Homotopy type of gauge groups of quaternionic line bundles over spheres

Let P be a principal S(3)-bundle over a sphere S(n), with n >= 4. Let G(p) be the gauge group of P. The homotopy type of G(p) when n - 4 was studied by A. Kono in [A. Kono, A note on the homotopy type of certain gauge groups, Proc. Roy. Soc. Edinburgh Sect. A 117 (1991) 295-297]. In this paper we extend his result anti we study the homotopy type of the gauge group of these bundles for all n <= 25. (C) 2008 Elsevier B.V. All rights reserved.

The doodle of a finitely determined map germ from R(2) to R(3)

Let f : U subset of R(2) -> R(3) be a representative of a finitely determined map germ f : (R(2), 0) -> (R(3), 0). Consider the curve obtained as the intersection of the image of the mapping f with a sufficiently small sphere s(epsilon)(2) centered at the origin in R(3), call this curve the associated doodle of the map germ f. For a large class of map germs the associated doodle has many transversal self-intersections. The topological classification of such map germs is considered from the point of view of the associated doodles. (C) 2009 Elsevier Inc. All rights reserved.

Searching for planar signatures in WMAP

We search for planar deviations of statistical isotropy in the Wilkinson Microwave Anisotropy Probe (WMAP) data by applying a recently introduced angular-planar statistics both to full-sky and to masked temperature maps, including in our analysis the effect of the residual foreground contamination and systematics in the foreground removing process as sources of error. We confirm earlier findings that full-sky maps exhibit anomalies at the planar (l) and angular (l) scales (l; l) = (2; 5); (4; 7); and (6; 8), which seem to be due to unremoved foregrounds since this features are present in the full-sky map but not in the masked maps. On the other hand, our test detects slightly anomalous results at the scales (l; l) = (10; 8) and (2; 9) in the masked maps but not in the full-sky one, indicating that the foreground cleaning procedure (used to generate the full-sky map) could not only be creating false anomalies but also hiding existing ones. We also find a significant trace of an anomaly in the full-sky map at the scale (l; l) = (10; 5), which is still present when we consider galactic cuts of 18.3% and 28.4%. As regards the quadrupole (l = 2), we find a coherent over-modulation over the whole celestial sphere, for all full-sky and cut-sky maps. Overall, our results seem to indicate that current CMB maps derived from WMAP data do not show significant signs of anisotropies, as measured by our angular-planar estimator. However, we have detected a curious coherence of planar modulations at angular scales of the order of the galaxy`s plane, which may be an indication of residual contaminations in the full-and cut-sky maps.

The Schenberg spherical gravitational wave detector: the first commissioning runs

Here we present a status report of the first spherical antenna project equipped with a set of parametric transducers for gravitational detection. The Mario Schenberg, as it is called, started its commissioning phase at the Physics Institute of the University of Sao Paulo, in September 2006, under the full support of FAPESP. We have been testing the three preliminary parametric transducer systems in order to prepare the detector for the next cryogenic run, when it will be calibrated. We are also developing sapphire oscillators that will replace the current ones thereby providing better performance. We also plan to install eight transducers in the near future, six of which are of the two-mode type and arranged according to the truncated icosahedron configuration. The other two, which will be placed close to the sphere equator, will be mechanically non-resonant. In doing so, we want to verify that if the Schenberg antenna can become a wideband gravitational wave detector through the use of an ultra-high sensitivity non-resonant transducer constructed using the recent achievements of nanotechnology.

Hyperfine and magnetic properties of Fe-Cu clusters and Fe precipitates embedded in a Cu matrix

Using the first-principles real-space linear muffin-tin orbital method within the atomic sphere approximation (RS-LMTO-ASA) we study hyperfine and local magnetic properties of substituted pure Fe and Fe-Cu clusters in an fcc Cu matrix. Spin and orbital contributions to magnetic moments, hyperfine fields and the Mossbauer isomer shifts at the Fe sites in Fe precipitates and Fe-Cu alloy clusters of sizes up to 60 Fe atoms embedded in the Cu matrix are calculated and the influence of the local environment on these properties is discussed.

Self-dual hopfions

We construct static and time-dependent exact soliton solutions with nontrivial Hopf topological charge for a field theory in 3 + 1 dimensions with the target space being the two dimensional sphere S(2). The model considered is a reduction of the so-called extended Skyrme-Faddeev theory by the removal of the quadratic term in derivatives of the fields. The solutions are constructed using an ansatz based on the conformal and target space symmetries. The solutions are said self-dual because they solve first order differential equations which together with some conditions on the coupling constants, imply the second order equations of motion. The solutions belong to a sub-sector of the theory with an infinite number of local conserved currents. The equation for the profile function of the ansatz corresponds to the Bogomolny equation for the sine-Gordon model.

