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.     

Uniform Approximation Properties for Spaces of Analytic Functions

We prove that the Banach space of bounded analytic functions and the disc algebra have the uniform bounded approximation property of order p for 1 < p < ∞.     

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     

New 3,3′[2,2′‐oxy‐bis‐(oxazaborolidine)]‐ethylenes. Structural studies by NMR,X‐ray,and quantum chemistry methods

3,3′‐[2,2′‐Oxy‐bis‐(4S‐methyl, 5R‐phenyl‐1,3,2‐oxazaborolidine)]ethylene ( 4a ) and 3,3′‐[2, 2′‐oxy‐(4S‐methyl‐5R‐phenyl‐1,3,2‐oxazaborolidine)‐ (1,3,2‐benzoxazaborolidine)]ethylene ( 4b ) were synthesized by the reaction of N,N′‐bis‐[(1R,2S)‐norephedrine]oxalyl ( 3a ) or N,N′‐[((1R,2S)‐norephedrine, o‐hydroxyphenylamine]oxalyl ( 3b ) with BH₃‐THF. The molecular structure of these compounds was established by NMR and infrared spectroscopy. The molecular geometry for 4 was studied by means of theoretical methods, resulting in structures that were in total agreement with those obtained by spectroscopy data and X‐ray diffraction. © 2005 Wiley Periodicals, Inc. Heteroatom Chem 16:513–519, 2005; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/hc.20151     

Cobalt(II), nickel(II) and zinc(II) coordination compounds derived from aromatic amines

The structural and spectroscopic characterization of coordination compounds of four aromatic amines derived from benzimidazole, 2-aminobenzimidazole (L1), 1-(S-methylcarbodithioate)-2-aminobenzimidazole (L2), 2-(2-aminophenyl)-1H-benzimidazole (L3) and 6,6-dimethyl-5H-benzimidazolyl[1,2-c]quinazoline (L4) are reported. Cobalt(II) [Co(L1)₂(CH₃COO)₂] (1) and nickel(II) [Ni(L1)₂(CH₃COO)₂] (2) acetate coordination compounds of L1 are discussed. The synthesis and the X-ray crystal structure of the new 1-(S-methylcarbodithioate)-2-aminobenzimidazole (L2) is informed, together with its cobalt(II) [Co(L2)₂Cl₂] (3), [Co(L2)₂Br₂] (4) and zinc(II) [Co(L2)₂Cl₂] (5), [Zn(L2)₂Br₂] (6) coordination compounds. In these compounds the imidazolic nitrogen is coordinated to the metal center, while the ArNH₂ and the S-methylcarbodithioate groups do not participate as coordination sites. A co-crystal of L1 and L2 is analyzed. Structural analyses of the coordination compounds of L3 showed that this ligand behaves as a bidentate ligand through the aniline and the imidazole groups forming six membered rings in the cobalt(II) [Co(L3)Cl₂] (7) and zinc(II) [Zn(L3)Cl₂] (8) compounds, as well as the nickel(II) nitrate [Ni(L3)₂(H₂O)₂](NO₃)₂ (9). The quinazoline L4 was produced by insertion of one acetone molecule and water elimination in L3, its X-ray crystal diffraction analysis, as well as that of its zinc(II) coordination compound [Zn(L4)₂Cl₂] (10), are discussed.     

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.