The magnetic moment of composite leptons and quarks

We show that for a composite fermion of sufficiently small radius, the magnetic moment approaches the Dirac value corresponding to the overall charge and mass, regardless of the constituent values. This resolves a recently suggested difficulty in composite models of leptons and quarks.     

Studies in the eburnane series: a new dimerization process

The behaviour of the synthetic (−)-16-(aminomethyl)eburnamenine (prepared from apovincamine) with formaldehyde was studied. Carrying out the reaction in acetic acid led to an original dimer, while in trifluoroacetic acid a 12-functionalized eburnamonine was isolated.     

Influence of fine structure on the pyrolysis of cellulose. III. The influence of orientation

The effects of orientation upon the pyrolysis of cellulose were investigated by using a series of rayon fibers which differed only in orientation. The initial weight loss seen in low-temperature vacuum pyrolysis is due to crosslinking in the less ordered regions and was shown to be a first-order reaction whose rate varies directly with the degree of orientation. The extent of this reaction decreases with increasing orientation and is directly related to the amount of char formed at higher temperatures. The bulk pyrolysis rate increases with increasing orientation. DSC, air pyrolysis rates, and levoglucosan formation were also studied.     

The consistency with CH of some consequences of Martin’s axiom plus2^{\aleph _0 } > \aleph _1

We present here a (weak) axiom which implies some of the consequences of MA, but is consistent with GCH. We use the method of Jensen in his proof of consis (ZFC+GCH+SH). The third author wishes to thank the United States—Israel Binational Foundation for partially supporting this research by Grant 1110.     

Uranium oligomerization in chloride-based high temperature melts: in situ XAS studies

In situ EXAFS spectroscopic studies of uranium compounds in high temperature alkali chloride melts indicate the presence of oligomeric species. An investigation into UCl(3) and UCl(4) dissolved in LiCl reveals long range ordering of uranium atoms in the molten state which is not maintained on quenching. Studies of uranium dioxide dissolved in LiCl-KCl eutectic with HCl exhibit long range ordering in both molten and quenched states, and the EXAFS data can be modeled using multiple coordination shells.     

The bang-bang-bang problem revisited

The solution given by Isaacs to the bang-bang-bang problem is shown to be a solution in aweak sense only. A solution in a stronger sense is demonstrated involving the notions of extended closed-loop strategies and of extended value-function. The bang-bang-bang singular surface is interpreted in a new way.The author is grateful to Professor J. V. Breakwell for his criticism and valuable remarks.     

The Budan-Fourier theorem for splines

The Budan-Fourier theorem for polynomials connects the number of zeros in an interval with the number of sign changes in the sequence of successive derivatives evaluated at the end-points. An extension is offered to splines with knots of arbitrary multiplicities, in which case the connection involves the number of zeros of the highest derivative. The theorem yields bounds on the number of zeros of splines and is a valuable tool in spline interpolation and approximation with boundary conditions.