The nonlinear essence of gravitational waves

A critical review of gravitational wave theory is made. It is pointed out that the usual linear approach to the gravitational wave theory is neither conceptually consistent nor mathematically justified. Relying upon that analysis it is argued that-analogously to a Yang-Mills propagating field, which must be nonlinear to carry its gauge charge-a gravitational wave must necessarily be nonlinear to transport its own charge-that is, energy-momentum.

Gauge groups from brane-anti-brane systems at angles

We discuss a system formed by two pairs of brane-anti-brane that form an arbitrary angle in a plane. We identify the gauge groups from this system which presumably could be used to construct gauge theories.

Linear relations between N >= 4 supergravity and subleading-color SYM amplitudes

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Dimensional reduction of the ABJM model

We dimensionally reduce the ABJM model, obtaining a two-dimensional theory that can be thought of as a 'master action'. This encodes information about both T- and S-duality, i.e. describes fundamental (F1) and D-strings (D1) in 9 and 10 dimensions. The Higgsed theory at large VEV, (v) over tilde, and large k yields D1-brane actions in 9d and 10d, depending on which auxiliary fields are integrated out. For N = 1 there is a map to a Green-Schwarz string wrapping a nontrivial circle in C(4)/Z(k).

Neutrino masses and the scalar sector of a B-L extension of the standard model

We consider an electroweak model based on the gauge symmetry SU(2)(L) circle times U(1)(Y') circle times U(1)(B-L) which has right-handed neutrinos with different exotic B - L quantum numbers. Because of this particular feature we are able to write Yukawa terms, and right-handed neutrino mass terms, with scalar fields that can develop vacuum expectation values belonging to different energy scales. We make a detailed study of the scalar and the Yukawa neutrino sectors to show that this model is compatible with the observed solar and atmospheric neutrino mass scales and the tribimaximal mixing matrix. We also show that there are dark matter candidates if a Z(2) symmetry is included.

On codimensions k immersions of m-manifolds for k=1 and k=m-2

Let us consider M a closed smooth connected m-manifold, N a smooth ( 2m-2)-manifold and f: M -> N a continuous map, with m equivalent to 1( 4). We prove that if f*: H(1)(M; Z(2)) -> H(1)(f(M); Z(2)) is injective, then f is homotopic to an immersion. Also we give conditions to a map between manifolds of codimension one to be homotopic to an immersion. This work complements some results of Biasi et al. (Manu. Math. 104, 97-110, 2001; Koschorke in The singularity method and immersions of m-manifolds into manifolds of dimensions 2m-2, 2m-3 and 2m-4. Lecture Notes in Mathematics, vol. 1350. Springer, Heidelberg, 1988; Li and Li in Math. Proc. Camb. Phil. Soc. 112, 281-285, 1992).

Crystal structure of bis(benzyltriethylammonium) hexachlorotellurate(IV), [C7H7(C2H5)(3)N](2)(TeCI6)

C26H44Cl6N2Te, monoclinic, P12(1)/n1 (no. 14), a = 9.3981(5) Angstrom, b = 14.606(1) Angstrom, c = 12.4524(7) Angstrom, beta = 108.335(5)degrees, V = 1622.6 Angstrom(3), Z = 2, R-gt(F) = 0.024, wR(ref)(F-2) = 0.065, T = 293 K.

Crystal structure of 1,1,3-trimethyl-2-(2-(2,2,6-trimethyl-cyclohexyl)ethyl) cyclohexane, C20H34

C20H34, monoclinic, P12(1)/n1 (no. 14), a = 10.647(l) angstrom, b = 6.6844(9) angstrom, c = 11.723(1) angstrom, beta = 99.75(1)degrees, V = 822.3 angstrom(3) Z = 2, R-gt(F) = 0.043, wR(ref)(F-2) = 0.110, T = 93 K.

Crystal structure of bis(acetylacetonato)-bis(3-methylpyridine)-nickel(II) dihydrate, Ni(C6H7N)(2)(C5H7O2)(2)center dot 2H(2)O

C22H32N2NiO6, triclinic, P (1) over bar (no. 2), a = 8.335(1) angstrom, b = 9.314(1) angstrom, c = 17.045(2) angstrom, alpha = 88.45(1)degrees, beta = 82.12(1)degrees, gamma = 70.296(9)degrees, V = 1233.7 angstrom(3), Z = 2, R-gt(F) = 0.050, wR(ref)(F-2) = 0.177, T = 293 K.

