Direct Ferrier rearrangement on unactivated glycals catalyzed by indium(III) chloride

Anhydrous InCl₃ has been shown to efficiently catalyze the Ferrier rearrangement by a direct allylic substitution of the hydroxyl group at C-3 position of glycals to afford the corresponding 2,3-unsaturated glycosides in high yields at ambient temperature. This methodology obviates the need for protecting and/or activating the C-3 hydroxyl group of glycals. The reaction works in equal ease with both 4,6-di-O-benzyl-d-glucal and 4,6-di-O-benzyl-d-galactal. The mildness of InCl₃ makes this approach compatible for glycosyl acceptors with acid labile groups. The generality of the reaction has been demonstrated with a diversity of alcohols, phenols, and sugar nucleophiles.     

Barth type vanishing theorem

In this paper we give a vanishing result for cohomology groups of symmetric powers of the co-normal bundle of a non-degenerate smooth subvariety X of projective space, then we use this theorem to give a Barth type vanishing theorem.      

Sequence of four orthogonal smectic phases in an achiral bent-core liquid crystal: evidence for the SmAP(α) phase

The mesomorphic properties of an achiral bent-core liquid crystal derived from 4-cyanoresorcinol are studied by polarizing optical microscopy, x-ray diffraction, and second harmonic electro-optic response. It shows a novel sequence of four nontilted or orthogonal smectic phases on cooling: SmA-SmAP(R)-SmAP(X)-SmAP(A). Here SmAP(X) is the new orthogonal polar uniaxial smectic phase. The electric-field-induced transformations in the SmAP(X) phase give rise to two biaxial states separated by a uniaxial one. The second harmonic electro-optic response in this phase is interpreted in terms of the polar interaction with the electric field. A comparison of the experimental results with the next-nearest-neighbor model for the structure of the SmAP(X) phase shows it to be an SmAP(α) phase.     

One‐Pot Green Synthesis of Thiazolo[3,2‐a]pyridine Derivatives via Tandem Cyclization in Aqueous Media

Facile, three‐component domino reactions of readily available thioglycolic acid/ethyl thioglycolate, aromatic aldehydes, and malononitrile/ethyl cyanoacetate in aqueous potassium carbonate at room temperature afforded thiazolo[3,2‐a]pyridine derivatives chemoselectively in good to excellent yield. All the formed 4H‐chromenes were characterized by spectral and X‐ray methods.     

Debye process and dielectric state of an alcohol in a nonpolar solvent

To investigate the origin of the first order molecular kinetics of the most prominent, Debye-type polarization, a detailed dielectric relaxation study of 66.5, 40, and 20 mole% solutions of 5-methyl-2-hexanol in 2-methylpentane (2:1, 0.67:1, and 0.25:1 molar ratios) was performed. The Debye-type polarization remains prominent in the solutions, despite the extensive loss of intermolecular hydrogen bonds. At high temperatures, its contribution to permittivity extrapolates close to the statistically scaled values for the 2:1 solution. For others, the measured values of its contribution crossover the scaled values in a temperature plane. The faster relaxation process of about 4% magnitude has an asymmetric distribution of times in the solutions and, relative to those of the pure alcohol, their values decrease on heating more at high temperatures and less at low. This is attributed to an increase in the alcohol cluster size by consumption of monomers as well as the growth of smaller clusters as the solution is cooled. It is argued that structural fluctuation in solutions, as in the pure alcohol, is determined by the rates of both the Debye-type and the faster polarizations in the ultraviscous state.     

A new reverse analysis to determine the constitutive response of plastically graded case hardened bearing steels

A new reverse analysis is presented that determines the plastic response of both nongraded and plastically graded materials (PGMs) without the need for traditional tension or compression tests. The method utilizes the concepts of expanding cavity model for strain hardening materials, Tabor’s rule of converting Vickers hardness to flow stress, representative plastic strain induced by indentation, and finite element modeling of the macro indentation process. A unique flow curve is determined when the experimentally measured increase in micro Vickers hardness matches that predicted by the proposed method within the plastic zone of a macro Vickers indent. The method is validated for a nongraded stainless steel first and then extended to determine the gradient in flow curves of plastically graded, case-hardened M50 NiL material, a widely used bearing steel. Such knowledge of the plastic response of the case hardened region will help optimize the design of case hardened bearings with longer rolling contact fatigue life and higher thrust load capabilities.     

A new complexity measure for time series analysis and classification

Complexity measures are used in a number of applications including extraction of information from data such as ecological time series, detection of non-random structure in biomedical signals, testing of random number generators, language recognition and authorship attribution etc. Different complexity measures proposed in the literature like Shannon entropy, Relative entropy, Lempel-Ziv, Kolmogrov and Algorithmic complexity are mostly ineffective in analyzing short sequences that are further corrupted with noise. To address this problem, we propose a new complexity measure ETC and define it as the “Effort To Compress” the input sequence by a lossless compression algorithm. Here, we employ the lossless compression algorithm known as Non-Sequential Recursive Pair Substitution (NSRPS) and define ETC as the number of iterations needed for NSRPS to transform the input sequence to a constant sequence. We demonstrate the utility of ETC in two applications. ETC is shown to have better correlation with Lyapunov exponent than Shannon entropy even with relatively short and noisy time series. The measure also has a greater rate of success in automatic identification and classification of short noisy sequences, compared to entropy and a popular measure based on Lempel-Ziv compression (implemented by Gzip).     

Krull–Schmidt reduction of principal bundles in arbitrary characteristic

Let M be an irreducible projective variety defined over an algebraically closed field k, and let E_G be a principal G-bundle over M, where G is a connected reductive linear algebraic group defined over k. We show that for E_G there is a naturally associated conjugacy class of Levi subgroups of G. Given a Levi subgroup H in this conjugacy class, the principal G-bundle E_G admits a reduction of structure group to H. Furthermore, this reduction is unique up to an automorphism of E_G.     

Torsional vibrations of non-uniform rotating blades with attachment flexibility

The torsional vibrations of non-uniform pretwisted rotating blades are studied by using finite element methods based on both the Rayleigh-Ritz and Galerkin formulations. The apparent differences between the matrices obtained from these formulations are explained and, as obtained by using three different orders of elements, results are presented for blades with flexibly attached roots and for a non-uniform blade representative of a bearingless rotor. A parametric study is carried out to resolve a controversy regarding the relative importance of certain terms in the equations of motion of pretwisted rotating blades. In Appendix I, an exact solution is presented for the torsional vibrations of flexibly attached rotating blades with piecewise constant inertia and elastic properties, which serves as a benchmark solution for the finite element results.     

Remarks on Ramanujam-Kawamata-Viehweg Vanishing Theorem

In this article we prove a general result on a nef vector bundle E on a projective manifold X of dimension n depending on the vector space H^n,n(X,E): It is also shown that H^n,n(X,E) = 0 for an indecomposable nef rank 2 vector bundles E on some specific type of n dimensional projective manifold X. The same vanishing shown to hold for indecomposable nef and big rank 2 vector bundles on any variety with trivial canonical bundle.