La Classe Borélienne Ne Détermine Pas Le Type Topologique De Cp(x)

We prove that, for every countable ordinal α ≥ 3, there exists countable completely regular spaces Xα and Yα such that the spaces Cp (Xα ) and Cp (Yα ) are borelian of class exactly Mα , but are not homeomorphic.

On Minimizing ||S−(AX−XB)||Pp

In this paper, we minimize the map Fp (X)= ||S−(AX−XB)||Pp , where the pair (A, B) has the property (F P )Cp , S ∈ Cp , X varies such that AX − XB ∈ Cp and Cp denotes the von Neumann-Schatten class.

The Lindelöf number greater than continuum is u-invariant

2000 Mathematics Subject Classification: 54C35, 54D20, 54C60.

1, 2-Bis (diphenylphosphino) etane bridged dinuclear copper (I) complexes: Investigations of solid state and solution structures by CP/MAS31P NMR spectroscopy, X-ray crystallography, IR spectroscopy and solution 31P NMR and 63Cu NMR spectroscopy

Three different complexes of copper (I) with bridging 1, 2-bis(diphenylphosphino)ethane (dppe), namely [Cu2 (mu-dppe) (CH3CN)6] (ClO4)2 (1), [Cu2 (mu-dppe)2 (CH3 CN)2] (ClO4)2 (2), and [Cu2 (mu-dppe) (dppe)2 (CH3CN)2] (ClO4)2 (3) have been prepared. The structure of [Cu2 (mu-dppe) (dPPe)2 (CH3CH)2] (ClO4)2 has been determined by X-ray crystallography. It crystallizes in the space group PT with a=12.984(6) angstrom, b=13.180(6) angstrom, c=14.001(3) angstrom, alpha=105.23(3), beta=105.60(2), gamma=112.53 (4), V=1944 (3) angstrom3, and Z=1. The structure was refined by least-squares method with R=0.0365; R(w)=0.0451 for 6321 reflections with F0 greater-than-or-equal-to 3 sigma (F0). The CP/MAS P-31 and IR spectra of the complexes have been analysed in the light of available crystallographic data. IR spectroscopy is particularly helpful in identifying the presence of chelating dppe. P-31 chemical shifts observed in solid state are very different from those observed in solution, and change significantly with slight changes in structure. In solution, complex 1 remains undissociated but complexes 2 and 3 undergo extensive dissociation. With a combination of room temperature H-1, Cu-63, and variable temperature P-31 NMR spectra, it is possible to understand the various processes occurring in solution.

From the Icosahedron to Natural Triangulations of CP(2) and S(2) x S(2)

We present two constructions in this paper: (a) a 10-vertex triangulation CP(10)(2) of the complex projective plane CP(2) as a subcomplex of the join of the standard sphere (S(4)(2)) and the standard real projective plane (RP(6)(2), the decahedron), its automorphism group is A(4); (b) a 12-vertex triangulation (S(2) x S(2))(12) of S(2) x S(2) with automorphism group 2S(5), the Schur double cover of the symmetric group S(5). It is obtained by generalized bistellar moves from a simplicial subdivision of the standard cell structure of S(2) x S(2). Both constructions have surprising and intimate relationships with the icosahedron. It is well known that CP(2) has S(2) x S(2) as a two-fold branched cover; we construct the triangulation CP(10)(2) of CP(2) by presenting a simplicial realization of this covering map S(2) x S(2) -> CP(2). The domain of this simplicial map is a simplicial subdivision of the standard cell structure of S(2) x S(2), different from the triangulation alluded to in (b). This gives a new proof that Kuhnel's CP(9)(2) triangulates CP(2). It is also shown that CP(10)(2) and (S(2) x S(2))(12) induce the standard piecewise linear structure on CP(2) and S(2) x S(2) respectively.

The NMR-spectroscopic and X-ray crystal-structural characterization of two Cp*Ir halfsandwich complexes containing the 1,2-dicarba-closo-dodecaborane-1,2-diselenolato ligand

The reaction of [Cp*IrCl2](2) with dilithium 1,2-orthocarborane-1,2-diselenolate 3 leads to the green 16-electron diselenolene complex [Cp*Ir{Se2C2(B10H10)}] (4) which takes up two-electron ligands such as trimethylphosphane to give the 18-electron diselenolate derivative [Cp*Ir(PMe3)-{Se2C2(B10H10)}] (5). The molecular structures of 4 and 5 were determined by X-ray crystal structure analysis. The Se-77-nuclear shielding in 4 is lower by almost 500 ppm relative to that in 5.

