We introduce the concepts of degree inertia, diG(H), and compression, dcG(H), a finitely generated subgroup H given group G. For case direct products free-abelian free groups, we compute compression give an upper bound for inertia. Imposing some technical assumptions to supremum involved in definition notion called restricted diG′(H), and, again Zm×Fn, provide explicit formula relating it inert...

Exactness of the lowest order supersymmetric WKB (SWKB) quantization condition x 2 x 1 E − ω 2 (x)dx = n¯ hπ, for certain potentials, is examined, using complex integration technique. Comparison of the above scheme with a similar , but exact quantization condition, c p(x, E)dx = 2πn¯ h, originating from the quantum Hamilton-Jacobi formalism reveals that, the locations and the residues of the po...

Three new metal coordination polymers, namely, [Co(DPP)2(H2O)2]·(BS)2·2H2O (1), [Co(DPP)2(H2O)2]·(ABS)2·2H2O (2) and [Co(DPP)2(MBS)2] (3) [DPP = 1,3-di(pyridin-4-yl)propane, BS = phenyl sulfonic acid, ABS = p-aminobenzene sulfonic acid, MBS = p-methylbenzene sulfonic acid] were obtained under hydrothermal conditions. Complexes 1-3 were structurally characterized using X-ray single-crystal diffr...

We compute the photon asymmetry for near threshold parity violating (PV) pion photoproduction through sub-leading order. We find a potentially significant contribution from new PV low-energy constants not considered previously. We observe that a measurement of this asymmetry may help clarify the theoretical intepretation of backward angle PV electron-proton scattering, provided that the PV πNN ...

Using 3.3 Million BB̄ pairs accumulated with the CLEO detector we have measured B(B → Kπ) = (1.5 −0.4 ± 0.1± 0.1)× 10, B(B → Kπ) = (2.3 −1.0 ± 0.2± 0.2)× 10, and B(B → η′K+) = (7.8 −2.2±1.0)×10. These constitute the first observations of exclusive B decays to charmless hadronic final states. Furthermore, a measurement of B(B → hπ) = (1.6 +0.3 −0.5 −0.2 ± 0.1) × 10, as well as upper limits on var...

In this paper, we define invariant tensor product and study invariant tensor products associated with discrete series representations. Let G(V1) × G(V2) be a pair of classical groups diagonally embedded in G(V1 ⊕ V2). Suppose that dimV1 < dimV2. Let π be a discrete series representation of G(V1 ⊕ V2). We prove that the functor π⊗G(V1) maps unitary representations of G(V1) to unitary representat...

Notes taken by Stuart White during the lectures and not proof read. Errors will abound. 1. Nuclearity: Approximation and perturbation Recall: Definition 1.1. A C∗-algebra. Definition 1.2. A cp map Theorem 1.3. Stinespring’s theorem. Every cp map is a compression of a ∗-homomorphism. Definition 1.4. φ : A → B cp has order zero if a ⊥ b =⇒ φ(a) ⊥ φ(b). 1 Theorem 1.5. (i) φ : A→ B has order zero i...

We study CP asymmetries in B → hπ decays, where the hadronic states h = ρρ,KKπ, ππKK, etc., and h = ππ, KK, 2(ππ), etc., are taken on the resonances ηc and χc0, respectively. The relatively large ηc and χc0 decay widths, of about 10−15 MeV, provide the necessary absorptive phase in the interference between the resonance (going through b→ ccd) and the background (through b→ uud) contributions to...

With the 2-thienylselenoacetic acid ligand, four new organotin complexes, [Me3Sn(O2CCH2SeC4H3S-o)]n (), [(Ph3Sn)6(O2CCH2SeC4H3S-o)6] (), [(Me2Sn)4(μ3-O)2(O2CCH2SeC4H3S-o)4] (), and [(PhSn)6(μ3-O)6(O2CCH2SeC4H3S-o)6] (), have been synthesized and characterized by X-ray crystallography, elemental analysis, FT-IR and NMR ((1)H, (13)C, and (119)Sn) spectroscopy. The structure analysis indicates tha...