Highly diastereoselective multicomponent synthesis of polysubstituted 2-hydroxy-2-trifluoromethylpiperidineswith four and five stereogenic centers

The Michael–Mannich cascade cyclization of cyano olefins, ethyl 4,4,4-trifluoro-3-oxobutanoate, aromatic aldehydes and ammonium acetate provides convenient stereoselective formation of ethyl 5,5-dicyano-4,6-diaryl-2-hydroxy-2-(trifluoromethyl)piperidine-3-carboxylates with fourstereogenic centers and dialkyl 4,6-diaryl-5-cyano-2-hydroxy-2-(trifluoromethyl)piperidine-3,5-dicarboxylates with five stereogenic centers. Ammonium acetate plays dual role, acting as a base and as a nitrogen source.     

Chromatography-Free Multicomponent Synthesis of Thioureas Enabled by Aqueous Solution of Elemental Sulfur

The development of a new three-component chromatography-free reaction of isocyanides, amines and elemental sulfur allowed us the straightforward synthesis of thioureas in water. Considering a large pool of organic and inorganic bases, we first optimized the preparation of aqueous polysulfide solution from elemental sulfur. Using polysulfide solution, we were able to omit the otherwise mandatory chromatography, and to isolate the crystalline products directly from the reaction mixture by a simple filtration, retaining the sulfur in the solution phase. A wide range of thioureas synthesized in this way confirmed the reasonable substrate and functional group tolerance of our protocol.     

Modified Three-Dimensional Formulations of Bending Problems of Homogeneous Plates and Beams under Complex Fixing Conditions

Modified three-dimensional formulations of bending problems of homogeneous elastic plates and beams are considered. Modification of the known three-dimensional formulations reduces to using additional constraints imposed on displacement functions. An advantage of the formulations proposed is that complex fixing conditions of plates and beams can be taken into account.     

Ultraslow phonon-assisted collapse of tubular image states

We predict ultraslow collapse of “tubular image states” (TIS) on material surfaces. TIS are bound Rydberg-like electronic states formed at large distances (∼30 nm) from the surfaces of suspended circularly-symmetric nanowires, such as metallic C nanotubes. The states are formed in potential wells, resulting from a combination of the TIS-electron attraction to image charges in the nanotube and its centrifugal repulsion, caused by spinning around the tube. We demonstrate that TIS can collapse on the tube surface by passing their angular momentum l to circularly polarized flexural phonons excited in the tube. Our analysis shows that for highly detached TIS with l ? 6 the relaxation lifetimes are of the order of 10 ns-1 μs, while for l < 6 these lifetimes are reduced by several orders of magnitude.     

Synthesis of chiral 2′,3′-pyranone(pyrrolidinone)-fused tryptamines

Chiral pyrano- and pyrrolidino-fused tryptamines were prepared by a diasteroselective trimolecular condensation between indole, Garner's aldehyde and Meldrum's acid, followed by selective functional group transformations.     

Synthesis and characterization of linear tetrablock quarterpolymers of styrene,isoprene, dimethylsiloxane,and 2-vinylpyridine

A series of five tetrablock quarterpolymers of styrene, isoprene, dimethylsiloxane, and 2-vinylpyridine with molecular weights varying from 117 × 10³ to 177 × 10³ and having different compositions were synthesized. The synthesis was based on recent advances in the controlled high-vacuum anionic polymerization of hexamethylcyclotrisiloxane and on the selective linking of poly(dimethylsiloxane)lithium with the chlorosilane group of the heterofunctional linking agent chloromethylphenylethylene dimethylchlorosilane. Combined characterization results by size exclusion chromatography, membrane osmometry, and NMR spectroscopy suggested that the synthesized multiblock multicomponent polymers had a high degree of structural and compositional homogeneity. © 2003 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 42: 514–519, 2004     

Higher-order <Emphasis Type="Bold">?</Emphasis> corrections in the semiclassical quantization of chaotic billiards

In the periodic orbit quantization of physical systems, usually only the leading-order ? contribution to the density of states is considered. Therefore, by construction, the eigenvalues following from semiclassical trace formulae generally agree with the exact quantum ones only to lowest order of ?. In different theoretical work the trace formulae have been extended to higher orders of ?. The problem remains, however, how to actually calculate eigenvalues from the extended trace formulae since, even with ? corrections included, the periodic orbit sums still do not converge in the physical domain. For lowest-order semiclassical trace formulae the convergence problem can be elegantly, and universally, circumvented by application of the technique of harmonic inversion. In this paper we show how, for general scaling chaotic systems, also higher-order ? corrections to the Gutzwiller formula can be included in the harmonic inversion scheme, and demonstrate that corrected semiclassical eigenvalues can be calculated despite the convergence problem. The method is applied to the open three-disk scattering system, as a prototype of a chaotic system. Received 10 September 2001 and Received in final form 3 January 2002     

Spectral action and big desert

The values of the Higgs mass are obtained for two possibilities of extending the standard model in a way compatible with the existence of a noncommutative structure at high energies. We assume the existence of a big desert between the low energy electroweak scale and the high energy scale Λ=1.1×10¹⁷ GeV, where noncommutative features become relevant. We conclude that it is extremely difficult to depart from the Higgs mass value obtained from noncommutative geometry for the standard model with three generations only.     

Dirac constraint analysis and symplectic structure of anti-self-dual Yang-Mills equations

We present the explicit form of the symplectic structure of anti-self-dual Yang-Mills (ASDYM) equations in Yang’s J- and K-gauges in order to establish the bi-Hamiltonian structure of this completely integrable system. Dirac’s theory of constraints is applied to the degenerate Lagrangians that yield the ASDYM equations. The constraints are second class as in the case of all completely integrable systems which stands in sharp contrast to the situation in full Yang-Mills theory. We construct the Dirac brackets and the symplectic 2-forms for both J- and K-gauges. The covariant symplectic structure of ASDYM equations is obtained using the Witten-Zuckerman formalism. We show that the appropriate component of the Witten-Zuckerman closed and conserved 2-form vector density reduces to the symplectic 2-form obtained from Dirac’s theory. Finally, we present the Bäcklund transformation between the J- and K-gauges in order to apply Magri’s theorem to the respective two Hamiltonian structures.     

Mathematical topographical correction of XPS images using multivariate statistical methods

For rough heterogeneous samples, the contrast observed in XPS images may result from both changes in elemental or chemical composition and sample topography. Background image acquisition and subtraction are frequently utilized to minimize topographical effects so that images represent concentration variations in the sample. This procedure may significantly increase the data acquisition time. Multivariate statistical methods can assist in resolving topographical and chemical information from multispectral XPS images. Principal component analysis (PCA) is one method for identification of the highest correlation/variation between the images. Topography, which is common to all of the images, will be resolved in the first most significant component. The score of this component contains spatial information about the topography of the surface, whereas the loading is a quantitative representation of the topography contribution to each elemental/chemical image. The simple‐to‐use self‐modelling mixture analysis (Simplisma) method is a pure variable method that searches for the source of most differences in the data and therefore has the potential to distinguish between chemical and topographical phases in images. The mathematical background correction scheme is developed and validated by comparing results to the experimental background correction for samples with differing degrees of topography. Copyright © 2004 John Wiley & Sons, Ltd.