Über zwei Sätze des Herrn G. H. Hardy

Ohne Zusammenfassung     

Continuous proportion relations and functions

Continuous proportion functions in three or more dimensions are classical.Dedicated to Helmut Salzmann on the occasion of his 60th birthday     

Adenine and thymine grafts on polyethyleneimine

Graft polymers of three different molecular weights of polyethyleneimine (PEI) with 9-(vinylsulfonylethyl) (9-VSE)-adenine and 1-(vinylsulfonylethyl) (1-VSE)-thymine were prepared. PEI's having molecular weights of 600, 1200, and 1800 were used and various ratios of VSE-nucleobases to ethyleneimine were employed in the grafting process. As expected, a decrease in the nucleobase substitution in the resulting graft polymer resulted in an increase in its water solubility. The degree of substitution in the graft polymers was calculated from sulfur determinations: in most cases this degree of substitution indicated that not all of the VSE derivative has reacted with the PEI due to the highly branched nature of the latter. The presence of nucleobase stacking in the polymers was studied by UV spectroscopy. Stacking was observed for the adenine polymers in both DMSO and 0.1N HCl while stacking in the thymine polymers was observed in 0.1N HCl but not in DMSO. The absence of stackingwithin the thymine polymers in DMSO was attributed to complexation of primary amino groups of the PEI backbone with the pyrimidine ring.     

Radiative spectra of thermal electromagnetic noise induced by planar realistic dielectrics

Spectral characteristics of stochastic fields and their spatial derivatives in various planar structures composed by lossy materials described by realistic dielectric functions are numerically calculated based on solutions to the problems of multipolar electromagnetic fields in a plane layered geometry. A displacement of the maximum of the spectral power densities for spatial derivatives of fluctuating fields to the high-frequency domain, a resonant increase in the density of states of the fluctuating fields at the frequencies of interface excitations and interference modes for the radiative part of the spectra, the influence of geometry on the density of states, and other peculiarities are found by numerical calculations and graphically demonstrated. Interpretations of the above effects are provided.     

George B. Dantzig and systems optimization

We pay homage to George B. Dantzig by describing a less well-known part of his legacy–his early and dedicated championship of the importance of systems optimization in solving complex real-world problems.     

Die Identität des Cesàroschen und Hölderschen Grenzwertes

Ohne Zusammenfassung     

Über einige Azine und Chinondiazide der Anthrachinonreihe

Ohne ZusammenfassungVorgelegt in der Sitzung am 12. Oktober 1911.