Duality-invariant orthogonality relation between the magnetic monopole and associated quark charges

Duality invariance of the Dirac-Schwinger charge-symmetric theory for electromagnetism leads one to consider the complex-valued amplitudes ₁ and ₂ for the separation between the magnetic monopole and quarks in the logarithmic charge plane. It is observed that the orthogonality relation on the latter amplitudes, Re( ₁ ^* ₂)=0, is equivalent to the equation (ln 9 ^–1)(ln 2)=(1/2) ², which is indeed satisfied by the experimental value fora to within 0.027%. In addition to fixing the unit of electric charge at a primary physical value, the orientation of ₁, ₂ may also prescribe the Cabibbo angle to have the theoretical value 12.4438.     

Synergism in the spreading of hydrocarbon-chain surfactants on polyethylene film-anionic and cationic mixtures by a two-step procedure

A study has been made of the adsorption, interaction, and spreading of mixtures of anionic and cationic surfactants at the aqueous solution/polyethylene (PE) interface. When a drop of an aqueous solution of an anionic or cationic hydrocarbon-chain surfactant is placed on a highly hydrophobic PE film (contact angle of water > 90 degrees ), it spreads to an area very little larger than that of a drop of water of the same volume. If the anionic and cationic hydrocarbon-chain surfactant solutions are mixed prior to being applied to PE film, synergism is small, if any, and the reproducibility of the experimental results is poor. However, when the cationic and anionic aqueous solutions are applied on the PE film in a sequential manner, a remarkable synergism in spreading is observed and the results are very reproducible. The area spread by an aqueous solution of the anionic-cationic mixture may be more than 400 times that of aqueous solutions of the same volume and surfactant concentration of the individual surfactant components. Previous work in this laboratory on surfactant systems showing synergism in spreading on PE film, but only weak interaction at the aqueous solution/air interface, showed that the synergy was due to changes at the aqueous solution/PE interface and not to the changes at the aqueous solution/air or PE/air interface. Investigation of the adsorption behavior at the aqueous solution/solid interface of two of the anionic-cationic mixtures studied here indicates the reason for differences in spreading behavior observed with different anionic-cationic mixtures. The more similar the adsorption tendencies at the solid/aqueous solution interface of the anionic and cationic surfactants, and the closer their adsorption to an equimolar monolayer there, the stronger their interaction there and the greater their enhancement of the spreading. A mechanism is proposed for the synergy in spreading observed, based upon the difference between the surface tension in the precursor film at the spreading interface and that at the top of the spreading drop.     

Structural determination of ascorbic acid 2-o-phosphate formed via acid hydrolysis of an ascorbic acid 3-O-phosphinate

The synthesis and X-ray structural determination of 3-O-[(bis-morpholino)phosphinyl]-5,6-O-isopropylidene-l-ascorbate (9) are described. Acid-catalyzed hydrolysis of 9 afforded the 2-O-phosphate 6. Definitive structural proof of 6 is based on a study of the pH profile of its UV spectra as compared with those of ascorbic esters, 2 and 9 (Figs. 1–3).     

Bimetric general relativity and cosmology

A modification of the general relativity theory is proposed (bimetric general relativity) in which, in addition to the usual metric tensorg _v describing the space-time geometry and gravitation, there exists also a background metric tensor _v The latter describes the space-time of the universe if no matter were present and is taken to correspond to a space-time of constant curvature with positive spatial curvature (k=1). Field equations are obtained, and these agree with the Einstein equations for systems that are small compared to the size of the universe, such as the solar system. Energy considerations lead to a generalized form of the De Donder condition. One can set up simple isotropic closed models of the universe which first contract and then expand without going through a singular state. It is suggested that the maximum density of the universe was of the order ofc ^{5 –1} G ^–210⁹³ g/cm³. The expansion from such a high-density state is similar to that from the singular state (big bang) of the general relativity models. In the case of the dust-filled model one can fit the parameters to present cosmological data. Using the radiation-filled model to describe the early history of the universe, one can account for the cosmic abundance of helium and other light elements in the same way as in ordinary general relativity.     

Synthesis of a selective estrogen receptor β-modulator via asymmetric phase-transfer catalysis

An efficient asymmetric synthesis of selective estrogen receptor β-modulator (S)-4-bromo-9a-butyl-8-chloro-6-fluoro-7-hydroxy-1,2,9,9a-tetrahydro-fluoren-3-one was developed. The route features a chemoselective aromatic chlorination reaction, an asymmetric phase-transfer-catalyzed alkylation of an indanone with efficient ee upgrade by racemate crystallization, and a robust bromination reaction using imidazole as an in situ bromine trap to avoid overreaction. The synthesis proceeds in 34% yield over 8 steps from 2-fluoroanisole, and provides material with >99.5% ee.     

Weyl's geometry and physics

It is proposed to remove the difficulty of nonitegrability of length in the Weyl geometry by modifying the law of parallel displacement and using standard vectors. The field equations are derived from a variational principle slightly different from that of Dirac and involving a parameter . For =0 one has the electromagnetic field. For <0 there is a vector meson field. This could be the electromagnetic field with finite-mass photons, or it could be a meson field providing the missing mass of the universe. In cosmological models the two natural gauges are the Einstein gauge and the cosmic gauge. With the latter the universe has a fixed size, but the sizes of small systems decrease with time and their masses and energies increase, thus producing the Hubble effect. The field of a particle in this gauge is investigated, and it leads to an interesting solution of the Einstein equations that raises a question about the Schwarzschild solution.