Four novel mononuclear and polynuclear Cu(I) thiosaccharinates with triphenylphosphane and bis(diphenylposphino)methane. Synthesis and structural study of Cu(4)(tsac)(4)(PPh(3))(3), Cu(tsac)(PPh(3))(2), Cu(4)(tsac)(4)(dppm)(2), and Cu(2)(tsac)(2)(dppm)(2)

Four new ternary complexes of copper(I) with thiosaccharin and phosphanes were prepared. The reaction of [Cu(4)(tsac)(4)(CH(3)CN)(2)] (1) (tsac: thiosaccharinate anion) with PPh(3) in molar ratios Cu(I)/PPh(3) 1:075 and 1:2 gave the complexes [Cu(4)(tsac)(4)(PPh(3))(3)] center dot CH(3)CN (2) and Cu(tsac)(PPh(3))(2) (3), respectively. The reaction of 1 with Ph(2)PCH(2)PPh(2) (dppm) in molar ratios Cu(I)/dppm 2:1 and 1:1 gave the complexes [Cu(4) (tsac)(4)(dppm)(2)] center dot 2CH(2)Cl(2) (4) and [Cu(2)(tsac)(2)(dppm)(2)] center dot CH(2)Cl(2) (5), respectively. All the compounds have been characterized by spectroscopic and X-ray crystallographic methods. Complex 2 presents a tetra-nuclear arrangement with three metal centers in distorted tetrahedral S(2)NP environments, the fourth one with the Cu(I) ion in a distorted trigonal S(2)N coordination sphere, and the tsac anions acting as six electron donor ligands in mu(3)-S(2)N coordination forms. Complex 3 shows mononuclear molecular units with copper(I) in a distorted trigonal planar coordination sphere, built with the exocyclic S atom of a mono-coordinated thiosaccharinate anion and two P-atoms of triphenylphosphane molecules. With dppm as secondary ligand the structures of the complexes depends strongly on the stoicheometry of the preparation reaction. Complex 4 has a centrosymmetric structure. Two triply bridged Cu(2)(tsac)(2)(dppm) units are joined together by the exocyclic S-atoms of two tsac anions acting effectively as bridging tridentate ligands. Complex 5 is conformed by asymmetric dinuclear moieties where the two dppm and one tsac ligands bridge two Cu(I) atoms and the second tsac anion binds one of the metal centers through its exocyclic S-atom. (C) 2009 Elsevier B.V. All rights reserved.

Copper(II) and zinc(II) complexes with 2-benzoylpyridine-methyl hydrazone

2-Benzoylpyridine-methyl hydrazone (HBzMe) has been obtained as well as its copper(II) [Cu(HBzMe)Cl(2)] (1) and zinc(II) [Zn(HBzMe)Cl(2)] (2) complexes. Upon re-crystallization in 1 - 9 DMSO:acetone conversion of I into dimeric [Cu(BzMe)Cl](2) (1a) occurred. The crystal structures of HBzMe, 1, 1a, and 2 were determined. HBzMe adopts the ZE conformation in the solid. In all complexes the hydrazone adopts the E configuration to attach to the metal through the N(py)-N2-O chelating system. In 1 and 2 a neutral hydrazone coordinates to the metal center while in 1a deprotonation occurs with coordination of an anionic ligand. la presents a dimeric structure. having two copper(II) ions per asymmetric unit. Two chlorides are also present in the copper coordination sphere, which act as bridging ligands and connect the copper centers to each other. (C) 2008 Elsevier B.V. All rights reserved.

Combined Crystallographic and Solution Molecular Dynamics Study of Allosteric Effects in Ester and Ketone p-tert-Butylcalix[4]arene Derivatives and Their Complexes with Acetonitrile, Cd(II), and Pb(II)

We describe here a procedure to bridge the gap in the field of calixarene physicochemistry between solid-state atomic-resolution structural information and the liquid-state low-resolution thermodynamics and spectroscopic data. We use MD simulations to study the kinetics and energetics involved in the complexation of lower rim calix[4]arene derivatives (L), containing bidentate ester (1) and ketone (2) pendant groups, with acetonitrile molecule (MeCN) and Cd2+ and Pb2+ ions (M2+) in acetonitrile solution. On one hand, we found that the prior inclusion of MeCN into the calix to form a L(MeCN) adduct has only a weak effect in preorganizing the hydrophilic cavity toward metal ion binding. On the other hand, the strong ion-hydrophilic cavity interaction produces a wide open calix which enhances the binding of one MeCN molecule (allosteric effect) to stabilize the whole (M2+)1(MeCN) bifunctional complex. We reach two major conclusions: (i) the MD results for the (M2+)1(MeCN) binding are in close agreement with the ""endo"", fully encapsulated, metal complex found by X-ray diffraction and in vacuo MD calculations, and (ii) the MD structure for the more flexible 2 ligand, however, differs from the also endo solid-state molecule. In fact, it shows strong solvation effects at the calixarene lower bore by competing MeCN molecules that share the metal coordination sphere with the four C=O oxygens of an ""exo"" (M2+)2(MeCN) complex.