Crystal and molecular structures of 4-substituted 3,4-dihydropyrimidin-2(1H)-ones studied by X-ray and AM1 and B3LYP calculations

(1) C13H13N3O5, Mr = 291.26, P (1) over bar, a = 7.4629(9), b = 7.9203(9), c = 12.126(2) angstrom, alpha = 86.804(5), beta = 78.471(7), gamma = 69.401(8)degrees, V = 657.3(2)angstrom(3), Z = 2, R-1 = 0.0454; (2) C11H12N2O4, Mr=236.23, Pbca, a=7.2713(9), b=14.234(1), c=20.848(3)angstrom, V= 2157.8(4) angstrom(3), Z=8, R-1=0.0504; (3) C13H13N2O3Cl, Mr = 280.70, P2/n, a = 17.344(2), b = 9.237(1), c = 18.398(2) angstrom; beta = 92.61(2)degrees, V = 2944.4(6) angstrom(3), Z = 8, R-1 = 0.0714. The conformational features of three 4-substituted-3-4-dihydropyrimidin-2(1H)-ones were investigated by computational and single crystal X-ray crystallographic studies. The geometries were optimized using semiempirical (AM1) and first principle calculations (B3LYP/6-31G**) methods, the rotational barriers for important functional groups were studied. In all structures the pyrimidinone rings are in a more or less distorted boat conformation. The phenyl and the furane rings are almost perpendicular to the best least-squares plane through the dihydropyrimidinone ring.

Remark on the vectorlike nature of electromagnetism and electric charge quantization

In this work we study the structure of electromagnetic interactions and electric charge quantization in gauge theories of electroweak interactions based on semisimple groups. We show that in the standard model of electroweak interactions the structure of electromagnetic interactions is strongly correlated to the quantization pattern of electric charges. We examine these two questions also in all possible chiral bilepton gauge models of electroweak interactions. In all, we can explain the vectorlike nature of electromagnetic interactions and electric charge quantization together demanding nonvanishing fermion masses and anomaly cancellations. ©1999 The American Physical Society.

Crystal structures and magnetic properties of CuX2(pdmp)2 complexes (X = Br, Cl)

We report the synthesis and the structural and magnetic characterization of two new compounds: dibromobis-(pdmp)copper(II), CuBr2C22H24N4 (1), and dichlorobis(pdmp)copper(II), CuCl2C22H24N4 (2), where pdmp = 1-phenyl-3,5-dimethylpyrazole. The structures were refined by full-matrix least-squares techniques to R1 = 0.0620 and 0.0777, respectively. Compound 1 belongs to the space group P21/n with a = 8.165(5) Å, b = 10.432(3) Å, c = 13.385(4) Å, β = 100.12(4)̊, and Z = 2. Compound 2 belongs to the space group P21/c with a = 8.379(2) Å, b = 22.630(2) Å, c = 12.256(2) Å, β= 98.43(3)°, and Z = 4. It has the same molecular formula as a compound reported previously but a different crystal structure. Detailed single-crystal EPR measurements were performed for single-crystal samples of 1 and 2 at 9 and 35 GHz and at room temperature. The positions and line widths of the EPR lines were measured as a function of the magnetic field orientation in three orthogonal planes. The data were used to study the electronic properties of the copper ions and to evaluate the exchange interactions between them. Our results are discussed in terms of the electronic pathways for superexchange between copper ions, which are provided by the stacking of pyrazole and phenyl rings of neighboring molecules and by hydrogen-halogen bonds. © 1999 American Chemical Society.

double-struck D signn-forced symmetry breaking of double-struck O sign (2)-equivariant problems

We use singularity theory to classify forced symmetry-breaking bifurcation problems f(z, λ, μ) = f1 (z, λ) + μf2(z, λ, μ) = 0, where f1 is double-struck O sign (2)-equivariant and f2 is double-struck D sign n-equivariant with the orthogonal group actions on z ∈ ℝ2. Forced symmetry breaking occurs when the symmetry of the equation changes when parameters are varied. We explicitly apply our results to the branching of subharmonic solutions in a model periodic perturbation of an autonomous equation and sketch further applications.

Construction of exact Riemannian instanton solutions

We present the exact construction of Riemannian (or stringy) instantons, which are classical solutions of 2D Yang-Mills theories that interpolate between initial and final string configurations. They satisfy the Hitchin equations with special boundary conditions. For the case of U(2) gauge group those equations can be written as the sinh-Gordon equation with a delta-function source. Using the techniques of integrable theories based on the zero curvature conditions, we show that the solution is a condensate of an infinite number of one-solitons with the same topological charge and with all possible rapidities.

Exact time dependent Hopf solitons in 3+1 dimensions

We construct an infinite number of exact time dependent soliton solutions, carrying non-trivial Hopf topological charges, in a 3+1 dimensional Lorentz invariant theory with target space S2. The construction is based on an ansatz which explores the invariance of the model under the conformal group SO(4,2) and the infinite dimensional group of area preserving diffeomorphisms of S2. The model is a rare example of an integrable theory in four dimensions, and the solitons may play a role in the low energy limit of gauge theories. © SISSA 2006.