Defining Relations for the Algebra of Invariants of 2×2 Matrices

We obtain defining relations of the algebra of invariants of the classical subgroups of GL ₂(C) acting by simultaneous conjugation on m-tuples of 2×2 complex matrices. The sets of defining relations look uniformly for all m2 and are derived by translation of classical results on invariant theory of orthogonal groups in the language of 2×2 matrix invariants, combined with arguments of representation theory of the general linear group GL _m (C) and ideas coming from the theory of algebras with polynomial identities.     

R(1rho) relaxation for two-site chemical exchange: general approximations and some exact solutions

Analytic expressions for the nuclear magnetic spin relaxation rate constant for magnetization spin-locked in the rotating reference frame under an applied radiofrequency field, R(1rho), are obtained for two-site chemical exchange. The theoretical approach is motivated by Laguerre's method and obtains R(1rho) as the root of a (p1,q1) Padé approximant. The general formula for R(1rho) obtained by this approach is substantially simpler than existing expressions and is equally or slightly more accurate, in most cases. In addition, particular solutions for the R(1rho) rate constant are presented for two special cases: equal populations of the two exchanging sites, or placement of the radiofrequency carrier at the average resonance frequency of the two sites. The solutions are exact when the R1 and R2 relaxation rate constants are identical, and nearly exact under realistic experimental conditions.     

New types of unstable step-flow growth on Si(111)-(7 x 7) during molecular beam epitaxy: scaling and universality

New types of unstable homoepitaxial growth of vicinal surfaces are studied using ex situ atomic force microscopy. The growth features are two types of step bunching with straight step edges between 700 and 775 degrees C and one type of simultaneous bunching and meandering at 800 degrees C. The results of a quantitative size scaling analysis of the straight steps are discussed from the perspective of universality classes in bunching theory.     

On the Reality of Minkowski Space

Should physicists deal with the question of the reality of Minkowski space (or any relativistic spacetime)? It is argued that they should since this is a question about the dimensionality of the world at the macroscopic level and it is physics that should answer it.     

IR-Spektralanalyse von Gläsern des Systems TeO2−V2O5

Studies of glasses and their crystalline products in the TeO₂–V₂O₅ system were made in the 1400–400 cm^–1 range. A continuous shift of the V=O-band from 1020 cm^–1 to 940 cm^–1 was found in the glasses with decreasing concentration of V₂O₅, as well as a sharp decrease in the intensity at 830 cm^–1. On the basis of the results obtained, it is concluded that with increasing TeO₂ content, the structure of the glasses is changed, caused by the breaking of the V–O–V bonds and the formation of Te–O–Te bridges.The IR-spectrum of the 2TeO₂·V₂O₅ compound in both crystalline and vitreous states was studied for the first time. The behaviour of the absorption bands is related to the structure of the glasses studied.

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2′-Hydroxyflavylium: introducing flavanones into the flavylium network of chemical reactions

Chalcones possessing a hydroxyl group in position 2 cyclize to form flavylium salts in acidic media, this reaction being reversible under neutral-basic conditions. On the other hand, chalcones possessing a hydroxyl group in position 2′ cyclize to form flavanones in basic media. By synthesizing 2′-hydroxyflavylium tetrafluoroborate, it was possible to obtain trans-2,2′-dihydroxychalcone that in solution can evolve to 2′-hydroxyflavanone or back to 2′-hydroxyflavylium depending on the pH. The several equilibria established in aqueous solution were fully characterized. The importance of including flavanones into the flavylium network of chemical reactions is briefly exploited.     

On a Polynomial Inequality of Paul Erd s

Let f be a real polynomial having no zeros in the open unit disk. We prove a sharp evaluation from above for the quantity f′_∞/f_p, 0p<∞. The extremal polynomials and the exact constants are given. This extends an inequality of Paul Erd s [7].     

Transacylation. Biomimetic synthesis of esters of acetic acid

By mixing of β‐hydroxypropyl phosphate and acetic acid in ethanol solution, ethyl acetate is produced. As found, acetyl phosphate is first formed, then it reacts with the solvent to give the final ethyl acetate product. By similar procedures, acetates of methanol, n‐propanol, and n‐butanol are also produced. Propylene oxide serves as a condensing agent. © 2006 Wiley Periodicals, Inc. Heteroatom Chem 17:350–352, 2006; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/hc.20216     

Sufficiency of Lakshmibai–Sandhya Singularity Conditions for Schubert Varieties

We establish one direction of a conjecture by Lakshmibai and Sandhya which describes combinatorially the singular locus of a Schubert variety. We prove that the conjectured singular locus is contained in the singular locus.