3-manifolds in Euclidean space from a contact viewpoint

We study the geometry of 3-manifolds generically embedded in R(n) by means of the analysis of the singularities of the distance-squared and height functions on them. We describe the local structure of the discriminant (associated to the distribution of asymptotic directions), the ridges and the flat ridges.

An Invariant Theory of Surfaces in the Four-Dimensional Euclidean or Minkowski Space

2010 Mathematics Subject Classification: 53A07, 53A35, 53A10.

From Galilean-invariant to relativistic wave equations

Through an imaginary change of coordinates in the Galilei algebra in 4 space dimensions and making use of an original idea of Dirac and Lvy-Leblond, we are able to obtain the relativistic equations of Dirac and of Bargmann and Wigner starting with the (Galilean-invariant) Schrdinger equation.

From Galilean-invariant to relativistic wave equations

Through an imaginary change of coordinates in the Galilei algebra in 4 space dimensions and making use of an original idea of Dirac and Lvy-Leblond, we are able to obtain the relativistic equations of Dirac and of Bargmann and Wigner starting with the (Galilean-invariant) Schrdinger equation.

SYNTHESIS AND CRYSTAL-STRUCTURE OF THE NOVEL CYCLOPALLADATED COMPLEX DI(MU,N-S-ETA(2)-QUINOLINE-2-THIOLATE)-BIS[(N,N-DIMETHYLBENZYLAMINE-C(2),N) PALLADIUM(II)]

The compound di(mu,N-Seta2-2-quinoline-2-thiolate)-bis[(N,N-dimethylbenzylamine-C2,N)palladium(II)] was synthesized and studied by IR, NMR and X-ray diffraction: monoclinic, a = 20.138(3), b = 10.831(1), c = 14.973(2) angstrom, beta = 98.04(1)-degrees, Z = 4, space group P2(1)/c, R = 0.032. The compound is dimeric with the two [Pd(N,N-dimethylbenzylamine)]moieties being connected by the two vicinal bridging eta2-N,S-quinoline-2-thiolate anions in a square-planar coordination geometry for the palladium atoms.

Modeling the gluon propagator in Landau gauge: Lattice estimates of pole masses and dimension-two condensates

We present an analytic description of numerical results for the Landau-gauge SU(2) gluon propagator D(p(2)), obtained from lattice simulations (in the scaling region) for the largest lattice sizes to date, in d = 2, 3 and 4 space-time dimensions. Fits to the gluon data in 3d and in 4d show very good agreement with the tree-level prediction of the refined Gribov-Zwanziger (RGZ) framework, supporting a massive behavior for D(p(2)) in the infrared limit. In particular, we investigate the propagator's pole structure and provide estimates of the dynamical mass scales that can be associated with dimension-two condensates in the theory. In the 2d case, fitting the data requires a noninteger power of the momentum p in the numerator of the expression for D(p(2)). In this case, an infinite-volume-limit extrapolation gives D(0) = 0. Our analysis suggests that this result is related to a particular symmetry in the complex-pole structure of the propagator and not to purely imaginary poles, as would be expected in the original Gribov-Zwanziger scenario.

Crystal structure of [{Cu(H2O)(en)2}{Cu(en)2}Re6Te8(CN)6]·3H2O

The reaction of Cs4[Re6Te8(CN)6]·2H2O with Cu(en)2Cl2 in water affords crystals of a cluster complex [{Cu(H2O)(en) 2}{Cu(en)2}Re6Te8(CN)6]·3H2O. The structure of the compound is determined by single crystal X-ray diffraction (a = 10.8082(4) Å, b = 16.5404(6) Å, c = 24.6480(7) Å, β = 92.696(1)°, V = 4401.5(3) Å3, Z = 4, space group P21/n, R 1 = 0.0331, wR 2 (all data) = 0.0652). In the complex, cluster [Re6Te8(CN)6]4- anions are linked by Cu2+ cations into zigzag chains through cyanide bridges. The coordination environment of the copper cations is complemented by ethylenediamine molecules. Each of the cluster anions is additionally coordinated by a terminal fragment {Cu(H2O)(en)2}. © 2014 Pleiades Publishing, Ltd.

Massless minimally coupled fields in de Sitter space: O(4)-symmetric states versus de Sitter invariant vacuum

The issue of de Sitter invariance for a massless minimally coupled scalar field is examined. Formally, it is possible to construct a de Sitterinvariant state for this case provided that the zero mode of the field is quantized properly. Here we take the point of view that this state is physically acceptable, in the sense that physical observables can be computed and have a reasonable interpretation. In particular, we use this vacuum to derive a new result: that the squared difference between the field at two points along a geodesic observers spacetime path grows linearly with the observers proper time for a quantum state that does not break de Sitter invariance. Also, we use the Hadamard formalism to compute the renormalized expectation value of the energy-momentum tensor, both in the O(4)-invariant states introduced by Allen and Follaci, and in the de Sitterinvariant vacuum. We find that the vacuum energy density in the O(4)-invariant case is larger than in the de Sitterinvariant case.