a variation of the action integral, i.e., by a variation of the space–time volume integral of the Lagrange function. If one demands that the properties of an atom in a molecule be derived from physics, the atom must generate its own space–time volume, requiring that its boundaries be defined in real space. The variations in the action are related to the actions of generators of infinitesimal unitary transformations. In the general case, the action integral is altered by generators acting in both the spacelike and timelike surface bounding the space–time volume, whereas for a total isolated system, the physics is totally determined by their action in just the spacelike surfaces at the two time endpoints. It is shown and illustrated for a one-dimensional system that the definition of an atom corresponds to the possibility of choosing a subsystem in such a way that the contributions to the change in action resulting from the evolution in time of its spatial boundaries vanishes identically. The properties of these subsystems and of the total system of which they are a part are, therefore, determined by one and the same action principle. This choice of subsystem corresponds to the possibility of augmenting the Lagrange function by the divergence of the gradient of the electron density a step that, while leaving the equations of motion unchanged, modifies the generating operators in the required manner. © 1994 John Wiley & Sons, Inc.     

Synthesis and Reactions of Some New Pyrrolylfuro[2,3‐d]Pyrimidines and Pyrrolopyrazinofuropyrimidines

5‐Amino‐4‐methyl‐2‐phenyl‐6‐substitutedfuro[2,3‐d]pyrimidines ( 2a‐c ) were reacted with 2,5‐dimethoxytetrahydrfuran to afford the pyrrolyl derivatives 3a‐c . Compound 3a was chosen as intermediate for the synthesis of poly fused heterocycles incorporated furopyrimidines moiety 4–11 . Some of the synthesized compounds were screened for their antibacterial and antifungal activities.     

Magnetic charge type equations from torsion

It is shown that torsion can be built from two independent vector fields, and that these vector fields obey, for the Lagrangian chosen, the equations of electromagnetism with magnetic charge from the two photon formalism. The equation of motion follows from the Bianchi identity ofU ₄ spacetime, and finally the interpretation of these fields is discussed.     

Angular self-intersections for closed geodesics on surfaces

In this note we consider asymptotic results for self-intersections of closed geodesics on surfaces for which the angle of the intersection occurs in a given arc. We do this by extending Bonahon's definition of intersection forms for surfaces.

     

Three New Polyoxygenated Steroids from Two Species of the South China Sea Gorgonian Muricella flexuosa and Menella verrucosa Brundin

Three new polyoxygenated steroids, muricesteroid ( 1 ), and menellsteroids A ( 2 ) and B ( 3 ), were isolated from two species of the South China Sea gorgonian Muricella flexuosa and Menella verrucosa Brundin , respectively. The structures of these new compounds were elucidated on the basis of extensive spectroscopic analysis, chemical methods and comparison with known related compounds.