Synthesis and x-ray structure of a highly symmetrical selenium-centered hexanuclear neodymium complex, [(Cp6Nd6Se13)-Nd-t](-) (Cp-t=eta(5)-(BuC5H4)-C-t)

The half-sandwich tert-buthylcyclopentadienyl neodymium complex [(CpNdCl2)-Nd-t(THF)(2)](2) (1) reacts with Na2Se5 to give organoneodymium polyselenide complex [Na(THF)(6)][(Cp6Nd6)-Nd-t(mu(6)-Se)(mu(2)-Se-2)(6)] (2) which has been characterized by X-ray crystallography.

SYNTHESES AND X-RAY STRUCTURES OF BIS(T-BUTYLCYCLOPENTADIENYL)LANTHANIDE CHLORIDE COMPLEXES [(BU(T)CP)2LNCL]2 (LN = PR, GD, ER)

Reaction of lanthanide trichlorides with two equivalents of sodium t-butylcyclopentadienide in THF gave rise to the bis(t-butylcyclopentadienyl)lanthanide chloride complexes [(Bu(t)Cp)2LnCl]2 (Ln = Pr, Gd, Er), which were characterized by elemental analysis, IR and H-1 NMR spectroscopy. In addition, the crystal structures of [(ButCp)2PrCl]2 (1) and [(ButCp)2GdCl]2 (2) were determined by single crystal X-ray diffraction at room temperature. The coordination number for Pr3+ and Gd3+ is 8 and the bond lengths Pr-Cl and Gd-Cl are 2.864(2) and 2.771(3) angstrom, respectively. The structural studies showed the complexes to have C2h symmetry.

SYNTHESIS AND X-RAY CRYSTAL-STRUCTURE OF AN ORGANOLANTHANIDE COMPLEX [(BU(T)CP)3NDBRLI(THF)3]

(ButCp)2NdCl.2THF reacts with one equivalent of phenyllithum in THF yielding tris(tert-butylcyclopentadienyl)neodymium lithium bromide tetrahydrofuran, [(ButCP)3 NdBrLi(THF)3], as a by-product, whose structure has been determined by X-ray crystallography. The 10-coordinated neodymium atom is bonded to three tert-butyl-cyclopentadienyl groups and one bromine atom, forming a distorted pseudo-tetrahedron.

Synthesis and Electronic Structure of Dissymmetrical, Naphthalene-Bridged Sandwich Complexes [Cp′Fe(μ‑C10H8)MCp*]x (x = 0, +1; M =Fe, Ru; Cp′ = η5‑C5H2‑1,2,4‑tBu3; Cp* = η5‑C5Me5)

The dissymmetrical naphthalene-bridged complexes [Cp′Fe(μ-C10H8)FeCp*] (3; Cp* = η5-C5Me5, Cp′ = η5-C5H2-1,2,4-tBu3) and [Cp′Fe(μ-C10H8)RuCp*] (4) were synthesized via a one-pot procedure from FeCl2(thf)1.5, Cp′K, KC10H8, and [Cp* FeCl(tmeda)] (tmeda = N,N,N′,N′- tetramethylethylenediamine) or [Cp*RuCl]4, respectively. The symmetrically substituted iron ruthenium complex [Cp*Fe(μ-C10H8)RuCp*] (5) bearing two Cp* ligands was prepared as a reference compound. Compounds 3−5 are diamagnetic and display similar molecular structures, where the metal atoms are coordinated to opposite sides of the bridging naphthalene molecule. Cyclic voltammetry and UV/vis spectroelectrochemistry studies revealed that neutral 3−5 can be oxidized to monocations 3+−5+ and dications 32+−52+. The chemical oxidation of 3 and 4 with [Cp2Fe]PF6 afforded the paramagnetic hexafluorophosphate salts [Cp′Fe(μ-C10H8)FeCp*]PF6 ([3]PF6) and [Cp′Fe(μ-C10H8)RuCp*]PF6 ([4]PF6), which were characterized by various spectroscopic techniques, including EPR and 57Fe Mössbauer spectroscopy. The molecular structure of [4]PF6 was determined by X-ray crystallography. DFT calculations support the structural and spectroscopic data and determine the compositions of frontier molecular orbitals in the investigated complexes. The effects of substituting Cp* with Cp′ and Fe with Ru on the electronic structures and the structural and spectroscopic properties are analyzed.