New insights on the Lewis acidity of diorganolead(IV) compounds: Diphenyllead(IV) complexes with N,O,S-chelating ligands

The reactions of PbPh2(OAC)(2) with alkylglyoxylate thiosemicarbazones (HRGTSC, R = Et, Bu) afforded complexes of the type [PbPh2(GTSC)] center dot H2O, [PbPh2(RGTSC)(2)] and [PbPh2Cl(BUGTSC)]. The structures of HRGTSC (R = Me, Et, Bu), [PbPh2(OAc)(RGTSC)](R = Me, Et, Bu), [PbPh2Cl(BuGTSC)] and [PbPh2(GTSC)] center dot H2O have been studied by X-ray diffraction. [PbPh2(OAc)(RGTSC)] and [PbPh2(GTSC)] center dot H2O have [PbC2NO3S] kernels and the coordination sphere of the metal is pentagonal bipyramidal. [PbPh2Cl(BuGTSC)] has a [PbC2NOSCI] kernel and the coordination geometry around lead is pentagonal bipyramidal with one vacant site. Analysis of the bond distances in [PbPh2(GTSC)] center dot H2O suggests a significant affinity between diphenyllead(IV) and carboxylate donor groups, supporting a borderline acidic character for this organometallic cation. H-1 and C-13 NMR spectra in DMSO-d(6) suggest the partial dissociation of the acetate in [PbPh2(OAc)(RGTSC)] solutions and indicate some differences in the coordination mode of the two RGTSC(-) ligands in [PbPh2(RGTSC)(2)] complexes. (C) 2007 Elsevier Ltd. All rights reserved.

Lead and aluminum bonding in Pb-Al metaphosphate glasses

The bonding properties of cations in phosphate glasses determine many short- and medium-range structural features in the glass network, hence influencing bulk properties. In this work, Pb-Al-metaphosphate glasses (1 - x)Pb-(PO(3))(2)center dot xAI(PO(3))(3) with 0 <= - x <= 1 were analyzed to determine the effect of the substitution of Pb by Al on the glass structure in the metaphosphate composition. The glass transition temperature and density were measured as a function of the Al concentration. The vibrational and structural properties were probed by Raman spectroscopy and nuclear magnetic resonance of (31)P, (27)Al, and (207)Pb. Aluminum incorporates homogeneously in the glass creating a stiffer and less packed network. The average coordination number for Al decreases from 5.9 to 5.0 as x increases from 0.1 to 1, indicating more covalent Al-O bonds. The coordination number of Pb in these glasses is greater than 8, showing an increasing ionic behavior for compositions richer in Al. A quantitative analysis of the phosphate speciation shows definite trends in the bonding of AlO(n) groups and phosphate tetrahedra. In glasses with x < 0.48, phosphate groups share preferentially only one nonbridging O corner with an AlO(n) coordination polyhedron. For x > 0.48 more than one nonbridging O can be linked to AlO(n) polyhedra. There is no corner sharing of O between AlO(n) and PbO(n) polyhedra nor between AlO(n) themselves throughout the compositional range. The PbO(n) coordination polyhedra show considerable nonbridging O sharing, with each O participating in the coordination sphere of at least two Pb. The bonding preferences determined for Al are consistent with the behavior observed in Na-Al and Ca-Al metaphosphates, indicating this may be a general behavior for ternary phosphate glasses.

Paper surfaces and dynamical limits

It is very common in mathematics to construct surfaces by identifying the sides of a polygon together in pairs: For example, identifying opposite sides of a square yields a torus. In this article the construction is considered in the case where infinitely many pairs of segments around the boundary of the polygon are identified. The topological, metric, and complex structures of the resulting surfaces are discussed: In particular, a condition is given under which the surface has a global complex structure (i.e., is a Riemann surface). In this case, a modulus of continuity for a uniformizing map is given. The motivation for considering this construction comes from dynamical systems theory: If the modulus of continuity is uniform across a family of such constructions, each with an iteration defined on it, then it is possible to take limits in the family and hence to complete it. Such an application is briefly discussed.

Minimal surfaces in S(3) with constant contact angle

We provide a characterization of the Clifford Torus in S(3) via moving frames and contact structure equations. More precisely, we prove that minimal surfaces in S(3) with constant contact angle must be the Clifford Torus. Some applications of this result are then given, and some examples are discussed.

ENERGY OF GLOBAL FRAMES

The energy of a unit vector field X on a closed Riemannian manifold M is defined as the energy of the section into T(1) M determined by X. For odd-dimensional spheres, the energy functional has an infimum for each dimension 2k + 1 which is not attained by any non-singular vector field for k > 1. For k = 1, Hopf vector fields are the unique minima. In this paper we show that for any closed Riemannian manifold, the energy of a frame defined on the manifold, possibly except on a finite subset, admits a lower bound in terms of the total scalar curvature of the manifold. In particular, for odd-dimensional spheres this lower bound is attained by a family of frames defined on the sphere minus one point and consisting of vector fields parallel along geodesics.

The Borsuk-Ulam theorem for homotopy spherical space forms

In this work, we show for which odd-dimensional homotopy spherical space forms the Borsuk-Ulam theorem holds. These spaces are the quotient of a homotopy odd-dimensional sphere by a free action of a finite group. Also, the types of these spaces which admit a free involution are characterized. The case of even-dimensional homotopy spherical space forms is basically known.