Slowly rotating drops

We study the existence of gyrostatic equilibria of slowly rotating liquid masses subject only to the force of surface tension. We give a rigorous proof of the existence of non-axisymmetric equilibria. The shape of such an equilibrium approximates a number of spherical lobes connected by thin necks and symmetrically arranged around the axis of rotation.     

Stable mixed moving averages

Summary The class of (non-Gaussian) stable moving average processes is extended by introducing an appropriate joint randomization of the filter function and of the stable noise, leading to stable mixed moving averages. Their distribution determines a certain combination of the filter function and the mixing measure, leading to a generalization of a theorem of Kanter (1973) for usual moving averages. Stable mixed moving averages contain sums of independent stable moving averages, are ergodic and are not harmonizable. Also a class of stable mixed moving averages is constructed with the reflection positivity property.Research supported by AFSOR Contract 91-0030Research also supported by ARO DAAL-91-G-0176Research also supported by AFOSR 90-0168Research also supported by ONR N00014-91-J-0277     

Innovations and Wold decompositions of stable sequences

Summary For symmetric stable sequences, notions of innovation and Wold decomposition are introduced, characterized, and their ramifications in prediction theory are discussed. As the usual covariance orthogonality is inapplicable, the non-symmetric James orthogonality is used. This leads to right and left innovations and Wold decompositions, which are related to regression prediction and least p ^th moment prediction, respectively. Independent innovations and Wold decompositions are also characterized; and several examples illustrating the various decompositions are presented.Research supported by the Air Force Office of Scientific Research Contract F49620 82 C 0009     

Synthesis,Structural and Physicochemical Characterization of a Titanium(IV) Compound with the Hydroxamate Ligand N,2-Dihydroxybenzamide

The siderophore organic ligand N,2-dihydroxybenzamide (H₂dihybe) incorporates the hydroxamate group, in addition to the phenoxy group in the ortho-position and reveals a very rich coordination chemistry with potential applications in medicine, materials, and physical sciences. The reaction of H₂dihybe with TiCl₄ in methyl alcohol and KOH yielded the tetranuclear titanium oxo-cluster (TOC) [Ti^IV₄(μ-O)₂(HOCH₃)₄(μ-Hdihybe)₄(Hdihybe)₄]Cl₄∙10H₂O∙12CH₃OH (1). The titanium compound was characterized by single-crystal X-ray structure analysis, ESI-MS, ¹³C, and ¹H NMR spectroscopy, solid-state and solution UV–Vis, IR vibrational, and luminescence spectroscopies and molecular orbital calculations. The inorganic core Ti₄(μ-O)₂ of 1 constitutes a rare structural motif for discrete Ti^IV₄ oxo-clusters. High-resolution ESI-MS studies of 1 in methyl alcohol revealed the presence of isotopic distribution patterns which can be attributed to the tetranuclear clusters containing the inorganic core {Ti₄(μ-O)₂}. Solid-state IR spectroscopy of 1 showed the presence of an intense band at ~800 cm⁻¹ which is absent in the spectrum of the H₂dihybe and was attributed to the high-energy ν(Ti₂–μ-O) stretching mode. The ν(C=O) in 1 is red-shifted by ~10 cm⁻¹, while the ν(N-O) is blue-shifted by ~20 cm⁻¹ in comparison to H₂dihybe. Density Functional Theory (DFT) calculations reveal that in the experimental and theoretically predicted IR absorbance spectra of the ligand and Ti-complex, the main bands observed in the experimental spectra are also present in the calculated spectra supporting the proposed structural model. ¹H and ¹³C NMR solution (CD₃OD) studies of 1 reveal that it retains its integrity in CD₃OD. The observed NMR changes upon addition of base to a CD₃OD solution of 1, are due to an acid–base equilibrium and not a change in the Ti^IV coordination environment while the decrease in the complex’s lability is due to the improved electron-donating properties which arise from the ligand deprotonation. Luminescence spectroscopic studies of 1 in solution reveal a dual narrow luminescence at different excitation wavelengths. The TOC 1 exhibits a band-gap of 1.98 eV which renders it a promising candidate for photocatalytic investigations.     

inflation from scale invariant supergravity and anomaly free superstrings with fluxes

The scale invariant gravity theory coupled to conformally invariant matter is investigated. We show that in the non‐supersymmetric case the conformally coupled scalars belong to an manifold, while in the supersymmetric case the scalar manifold becomes isomorphic to the Kählerian space =. In both cases when the underlying scale symmetry is preserved the vacuum corresponds to de Sitter space. Once the scale symmetry is broken by quantum effects, a transition to flat space becomes possible. We argue that the scale violating terms are induced by anomalies related to a symmetry. The anomaly is resolved via the gauging of a Peccei‐Quinn axion shift symmetry. The theory describes an inflationary transition from de Sitter to flat Minkowski space, very similar to the Starobinsky inflationary model. The extension to metastable de Sitter superstring vacua is also investigated. The scalar manifold is extended to a much richer manifold, but it contains always as a sub‐manifold. In superstrings the metastability is induced by axions that cure the anomalies in chiral (or even ) supersymmetric vacua via a Green‐Schwarz/Peccei‐Quinn mechanism generalized to four dimensions. We present some typical superstring models and discuss the possible stabilization of the no‐scale modulus.     

Effective Field Theory Description of the Higher Dimensional Quantum Hall Liquid

We derive an effective topological field theory model of the four dimensional quantum Hall liquid state recently constructed by Zhang and Hu. Using a generalization of the flux attachment transformation, the effective field theory can be formulated as a U(1) Chern–Simons theory over the total configuration space CP₃, or as a SU(2) Chern–Simons theory over S⁴. The new quantum Hall liquid supports various types of topological excitations, including the 0-brane (particles), the 2-brane (membranes), and the 4-brane. There is a topological phase interaction among the membranes which generalizes the concept of fractional statistics.     

One-pot synthesis of novel fused pentacyclic chromenopyrimidobenzimidazolones and benzimidazolyl-chromenyl-substituted thiazolidinones

The ultrasound promoted synthesis of a number of novel fused pentacyclic chromenopyrimido[1,2-α]benzimidazolones by the one-pot reaction of 3-formylchromones with 2-aminobenzimidazole is described. Moreover, the isolated pentacyclic chromone derivatives upon microwave irradiation with 2-mercaptocarboxylic acids afforded benzimidazolyl-chromenylthiazolidinones incorporating three pharmacophoric heterocycles; the same thiazolidinones were also formed through a multicomponent reaction under microwave irradiation involving 3-formylchromones, aminobenzimidazole and 2-mercaptocarboxylic acids. The structural elucidation of the products was accomplished by 1D and 2D NMR experiments and for thiazolidinones was also confirmed by X-ray crystallographic analysis. Full assignment of all ¹H and ¹³C NMR chemical shifts has been unambiguously achieved. The proposed reaction mechanism is also discussed.