Dynamical Casimir effect for a massless scalar field between two concentric spherical shells

In this work we consider the dynamical Casimir effect for a massless scalar field-under Dirichlet boundary conditions-between two concentric spherical shells. We obtain a general expression for the average number of particle creation, for an arbitrary law of radial motion of the spherical shells, using two distinct methods: by computing the density operator of the system and by calculating the Bogoliubov coefficients. We apply our general expression to breathing modes: when only one of the shells oscillates and when both shells oscillate in or out of phase. Since our results were obtained in the framework of the perturbation theory, under resonant breathing modes they are restricted to a short-time approximation. We also analyze the number of particle production and compare it with the results for the case of plane geometry.

cis-Bis{1,1-dibenzyl-3-[(furan-2-yl)carbonyl]thioureato-kappa 2 O,S}nickel(II)

In the title compound, [Ni(C(20)H(17)N(2)O(2)S)(2)], the NiII atom is coordinated by the S and O atoms of two 1,1-dibenzyl-3-[(furan-2-yl)carbonyl]thioureate ligands in a distorted square-planar geometry. The two O and two S atoms are mutually cis to each other. The Ni-S and Ni-O bond lengths lie within the range of those found in related structures. The dihedral angle between the planes of the two chelating rings is 20.33 (6)degrees.

1-furfuryl-3-furoylthiourea

The title compound, C11H10N2O3S, was synthesized from furoyl isothiocyanate and furfurylamine in dry acetone. The thiourea group is in the thioamide form. The trans-cis geometry of the thiourea group is stabilized by intramolecular hydrogen bonding between the carbonyl and cis-thioamide and results in a pseudo-S(6) planar ring which makes dihedral angles of 2.5 (3) and 88.1 (2)degrees with the furoyl and furfuryl groups, respectively. There is also an intramolecular hydrogen bond between the furan O atom and the other thioamide H atom. In the crystal structure, molecules are linked by two intermolecular N-H center dot center dot center dot O hydrogen bonds, forming dimers. These dimers are stacked within the crystal structure along the [010] direction.

Tris(N-benzoyl-N ',N ''-diphenylthioureato-kappa O-2,S)cobalt(III)

In the title compound, [Co(C20H15N2OS)(3)], the Co-III atom is coordinated by the S and O atoms of three N-benzoyl-N',N'-diphenylthiourea ligands in a slightly distorted octahedral geometry. The O and S atoms are in cis positions, while the positions between the O and S atoms are trans.

Bis(tetraphenylphosphonium) tris[N-(methylsulfonyl)dithiocarbimato(2-)-kappa(2)S,S ']stannate(IV)

In the title complex, (C(24)H(20)P)(2)[Sn(C(2)H(3)NO(2)S(3))(3)], the Sn(IV) atom is coordinated by three N-(methylsulfonyl) dithiocarbimate bidentate ligands through the anionic S atoms in a slightly distorted octahedral coordination geometry. There is one half-molecule in the asymmetric unit; the complex is located on a crystallographic twofold rotation axis passing through the cation and bisecting one of the (non-symmetric) ligands, which appears thus disordered over two sites of equal occupancy. In the crystal structure, weak intermolecular C-H center dot center dot center dot O and C-H center dot center dot center dot S interactions contribute to the packing stabilization.

Can quantum mechanics fool the cosmic censor?

We revisit the mechanism for violating the weak cosmic-censorship conjecture (WCCC) by overspinning a nearly-extreme charged black hole. The mechanism consists of an incoming massless neutral scalar particle, with low energy and large angular momentum, tunneling into the hole. We investigate the effect of the large angular momentum of the incoming particle on the background geometry and address recent claims that such a backreaction would invalidate the mechanism. We show that the large angular momentum of the incident particle does not constitute an obvious impediment to the success of the overspinning quantum mechanism, although the induced backreaction turns out to be essential to restoring the validity of the WCCC in the classical regime. These results seem to endorse the view that the ""cosmic censor"" may be oblivious to processes involving quantum effects.

1-Furoyl-3-[3-(trifluoromethyl)phenyl]thiourea

The title compound, C(13)H(9)F(3)N(2)O(2)S, crystallizes with two independent molecules in the asymmetric unit. The central thiourea core is roughly coplanar with the furan and benzene rings, showing O-C-N-C(S) torsion angles of 2.3 (4) and -11.4 (2) degrees and (S) C -N-C-C torsion angles of -2.4 (4) and -28.8 (4) degrees, respectively, in the two independent molecules. The trans-cis geometry of the thiourea fragment is stabilized by an intramolecular N-H center dot center dot center dot O hydrogen bond between the H atom of the cis thioamide and the carbonyl O atom. In the crystal structure, intermolecular N-H center dot center dot center dot S hydrogen bonds form centrosymmetric dimers extending along the b axis.

cis-Bis[1,1-dibenzyl-3-(furan-2-ylcarbonyl)thioureato-kappa(2)O,S]copper(II)

In the title compound, [Cu(C(20)H(17)N(2)O(2)S)(2)], the Cu(II) atom is coordinated by the S and O atoms of two 1,1-dibenzyl-3-(furan-2-ylcarbonyl)thioureate ligands in a distorted square-planar geometry. The two O and two S atoms are mutually cis to each other. The Cu-S and Cu-O bond lengths lie within the ranges of those found in related structures. The dihedral angle between the planes of the two chelating rings is 26.15 (6)degrees.

