It is known that perturbative invariants of rational homology 3-spheres can be formulated by using arithmetic perturbative expansion of quantum invariants of them. However, we could not make arithmetic perturbative expansion of quantum invariants for 3-manifolds with positive Betti numbers by the same method. In this paper, we explain how to make arithmetic perturbative expansion of quantum SO(...

carbon spheres were fabricated by hydrothermal method and their structural properties were investigated. carbon spheres with average sizes around of 230, 320 and 430 nm were synthesized in different concentration of glucose aqueous solution and different hydrothermal reaction time. the temperature of 180 °c by a hydrothermal reaction was fixed in all of glucose concentration and hydrothermal re...

A Dehn sphere Σ [P] in a closed 3-manifold M is a 2-sphere immersed in M with only double curve and triple point singularities. The sphere Σ fills M [Mo2] if it defines a cell-decomposition of M. The inverse image in S 2 of the double curves of Σ is the Johansson diagram of Σ [J1] and if Σ fills M it is possible to reconstruct M from the diagram. A Johansson representation of M is the Johansson...

A Dehn sphere Σ [P] in a closed 3-manifold M is a 2-sphere immersed in M with only double curve and triple point singularities. The sphere Σ fills M [Mo2] if it defines a cell-decomposition of M. The inverse image in S 2 of the double curves of Σ is the Johansson diagram of Σ [J1] and if Σ fills M it is possible to reconstruct M from the diagram. A Johansson representation of M is the Johansson...

In the Tolman model there exist two quite different branches of solutions generic Lemâıtre-Tolman-Bondi (LTB) ones and T-spheres as a special case. We show that, nonetheless, T-spheres can be obtained as a limit of the class of LTB solutions having no origin and extending to infinity with the areal radius approaching constant. It is shown that all singularities of T-models are inherited from th...

We show that the 2-parameter Podles sphere is a q-fuzzy sphere precisely interpolating between the fuzzy sphere as quotient of the angular momentum algebra U(su2) and the standard q-sphere Cq [S] as subalgebra of the quantum group Cq [SU2]. Whereas the classical sphere as CP 1 can be defined as the algebra generated by the matrix entries of a projector e with trace(e) = 1, the fuzzy-sphere is d...

We introduce an integral form U of the quantized enveloping algebra of sl2. The algebra U is just large enough so that the quasi-R-matrix is contained in a completion of U ⊗ U . We study several completions of the algebra U , and determine their centers. This study is motivated by a study of integrality properties of the quantum sl2 invariants of links and integral homology spheres.

Metallic quantum dots implanted in a silicon dioxide thin layer, grown on a silicon substrate, show promising field emission properties, giving an emission current of 1nA at electric fields as low as 5V/μm. This value is achieved for an implantation dose 5x10 16 ions/cm 2 , compared to 120 V/μm for the lowest dose. Electron microscopy reveals that the Co dots form metallic spheres, with a narro...

We show that the existent fuzzy S2 and S4 models are natural candidates for the quantum geometry on the corresponding spheres in AdS/CFT correspondence. These models fit nicely the data from the dipole mechanism for the stringy exclusion principle. In the AdS2 × S2 case, we show that a wrapped fractional membrane can be used to count for the large ground state degeneracy. We also propose a fuzz...