A short history of NMR

Published in Khimiya Geterotsiklicheskikh Soedinenii, No. 9, pp.1157–1158, september, 1995.     

Synthesis of LECBD grown cluster assembled SeO2 thin films

Cluster assembled selenium oxide (SeO₂) thin films, as a function of oxygen flow pressure (OFP) have been synthesized by a low energy cluster beam deposition (LECBD) technique. The OFP dependent surface morphology leading to well separated nanoclusters (size ranging from 50 to 200 nm) and fractal features are confirmed from transmission electron microscopic (TEM) measurements. A diffusion limited aggregation (DLA) mediated fractal growth with dimension as 1.71 ± 0.01 has been observed for high OFP (60 mbar). Structural analysis by glancing angle X-ray diffraction (GXRD) and selected area diffraction (SAD) studies identify the presence of tetragonal phase SeO₂ in the deposit. Micro-Raman studies indicate the shifts in bending and stretching vibrational phonon modes in cluster assembled SeO₂ as compared to their bulk counter part due to the phonon confinement effect.     

“Damage” in the low-temperature phase of the ±J spin glass in two to six dimensions

Indentical clones are made of configurations of the ±J spin glass at temperatures near and below the phase transition, and their damage is monitored as a function of temperature and time. Focal points with multiple bifurcations are found occurring near the onset of the phase transition temperature.     

Hopf algebras of set systems

Hopf algebras play a major rôle in such diverse mathematical areas as algebraic topology, formal group theory, and theoretical physics, and they are achieving prominence in combinatorics through the influence of G.-C. Rota and his school. Our primary purpose in this article is to build on work of Schmitt [18,19], and establish combinatorial models for several of the Hopf algebras associated with umbral calculus and formal group laws. In so doing, we incorporate and extend certain invariants of simple graphs such as the umbral chromatic polynomial, and Stanley's [21] recently introduced symmetric function. Our fundamental combinatorial components are finite set systems, together with a versatile generalization in which they are equipped with a group of automorphisms. Interactions with the Roman-Rota umbral calculus over graded rings of scalars which may contain torsion are a significant feature of our presentation.