Two Spectroscopies in One: Interference of Circular Dichroism and Raman Optical Activity

Previously, we and other laboratories have reported an unusual and strong Raman optical activity (ROA) induced in solvents by chiral dyes. Various theories of the phenomenon appeared, but they were not capable of explaining fully the observed ROA band signs and intensities. In this work, an analysis based both on the light scattering theory and dedicated experiments provides a more complete understanding. For example, double-cell magnetic circular dichroism and magnetic ROA experiments with copper-porphyrin complex show that the induced chirality is observed without any contact of the solvents with the complex. The results thus indicate that a combination of electronic circular dichroism (ECD) with the polarized Raman scattering is responsible for the effect. The degree of circularity of solvent vibrational bands is a principal molecular property participating in the event. The insight and the possibility to predict the chirality transfer promise future applications in spectroscopy, chemical analysis and polarized imaging.     

Formic Acid,a Ubiquitous but Overlooked Component of the Early Earth Atmosphere

Terrestrial volcanism has been one of the dominant geological forces shaping our planet since its earliest existence. Its associated phenomena, like atmospheric lightning and hydrothermal activity, provide a rich energy reservoir for chemical syntheses. Based on our laboratory simulations, we propose that on the early Earth volcanic activity inevitably led to a remarkable production of formic acid through various independent reaction channels. Large-scale availability of atmospheric formic acid supports the idea of the high-temperature accumulation of formamide in this primordial environment.     

Short communication the preparation of stable protected 3-ethynylpyrrole suitable for electrochemical polymerization

Stable protected 3-triisopropylsilylethynylpyrrole, 4b , was prepared in the yield 73% by first observed selective deprotection of double protected 1-triisopropylsilyl-3-triisopropylsilylethynylpyrrole, 3b , which was obtained in the yield 44%. This deprotection in preference proceeds at the pyrrole nitrogen leaving the 3-triisopropylsilylethynyl group intact. Due to its stability, ethynylpyrrole derivative 4b protected was like the first alkynyl pyrrole derivative electrochemically polymerized giving a black polypyrrole layer deposited on the platinum anode. Copyright © 2003 John Wiley & Sons, Ltd.     

Transverse sections for the Second Hamiltonian KdV Structure

In this paper we study regular and singular operators for the Second KdV Hamiltonian Structure. We prove that at some point of any regular symplectic leaf, one can move transversally to the leaf by simply adding constants to the coefficients of the operator. We also prove that given any leaf, one can move transversally to the leaf at some point by adding certain trigonometric polynomials to the coefficient of the operator. We discuss the implications of this result for the Poisson geometry of Adler-Gel’fand-Dikii manifolds and for the normal forms of scalar operators with periodic coefficients.     

Interpolatory Band-Limited Wavelet Bases on the Sphere

In the present paper, we construct space-localized bases for the space $W_n^n:=\oplus_{k=n+1}^{2n} Harm_k({\Bbb S}^2)$ of band-limited functions on the sphere. Each of the basis functions is a zonal polynomial centered at a point $\eta_i\in{\Bbb S}^2$. The goal of this work is to describe explicit fundamental systems $\lbrace\eta_j\rbrace_{j=1,\dots,M_n}$ for the space $W_n^n$ which finally lead to space- and frequency-localized polynomial bases for $L^2({\Bbb S}^2)$.     

On actually computable bijections between ℕ and Q +

We present three different ways of getting an actually computable enumeration of Q ⁺ in the sense of being able to know exactly which rational occupies a given position and vice versa. The first enumeration is based on the Pierce expansion model for representing real numbers. The other two are based on regular continued fractions.The first and third authors were supported by UPF Grant, Support d'Iniciació a la Recerca, # F3087613.     

Processing effects of nanometric rare earth-doped tin oxides on the synthesis of methyl vinyl ketone

Nanoparticle catalysts based on SnO₂ were processed by two different methods, víz.the polymeric precursor and high-energy mechanical milling. The sample morphology and catalytic performance in the aldol condensation between methanol and acetone were modified by the processing and rare earth doping. This revised version was published online in August 2006 with corrections to the Cover Date.     

On complex structures in 8-dimensional vector bundles

Necessary and sufficient conditions for the existence of a complex structure in an 8-dimensional spin vector bundle over a closed connected spin manifold of dimension 8 are given in terms of characteristic classes. The result completes the papers by Heaps [H] and Thomas [T] on the same topic. Research supported by the grant 201/96/0310 of the Grant Agency of the Czech Republic.