Weakly compact operators onH ∞

We prove that a weakly compact operator fromH or any of its even duals into an arbitrary Banach space is uniformly convexifying. By using this, we establish three dicothomies: (1) every operator defined onH or any of its even duals either fixes a copy ofl or factors through a Banach space having the Banach-Saks property; (2) every quotient ofH or any of its even duals either contains a copy ofl or is super-reflexive; (3) every subspace ofL ¹/H ₀ ¹ or any of its even duals either contains a complemented copy ofl ¹ or is super-reflexive.     

On the unusual 2J(C2-H(f)) coupling dependence on syn/anti CHO conformation in 5-X-furan-2-carboxaldehydes

A remarkable difference for (2)J(C(2)-H(f)) coupling constant in syn and anti conformers of 5-X-furan-2-carboxaldehydes (X = CH(3), Ph, NO(2), Br) and a rationalization of this difference are reported. On the basis of the current knowledge of the Fermi-contact term transmission, a rather unusual dual-coupling pathway in the syn conformer is presented. The additional coupling pathway resembles somewhat that of the J(H-H) in homoallylic couplings, which are transmitted by hyperconjugative interactions involving the pi(C=C) electronic system. The homoallylic coupling pathway can be labeled as sigma*(C-H) <-- pi(C=C) --> sigma*(C-H). In the present case, this additional coupling pathway, using an analogous notation, can be labeled as sigma*(C(2)-C(C)) <-- LP(1)(O(1))...LP(2)(O(C)) --> sigma*(C(C)-H(f)) (sigma*(C(2)-C(C))) where O(1) and O(C) stand for the ring and carbonyl O atoms, respectively. This additional coupling pathway is not activated in the anti conformers since both oxygen lone pairs do not overlap.     

Hand-portable gas chromatograph-toroidal ion trap mass spectrometer (GC-TMS) for detection of hazardous compounds

A novel gas chromatograph-mass spectrometer (GC-MS) based on a miniature toroidal ion trap mass analyzer (TMS) and a low thermal mass GC is described. The TMS system has an effective mass/charge (m/z) range of 50–442 with mass resolution at full-width half-maximum (FWHM) of 0.55 at m/z 91 and 0.80 at m/z 222. A solid-phase microextraction (SPME) fiber mounted in a simple syringe-style holder is used for sample collection and introduction into a specially designed low thermal mass GC injection port. This portable GC-TMS system weighs <13 kg (28 lb), including batteries and helium carrier gas cartridge, and is totally self-contained within dimensions of 47×36×18 cm (18.5×14×7in.). System start-up takes about 3 min and sample analysis with library matching typically takes about 5 min, including time for column cool-down. Peak power consumption during sample analysis is about 80 W. Battery power and helium supply cartridges allow 50 and 100 consecutive analyses, respectively. Both can be easily replaced. An on-board library of target analytes is used to provide detection and identification of chemical compounds based on their characteristic retention times and mass spectra. The GC-TMS can detect 200 pg of methyl salicylate on-column. n-Butylbenzene and naphthalene can be detected at a concentration of 100 ppt in water from solid-phase microextraction (SPME) analysis of the headspace. The GC-TMS system has been designed to easily make measurements in a variety of complex and harsh environments.     

Minimal Geometric Deformation: the inverse problem

In this paper we show that any static and spherically symmetric anisotropic solution of the Einstein field equations can be thought as a system sourced by certain deformed isotropic system in the context of Minimal Geometric Deformation-decoupling approach. To be more precise, we developed a mechanism to obtain an isotropic solution from any anisotropic solution of the Einstein field equations. As an example, we implement the method to obtain the sources of a simple static anisotropic and spherically symmetric traversable wormhole.     

Ricci Collineations for Non-degenerate, Diagonal and Spherically Symmetric Ricci Tensors

The expression of the vector field generator of a Ricci collineation for diagonal, spherically symmetric and non-degenerate Ricci tensors is obtained. The resulting expressions show that the time and radial first derivatives of the components of the Ricci tensor can be used to classify the collineation, leading to 64 families. Some examples illustrate how to obtain the collineation vector.     