Classical strings in AdS(4) x CP(3) with three angular momenta

In this paper, rotating strings in three directions of AdS(4) x CP(3) geometry are studied; its divergent energy limit, and conserved charges are also determined. An interpretation of these configurations as either giant magnons or spiky strings is discussed.

Heterobimetallic compounds [Ru(eta(5)-Cp)(dppf)X] (X = Cl, Br, I and N(3)): synthesis, electrochemical analysis, and the crystal structure of [Ru(eta(5)-Cp)(dppf)I] [dppf=1,1`-bis(diphenylphosphino)ferrocene]

A series of new ruthenium-iron based derivatives [Ru(eta(5)-Cp)(dppf)Cl] (1), [Ru(eta(5)-Cp)(dppf)Br] (2), [Ru(eta(5)-Cp)(dppf)I] (3) and [Ru(eta(5)-Cp)(dppf)N(3)] (4) were obtained by reactions of [Ru(eta(5)-Cp)(PPh(3))(2)Cl] with 1,1`-bis(diphenylphosphino) ferrocene (dppf) and characterized by IR, NMR ((1)H, (13)C and (31)P), (57)Fe Mossbauer spectroscopy and cyclic voltammetry. Additionally, the compound (3) was structurally characterized by X-ray crystallography, and the results were as follows: orthorhombic, Pbca, a = 18.2458(10), b = 20.9192(11), c = 34.4138(19) a""<<, alpha = beta = gamma = 90A degrees, V = 13135.3(12) a""<<(3) and Z = 16.

Measurement of the CP-violation parameter of B-0 mixing and decay with p(p)over-bar ->mu mu X data

We measure the dimuon charge asymmetry A in p (p) over bar collisions at a center of mass energy root s=1960 GeV. The data was recorded with the D0 detector and corresponds to an integrated luminosity of approximately 1.0 fb(-1). Assuming that the asymmetry A is due to asymmetric B-0 <->(B) over bar (0) mixing and decay, we extract the CP-violation parameter of B-0 mixing and decay: ((epsilon B0))/(1+vertical bar epsilon B0 vertical bar 2)=(AB0)/(4)= -0.0023 +/- 0.0011(stat)+/- 0.0008(syst).A(B)(0) is the dimuon charge asymmetry from decays of B-0(B) over bar (0) pairs. The general case, with CP violation in both B-0 and B-s(0) systems, is also considered. Finally we obtain the forward-backward asymmetry that quantifies the tendency of mu(+) to go in the proton direction and mu(-) to go in the antiproton direction. The results are consistent with the standard model and constrain new physics.

Search for CP violation in B-s(0) -> mu(+) D-s(-) X decays in p(p)over-bar collisions at root s=1.96 TeV

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Comprehensive study of surface chemistry of MCM-41 using 29Si CP/MAS NMR, FTIR, pyridine-TPD, and TGA

A comprehensive study was conducted on mesoporous MCM-41. Spectroscopic examinations demonstrated that three types of silanol groups, i.e., single, (SiO)3Si-OH, hydrogen-bonded, (SiO)3Si-OH-OH-Si(SiO)3, and geminal, (SiO)2Si(OH)2, can be observed. The number of silanol groups/nm2, ?OH, as determined by NMR, varies between 2.5 and 3.0 depending on the template-removal methods. All these silanol groups were found to be the active sites for adsorption of pyridine with desorption energies of 91.4 and 52.2 kJ mol-1, respectively. However, only free silanol groups (involving single and geminal silanols) are highly accessible to the silylating agent, chlorotrimethylsilane. Silylation can modify both the physical and chemical properties of MCM-41.