Excess in critical graphs

In this paper we prove that the cartesian product of two trees is a semistable graph and we exhibit several vertices of semistability. We show that in most cases the cartesian product of two paths is completely semistable and we list the exceptions. Finally, we characterize stable composite graphs.     

On a singular differential operator

Summary Study of the properties of a singular differential operator in one independent variable. Applications to ordinary and partial differential equations. To Giovanni Sansone on his 70^th birth day. This research was supported by the United States Air Force through the Air Force Office of Scientific Research of the Air Research and Development Command under Contract No. 49 (638)-228.     

Infrared and Raman spectroscopies of InP/II–VI core-shell nanoparticles

We use infrared (IR) and Raman spectroscopies to investigate the optically active phonon modes in InP nanoparticles and InP/II–VI core-shell nanoparticles fabricated by similar colloidal chemistry methods. The IR transmission spectra of several InP nanoparticle samples exhibit a common absorption feature, which we assign to the Fröhlich mode. The Raman results for the same samples show transverse and longitudinal optical phonon peaks, and scattering strength in between due to surface optical (SO) modes. Infrared spectra of the InP/ZnSe core-shell nanoparticles () exhibit three absorption features, one due to the InP core, and the others associated with the ZnSe shell layer. Raman measurements (12–292 K) also show three phonon-related peaks, whose intensities vary sharply with temperature. The frequencies of the IR and Raman lines are in approximate accord with dielectric continuum theory.     

Anomalous optical response with variation in band filling in linear chain conductors

We report the polarized infrared reflectance of ($\text{N}$-methylphenazinium)_x (phenazine)_1-x(tetracyanoquinodimethanide), (NMP)_x(Phen)_1-x(TCNQ) for 0.5≤x≤1.0. We demonstrate that the “Drude edge” in TCNQ salts is related to the conduction electron charge density. An anomalous rapid red shift of the plasma frequency, observed for $\text{x ～}\text{2}\text{3}$, may signal the emptying of the conduction electrons from half of the chains and/or a crossover from small U/W (coulomb repulsion/bandwidth) to large U/W behavior.     

Anwendungen der De Rhamschen Zerlegung auf Probleme der lokalen Flächentheorie

Various questions of classical differential geometry lead to the problem of determining all those hypersurfaces of euclidean space for which the covariant derivative of the second fundamental form vanishes identically. In the first part of this note, we investigate these hypersurfaces; the result is summarized in the theorem of the opening paragraph, whose proof is based in the decomposition theorem of De Rham (see e.g. [6], pp. 180–186). Applying this result in the second part of the note, we give local characterizations of the Euclidean sphere.