1-(3-cyanophenyl)-3-(2-furoyl)thiourea

The title compound, C13H9N3O2S, was synthesized from furoyl isothiocyanate and 3-aminobenzonitrile in dry acetone. The thiourea group is in the thioamide form. The thiourea fragment makes dihedral angles of 3.91 (16) and 37.83 (12)degrees with the ketofuran group and the benzene ring, respectively. The molecular geometry is stabilized by N-H center dot center dot center dot O hydrogen bonds. In the crystal structure, centrosymmetrically related molecules are linked by two intermolecular N-H center dot center dot center dot S hydrogen bonds to form dimers.

Density functional theory and ab initio molecular dynamics study of NO adsorption on Pd(111) and Pt(111) surfaces

The origin of the unique geometry for nitric oxide (NO) adsorption on Pd(111) and Pt(111) surfaces as well as the effect of temperature were studied by density functional theory calculations and ab initio molecular dynamics at finite temperature. We found that at low coverage, the adsorption geometry is determined by electronic interactions, depending sensitively on the adsorption sites and coverages, and the effect of temperature on geometries is significant. At coverage of 0.25 monolayer (ML), adsorbed NO at hollow sites prefer an upright configuration, while NO adsorbed at top sites prefer a tilting configuration. With increase in the coverage up to 0.50 ML, the enhanced steric repulsion lead to the tilting of hollow NO. We found that the tilting was enhanced by the thermal effects. At coverage of 0.75 ML with p(2 x 2)-3NO(fcc+hcp+top) structure, we found that there was no preferential orientation for tilted top NO. The interplay of the orbital hybridization, thermal effects, steric repulsion, and their effects on the adsorption geometries were highlighted at the end.

cis-Bis[N-(2-furoyl)-N ',N '-diphenylthioureato-kappa(2)O,S]nickel(II)

In the title compound, [Ni(C(18)H(13)N(2)O(2)S)(2)], the Ni(II) atom is coordinated by the S and O atoms of two N-furoyl-N ',N '-diphenylthioureate ligands in a slightly distorted squareplanar coordination geometry. The two O and two S atoms are cis to each other.

cis-bis(N-benzoyl-N ',N '-dibenzylthio-ureato-kappa O-2,S)nickel(II)

In the title compound, [Ni(C22H19N2OS)(2)], the Ni-II atom is coordinated by the S and O atoms of two N-benzoyl-N',N'-dibenzylthioureate ligands in a slightly distorted square-planar geometry. The two O atoms are cis, as are the two S atoms.

1-(2-furoyl)-3-(1-naphthyl)thiourea

In the title compound, C(16)H(12)N(2)O(2)S, the carbonylthiourea group forms dihedral angles of 75.4 (1) and 13.1 (2)degrees, respectively, with the naphthalene ring system and furan ring. The molecule adopts a trans-cis configuration with respect to the positions of the furoyl and naphthyl groups relative to the S atom across the thiourea C-N bonds. This geometry is stabilized by an N-H center dot center dot center dot center dot O intramolecular hydrogen bond. In the crystal structure, molecules are linked by N-H center dot center dot center dot S hydrogen bonds, forming centrosymmetric dimers which are interlinked through C-H center dot center dot center dot pi interactions.

INFERENCE FOR EIGENVALUES AND EIGENVECTORS OF GAUSSIAN SYMMETRIC MATRICES

This article presents maximum likelihood estimators (MLEs) and log-likelihood ratio (LLR) tests for the eigenvalues and eigenvectors of Gaussian random symmetric matrices of arbitrary dimension, where the observations are independent repeated samples from one or two populations. These inference problems are relevant in the analysis of diffusion tensor imaging data and polarized cosmic background radiation data, where the observations are, respectively, 3 x 3 and 2 x 2 symmetric positive definite matrices. The parameter sets involved in the inference problems for eigenvalues and eigenvectors are subsets of Euclidean space that are either affine subspaces, embedded submanifolds that are invariant under orthogonal transformations or polyhedral convex cones. We show that for a class of sets that includes the ones considered in this paper, the MLEs of the mean parameter do not depend on the covariance parameters if and only if the covariance structure is orthogonally invariant. Closed-form expressions for the MLEs and the associated LLRs are derived for this covariance structure.

Induced Modules for Affine Lie Algebras

We study induced modules of nonzero central charge with arbitrary multiplicities over affine Lie algebras. For a given pseudo parabolic subalgebra P of an affine Lie algebra G, our main result establishes the equivalence between a certain category of P-induced G-modules and the category of weight P-modules with injective action of the central element of G. In particular, the induction functor preserves irreducible modules. If P is a parabolic subalgebra with a finite-dimensional Levi factor then it defines a unique pseudo parabolic subalgebra P(ps), P subset of P(ps). The structure of P-induced modules in this case is fully determined by the structure of P(ps)-induced modules. These results generalize similar reductions in particular cases previously considered by V. Futorny, S. Konig, V. Mazorchuk [Forum Math. 13 (2001), 641-661], B. Cox [Pacific J. Math. 165 (1994), 269-294] and I. Dimitrov, V. Futorny, I. Penkov [Comm. Math. Phys. 250 (2004), 47-63].