Using the Simplex Code to Construct Relative Difference Sets in 2-groups

Relative Difference Sets with the parameters (2a, 2b, 2a, 2a-b) have been constructed many ways (see davis, EB, jung, maschmidt, and pottsurvey for examples). This paper modifies an example found in arasusehgal to construct a family of relative difference sets in 2-groups that gives examples for b = 2 and b = 3 that have a lower rank than previous examples. The Simplex code is used in the construction.     

CP violation in charmlessB 0 decays: A coupled channel approach

We consider the CP-violating asymmetry betweenB ⁰f and f in the case thatf is a CP-eigenstate containing no charmed quarks. The asymmetry is assumed to arise as a result of mixing with other channelsf having the same quantum numbers but containing ac pair. Inelastic unitarity is implemented by means of the K-Matrix formalism, in which the constraints of CPT are manifestly satisfied. The formalism is applied to a hypothetical two-channel problemB ⁰M ,M , and then to a realistic four-channel situationB ^{0 + –}, ^{0 0},D ⁺ D ^–,D ^{0 0}. Asymmetries and branching ratios are estimated for the decaysB ^{0 + –}, ^{0 0}.     

Bimetallic Ag‐Pt Sub‐nanometer Supported Clusters as Highly Efficient and Robust Oxidation Catalysts

A combined experimental and theoretical investigation of Ag‐Pt sub‐nanometer clusters as heterogeneous catalysts in the CO→CO₂ reaction (COox) is presented. Ag₉Pt₂ and Ag₉Pt₃ clusters are size‐selected in the gas phase, deposited on an ultrathin amorphous alumina support, and tested as catalysts experimentally under realistic conditions and by first‐principles simulations at realistic coverage. In situ GISAXS/TPRx demonstrates that the clusters do not sinter or deactivate even after prolonged exposure to reactants at high temperature, and present comparable, extremely high COox catalytic efficiency. Such high activity and stability are ascribed to a synergic role of Ag and Pt in ultranano‐aggregates, in which Pt anchors the clusters to the support and binds and activates two CO molecules, while Ag binds and activates O₂, and Ag/Pt surface proximity disfavors poisoning by CO or oxidized species.     

Energy spectra and energy correlations in the decayH→ZZ→μ+μ−μ+μ−

It is shown that in the sequential decay $H \to ZZ \to (f_1 \bar f_1 ) + (f_2 \bar f_2 )$ , the energy distribution of the final state particles provides a simple and powerful test of theHZZ vertex. For a standard Higgs boson, the energy spectrum of any final fermion, in the rest frame ofH, is predicted to be dΓ/dx～1+β⁴?2(x?1)², with $\beta = \sqrt {1 - 4m_Z^2 /m_H^2 } $ and 1?β≤x=4E/m _H ≤1+β. By contrast, the spectrum for a pseudoscalar Higgs is dΓ/dx～β²+(x?1)². There are characteristic energy correlations betweenf ₁ andf ₂ and betweenf ₁ andf ₂. These considerations are applied to the “gold-plated” reactionH→ZZ→μ⁺μ^?μ⁺μ^?, including possible effects ofCP-violation in theHZZ coupling. Our formalism also yields the energy spectra and correlations of leptons in the decay $H \to W^ + W^ - \to l^ + v_l l^ - \bar v_l $ .     

Group algebras whose units satisfy a group identity

Let be the group algebra of a torsion group over an infinite field . Let be the group of units of . We prove that if satisfies a group identity, then satisfies a polynomial identity. This confirms a conjecture of Brian Hartley.

     

Constructing free subgroups of integral group ring units

Let be an arbitrary group. It is proved that if contains a bicyclic unit , then is a nonabelian free subgroup of invertible elements.