C3(SINGLE BOND)Mα Bond contribution to polarizability tensor and 3J(C1Mα) NMR coupling constant in 1-X-3-M-bicyclo[1.1.1]pentanes

In the present work, the relationship between the large substituent effects on ³J(C₁H) in 1-X-3-M-bicyclo[1.1.1]pentanes, I , and the polarizability of the bridgehead C₃(SINGLE BOND)M_α bond is investigated. The existence of such a relationship is suggested by the finding that the effect of an electronegative substituent X on ³J(C₁M_α) couplings in I (M=H) is due to a distortion of the C₃(SINGLE BOND)H bond toward the C₁ center, which enhances the Fermi contact interaction. If such distortion originates in an electrostatic effect, then in other members of this series it can be expected that the substituent effects on ³J(C₁M_α) couplings should depend strongly on the C₃(SINGLE BOND)M_α bond polarizability. Two approaches are followed. First, the ab initio CLOPPA-IPPP method is applied to study the C₃(SINGLE BOND)M_α bond contribution to the molecular static polarizability tensor in I (M=H, F, CH₃). Such bond polarizabilities are found to follow the same trend as calculated as well as experimentally determined substituent effects on ³J(C₁M_α) couplings, which were measured as part of this work in I [X=H, Cl; M=F, CH₃ and X=OCH₃; M=Sn(CH₃)₃]. Second, ³J(C₁M_α) couplings (M=H, CH₃) are calculated at an ab initio level for X=H, F, and they are compared with those obtained in the parent compound (X=H) if the calculation is carried out in the presence of an inhomogeneous electric field. © 1998 John Wiley & Sons, Inc. J Comput Chem 19: 181–188, 1998     

Two new dibenzobicyclic penta- and hexacoordinated tin compounds

Two new dibenzobicyclic penta- andhexacoordinated tin compounds ( 1–2 ) were prepared, derived from bis(2-hydroxy-3,5-di-tert-butyl-phenol)imine and dichloro-dimethylstannane and trichloro-n-butylstannane, respectively. Each compound is an example of two different coordination forms of the ligand. The crystalline complexes have been characterized by magnetic moment, infrared and mass spectrometry, elemental analysis, and X-ray diffraction studies. Compound 1 crystallized in the monoclinic system, space group P2₁/n; it contains a five-coordinated trigonal bipyramidal tin atom with methyl groups in equatorial positions and a planar dibenzobicyclic ring. It is a paramagnetic compound (μ_eff = 1.59 μ_B) due to the radical dianion nature of the ligand. Compound 2 crystallized also in the monoclinic system, space group P2₁/c; it contains a six-coordinated tin atom with an octahedral geometry; the dibenzobicyclic ring is planar, and the chlorine atoms are in trans positions. It is diamagnetic with a delocalized monoanion structure of the ligand. © 1998 John Wiley & Sons, Inc. Heteroatom Chem 9:321–326, 1998     

Optical effects in stratified colloidal particles near transparency

Non-isotropic scattering patterns showing a minimum for small and almost transparent core-shell particles are discussed. It is shown that for any particle size, close to transparency, a core-shell particle behaves optically differently from a non-structured particle due to the presence of a minimum in the scattering pattern. Transparency criteria are discussed in the light of the non-isotropic character of the scattered light. Direct experimental evidence of the existence of this minimum is presented and compared with the theoretical predictions of the scattering by colloids having a distribution of particle composition.     

Action potential and weak KAM solutions

For convex superlinear lagrangians on a compact manifold M we characterize the Peierls barrier and the weak KAM solutions of the Hamilton-Jacobi equation, as defined by A. Fathi [9], in terms of their values at each static class and the action potential defined by R. Ma né [14]. When the manifold M is non-compact, we construct weak KAM solutions similarly to Busemann functions in riemannian geometry. We construct a compactification of by extending the Aubry set using these Busemann weak KAM solutions and characterize the set of weak KAM solutions using this extended Aubry set. Received: 13 November 2000 / Accepted: 4 December 2000 / Published online: 25 June 2001