Helmholtz operator with a quaternionic wave number and associated function theory. II. Integral representations

A theory of quaternion-valued hyperholomorphic functions (h.h.f.) is being developed which is closely related to the Maxwell equations for monochromatic electromagnetic fields. The main integral formulas are established, and some boundary-value properties are studied.     

Testing general relativity: Progress,problems, and prospects

Recent results from radar and radio gravity experiments are:

1. Retardation of radar signals: 1.02 +?0.05 (planetary radar), 1.00 +? 0.04 (spacecraft);
2. Deflection of radio waves: 0.99 +? 0.12 (short baseline interferometry), +0.15 1.04 (short baseline interferometry), ?0.10. 0.90 +? 0.05 (short baseline interferometry);
3. Relativistic perihelion advance of Mercury: 0.99 +? 0.03 (planetary radar), 1.00 +? 0.01 (radar plus optical);
4. Time variation of the gravitational constant: (G/G) < 4 ×10^?10/yr (planetary radar). The first three results are expressed as fractions of the corresponding effects predicted by general relativity. In terms of the Eddington-Robertson parameters, the first two are approximately equal to (1+γ)/2 and the third to (2 + 2γ-β)/3. The third result depends on the assumption that the solar gravitational quadrupole moment vanishes; its effects cannot be separated usefully from those of general relativity with the present data set. The uncertainties are as given by the individual experimenters; in some cases they represent formal standard errors, in others an allowance for possible systematic errors is included.

     

Structure determination of some quinazolone lactones

A series of quinazolone lactones were prepared and their structures analyzed by 360 MHz proton and carbon-13 nmr. It was found that the compound capable of lactonization to yield either a six or seven-membered ring forms only the six-membered system.     

Formation of benzoyl ions: A complicated simple cleavage reaction

Charge exchange and electron-impact induced cleavages of some N-phenyl benzamides, phenyl benzoates and benzophenones are reported. The data obtained appear to be consistent with energy being lost from ions by photon emission or stored in isolated states of the molecular ions.     

Wide-angle high-energy proton spectra by 800 MeV/A C,Ne, and Ar beams

Inclusive proton spectra, as well as two-particle correlations, resulting from collisions between energetic nuclei have been measured. Protons associated with large momentum transfers show exponential-type energy distributions having a decay constant about (70–90 MeV)^?1. For light-mass targets a strong two-particle correlation has been observed, which is kinematically consistent with quasi-elastic pp scatterings.     

Quasi-linear theory of multimode free-electron lasers with an inhomogeneous frequency broadening

assuming that the number of excited modes is large and their phases are random a quasi-linear theory of interaction of ultrarelativistic electron beam with the field of a high-quality cavity is developed. The saturation effects in FELs with an inhomogeneous frequency broadening are described. It is shown that in the case of very large excesses over threshold the efficiency of FELs tends to 50% but the emitted energy is distributed in a very wide spectral interval.