Solution of a Duffing-harmonic oscillator by the method of harmonic balance

The first-order harmonic balance method via first Fourier coefficient is used to construct an approximate frequency-amplitude relation for a Duffing-harmonic oscillator. This relation is in agreement with the result obtained by the Ritz procedure.     

Structural studies of Cr-doped mullite derived from single-phase precursors

Cr-doped mullites were prepared from single-phase precursors containing up to 9.60 wt% Cr₂O₃ using a sol-gel technique followed by thermal treatment. Particle induced X-ray emission spectroscopy and X-ray powder diffraction were used to characterize the samples. Mullites were orthorhombic, space group Pbam. Cr doping caused the increase of unit-cell parameters. Strongest expansion was noticed along c-axis followed by a and b (Δc/c=0.089, Δa/a=0.061, Δb/b=0.045% per mole Cr₂O₃). A second phase, namely θ-(Al,Cr)₂O₃, was revealed by XRD in the sample containing 9.60 wt% Cr₂O₃. The structure of mullites was refined by the Rietveld method, location of Cr³⁺ was performed by the EPR spectroscopy. At low chromium doping level (Cr₂O₃ content less than ∼5 wt%) Cr³⁺ ions were substituted for Al³⁺ in the AlO₆ octahedra of the mullite structure (M1 site). For higher doping level, Cr³⁺ ions were additionally substituted for Al³⁺ in the AlO₆ octahedra of the second phase [θ-(Al,Cr)₂O₃ at 1400 °C, or α-(Al,Cr)₂O₃ at 1600 °C] which segregated in the system. Substitution of Cr³⁺ for Al³⁺ on M1 site in the mullite structure resulted in increase of average distances in (M1)O₆ octahedron and decrease of average distances in T*O₄ tetrahedron, while average distances in TO₄ tetrahedron stayed almost constant.     

Studies on cardiac ingredients of plants. VII: Chemical transformation of proscillaridin by means of the Diels-Alder reaction and biological activities of its derivatives.

The Diels-Alder reactions of a cardiac glycoside, proscillaridin (1), with some dienophiles were investigated. The reaction of 1 with alkenes such as methyl vinyl ketone and methyl acrylate afforded 3-oxo-2-oxabicyclo[2.2.2]oct-7-enes (2-5) and para-substituted benzene derivatives (6 and 7), while 1 reacted with alkynes (3-butyn-2-one, methyl propiolate) to yield para- or meta-substituted benzene derivatives (6-9). The biological activities of the resulting derivatives were evaluated by the use of isolated guinea-pig papillary muscle preparations and Na+,K(+)-adenosine triphosphatase (ATPase) preparation from dog kidney. Among the proscillaridin derivatives, compounds 4 and 7 moderately inhibited Na+,K(+)-ATPase activity. Furthermore, the concentration range of 7 over which its positive inotropic effect on guinea-pig papillary muscle preparations, increased from 5% to 95% of maximum was broader than that of 1, i.e., concentration dependency was maintained over a greater range of concentration.     

Idempotents in compact semigroups and Ramsey theory

We prove a theorem about idempotents in compact semigroups. This theorem gives a new proof of van der Waerden’s theorem on arithmetic progressions as well as the Hales-Jewett theorem. It also gives an infinitary version of the Hales-Jewett theorem which includes results of T. J. Carlson and S. G. Simpson. Research supported by the National Science Foundation under Grant No. DMS86-05098.     

A novel method for the preparation of T3 free plasma/serum for routine RIA

A novel method to eliminate T₃ from gross sera/plasma based on prior treatment with 8-anilino-1-naphthalene sulphonic acid has been standardized. This method is rapid with a minimum loss of protein and uses only small quantities of charcoal. The treated sera have been tested for acceptance in the RIA system for routine assays.     

Influence of internal degrees of freedom on the structure of one-dimensional systems

Summary The influence of internal degrees of freedom on the behaviour of one-dimensional systems is discussed. For systems with half-filled bands the coupling to internalviz. lattice coordinates decides whether Peierls distortion is caused by intramonomer coordinates or by a lattice coordinate. Thereby the various intramonomer degrees of freedom act cooperatively. We show that there is a small regime of parameters where both kinds of distortion exist simultaneously. For increasing temperature we find that distortions can also move from the lattice coordinate to the intramonomer coordinate.