and Applied Analysis 3 where we assume that the spatial variable x : x, y, z varies in the cubic domain Ω : { x, y, z : −1 ≤ x, y, z ≤ 1}, andΨ x, μ, θ : Ψ x, y, z, μ, θ is the angular flux in the direction defined by μ ∈ −1, 1 and θ ∈ 0, 2π . σt and σs denote the total and the differential cross section, respectively, σs μ′, φ′ → μ, φ describes the scattering from an assumed pre-collision angu...

Deprotonation of 1-arylimidazoles (aryl = mesityl (Mes), 2,6-diisopropylphenyl (Dipp)), with n-butyl lithium afforded the corresponding derivatives (1-aryl-1H-imidazol-2-yl)lithium (1a, Ar = Mes; 1b, Ar = Dipp) in good yield. Reaction of 1a with 0.5 equiv. of [Ir(cod)(μ-Cl)]2 yielded two geometrical isomers of a doubly C2,N3-bridged dinuclear complex [Ir(cod){μ-C3H2N2(Mes)-κC2,κN3}]2 (3), 3H-H,...

The grand unification scale MGUT ∼ 10GeV may arise from dynamical effects. With the advances in understanding of supersymmetric dynamics, we can break the grand unified group by introducing a strong gauge group which generates the grand unification scale. We also show how this mechanism can be combined with solutions to the doublet-triplet splitting problem. The same method can also be used for...

Two-dimensional lattices provide the arena for many physics problems of essential importance, a scale symmetry, which rarely exists as noticed by Galileo, in such lattices can help reveal the underlying physics. Here we report the discovery and proof of directional scaling symmetry for high symmetry 2D lattices, i.e., the square lattice, the equilateral triangular lattice and thus the honeycomb...

Explicit forms of IBM Hamiltonians with a generalized partial dynamical O(6) symmetry are presented and compared with empirical data in 162Dy. A dynamical symmetry corresponds to a situation in which the Hamiltonian is written in terms of the Casimir operators of a chain of nested algebras G1 ⊃ G2 ⊃ . . . ⊃ Gn , (1) and has the following properties. (i) Solvability. (ii) Quantum numbers related...

Recently we proposed an attractive scenario of grand unified theories with anomalous U(1)A gauge symmetry, in which doublet-triplet splitting is naturally realized in SO(10) unification using Dimopoulos-Wilczek mechanism and realistic quark and lepton mass matrices can be obtained in a simple way. In this paper we show that there is a mechanism in which the doublet Higgs obtains the supersymmet...

In the crystal structure of the title compound, [Cd(NCS)(C(6)H(4)NO(2))(C(2)H(5)OH)](n), the Cd(2+) cation is coordinated by one N and two O atoms of two symmetry-related isonicotinate anions, one ethanol mol-ecule and two μ-1,3-bridging thio-cyanate anions in a distorted octa-hedral N(2)O(3)S geometry. The metal cations are μ-1,3-bridged via thio-cyanate anions into chains that are further con...

The crystal structure of the title complex, [Cu(2)Br(3)(OH)(C(11)H(13)Br(0.5)Cl(1.5)N(2)O)(2)], consists of two (2-halo-6-oxazolin-yl)pyridine·CuBr units bridged by a Br atom and a hydroxide group. The Cu(II) atoms are five-coordinate with an (N,N)BrCu(Br)(OH) distorted tetra-gonal-pyramidal core, and relatively short contacts to the bridging atoms (Cu-μ-OH and Cu-μ-Br). There are two symmetry-...

The tetra-nuclear title complex, [Cu(4)(C(7)H(4)O(3))(2)(OH)(2)(C(10)H(8)N(2))(4)](NO(3))(2)·4H(2)O, has a crystallographically imposed centre of symmetry. The Cu(II) atoms display a distorted square-pyramidal coordination geometry and are linked by two μ(2)-phenolate O atoms from the salicylate ligands and two μ(3)-hydroxo groups, forming a Cu(4)O(4) core that adopts a 'stepped-cubane' geometr...

One of the most popular extensions of the Minimal Supersymmetric Standard Model (MSSM) is that of the Next-to-Minimal Supersymmetric Standard Model (NMSSM) where the usual Higgs sector of two doublets is supplemented by a gauge singlet superfield coupling only through the Higgs sector superpotential. Apart from the important phenomenological consequences, this allows the elimination of the μ te...