Letter: Global Hyperbolicity of Sliced Spaces

We show that for generic sliced spacetimes global hyperbolicity is equivalent to space completeness under the assumption that the lapse, shift and spatial metric are uniformly bounded. This leads us to the conclusion that simple sliced spaces are timelike and null geodesically complete if and only if space is a complete Riemannian manifold.     

Universal WCG banach spaces and universal Eberlein Compacts

We prove that for cardinalsτ satisfying τ^ω=τ and forτ=ω ₁, there do not exist universal Eberlein Compacts of weightτ, or universal WCG spaces of density characterτ. Ifτ is a strong limit cardinal of countable cofinality such universal spaces do exist. Thus under GCH universal spaces exist forτ iff cof(τ)=ω. The research of the second author was supported by a grant from the United States-Israel Binational Science Foundation and the Fund for the Promotion of Research at the Technion.     

Synthesis,spectroscopy and thermal properties of the nickel(II), palladium(II) and copper(II) complexes of bis(aminoalkyl)-oxamides (=LH2) including the crystal structure of Cu2L(NO3)2

Summary The synthesis of the Ni^II, Pd^II and Cu^II complexes of N, N-bis(aminoalkyl)oxamides (LH₂) is described and structures are proposed on the basis of their physical and spectroscopic properties. With Ni^II and Pd^II only one complex is formed with general formula NiL or PdL, characterised by coordination through two deprotonated amide N-atoms and two terminal NH₂ groups. With Cu^II it proved possible to obtain three structurally different compounds, depending on the pH, with general formulae Cu(LH₂)X₂, Cu₂(L)X₂ and CuL in which X=Cl, Br or NO₃. The structure of [Cu₂(C₈O₂N₄H₁₆](NO₃)₂ was solved by means ofx-ray diffraction; Mr=451.33, monoclinic, space group P2₁/n, a=9.503(4), b=7.614(1), c=10.407(3) Å, =98.43(3)°, V=744.3(7)ų, Z=2, Dx=1.202 g cm^–3, =1.33 cm^–1, (MoK)=0.71073 Å, F(000)=520, room temperature, R=0.043, wR=0.047 for 1080 observed [I>-3(I)] not systematically absent reflections out of 1423 measurements and 137 variables. The compound has a conformational chair/boat disorder with 82% in the more stable chair form.     

Novel approach to the zaragozic acids. Enantioselective total synthesis of 6,7-dideoxysqualestatin H5

The total synthesis of 6,7-dideoxysqualestatin H5 (3) has been completed by a concise approach that features the stereoselective intramolecular vinylogous aldol reaction of the furoic ester 25a to give 30 or its trimethylsilyl ether derivative 34, which possess the requisite absolute stereochemistry at C(3)-C(5) of 3. Compound 34 was reduced to the saturated bislactone 39, and the C(1) side chain subunit 47 was introduced leading to a mixture of the hemiacetals 48 and the corresponding ketone 49. When this mixture was stirred with methanolic acid, transketalization occurred to give a mixture of 50 and the spirocyclic methyl acetals 51a,b. Oxidation of the primary alcohol group in 50 followed by saponification of the two remaining ester groups gave 3. The longest linear sequence in the synthesis commences with commercially available erythronolactone (26) and requires 17 chemical steps with only 10 isolated intermediates.     

Arsenic biomethylation by the microorganism apiotrichum humicola in the presence of l-methionine-methyl-d3

The microorganism Apiotrichum humicola (previously known as Candida humicola) grown in the presence of either arsenate, arsenite, methylarsonic acid or dimethylarsinic acid, produces arsenic-containing metabolites in the growth medium. When L-methionine-methyl-d₃ is added to the cultures, the CD₃ label is incorporated intact into the metabolites to a considerable extent to form deuterated dimethylarsenic and trimethyl-arsenic species, indicating that S-adenosylmethionine, or some related sulphonium compound, is involved in the biological methylation. Conclusive evidence of CD₃ incorporation in the arsenicals found in the growth medium was provided by using a specially developed hydride generation-gas chromatography-mass spectrometry system (HG–GC–MS).     

Entropy and enthalpy of formation and migration of lattice defects in Na(I)

The self-diffusion coefficients of Na⁺ and I^?, as well as the ionic conductivity, are measured in Na(I) single crystals, pure and doped with Ca²⁺ ions. The computer analysis of the whole set of data shows that the atom transport in Na(I) is ensured essentially by the free vacancies with a very small contribution (～4%) of the vacancy pairs. The thermodynamic parameters of vacancy formation and migration are derived by taking the long range interactions into account (activity coefficients on the concentrations and relaxation factors on the mobilities). The respective entropies of Schottky defect formation, cation migration and anion migration are equal to 7.64, 3.23 and 2.91 k while the corresponding enthalpies are equal to 2.00, 0.58 and 0.77 eV.     

Hybrid artificial neural networks for efficient valuation of real options and financial derivatives

A hybrid valuation methodology is proposed and tested for improving the efficiency of contingent claims pricing by combining Artificial Neural Networks (ANN) and conventional parametric option pricing techniques. With one application on financial derivatives and one on real options the methods superiority is demonstrated. The resulting efficiency is instrumental for real time applications.MSC code: 90-08 Acknowledgements: Both authors are thankful for partial financial support to the HERMES European Center of Excellence on Computational Finance and Economics of the University of Cyprus and a University of Cyprus grant for research in ANNs and Derivatives, and to the anonymous referees for their helpful comments and discussions.     

A universal property of reflexive hereditarily indecomposable Banach spaces

It is shown that every separable Banach space universal for the class of reflexive Hereditarily Indecomposable space contains isomorphically and hence it is universal for all separable spaces. This result shows the large variety of reflexive H.I. spaces.

     

Quantitative combination of volumetric MR imaging and MR spectroscopy data for the discrimination of meningiomas from metastatic brain tumors by means of pattern recognition

The analysis of information derived from magnetic resonance imaging (MRI) and spectroscopy (MRS) has been identified as an important indicator for discriminating among different brain pathologies. The purpose of this study was to investigate the efficiency of the combination of textural MRI features and MRS metabolite ratios by means of a pattern recognition system in the task of discriminating between meningiomas and metastatic brain tumors. The data set consisted of 40 brain MR image series and their corresponding spectral data obtained from patients with verified tumors. The pattern recognition system was designed employing the support vector machines classifier with radial basis function kernel; the system was evaluated using an external cross validation process to render results indicative of the generalization performance to “unknown” cases. The combination of MR textural and spectroscopic features resulted in 92.15% overall accuracy in discriminating meningiomas from metastatic brain tumors. The fusion of the information derived from MRI and MRS data might be helpful in providing clinicians a useful second opinion tool for accurate characterization of brain tumors.