Sigma Models and Minimal Surfaces

Correspondence is established between sigma models, minimal surfaces and the Monge–Ampére equation. The Lax pairs of the minimality condition of the minimal surfaces and the Monge–Ampére equations are given. Existence of infinitely many nonlocal conservation laws is shown and some Bäcklund transformations are also given.     

Charmless Hadronic Decays B→VV in the Topcolor-Assisted Technicolor Model

Based. On the effective Hamiltonian with the generalized factorization approach, we calculate the branchingratios and CP asymmetries of B → VV decays in the Topcolor-assisted Technicolor (TC2) model. Within the consideredparameter space we find that: (a) for the penguin-dominated B → K* φ and K*0 φ decays, the new physics enhancementsto the branching ratios are around 40%; (b) the measured branching ratios of B →K* φ and K*0φ decays prefer therange of 3 Neffc 5; (c) the SM and TC2 model predictions for the branching ratio B(B →ρ ρ0) are only about halfof the Belle‘s measurement; and (d) for most B → VV decays, the new physics corrections on their CP asymmetries are generally small or moderate in magnitude and insensitive to the variation of mπ and Neffc.     

Countable network weight and multiplication of Borel sets

A space Borel multiplies with a space if each Borel set of is a member of the -algebra in generated by Borel rectangles. We show that a regular space Borel multiplies with every regular space if and only if has a countable network. We give an example of a Hausdorff space with a countable network which fails to Borel multiply with any non-separable metric space. In passing, we obtain a characterization of those spaces which Borel multiply with the space of countable ordinals, and an internal necessary and sufficient condition for to Borel multiply with every metric space.

     

π -Type and σ -type cation- π complexes of atomic cations

MP2/6-31+G* calculations were performed on the cation- complexes of ethylene, cyclobutadiene and benzene with a number of atomic cations. It was found that except B⁺ all the atomic cations form -type cation- complexes with ethylene. On the other hand, with cyclobutadiene Li⁺, N⁺, Na⁺, P⁺ and K⁺ form -type complexes, whereas H⁺, F⁺, and Cl⁺ form covalent -type complexes. With benzene Li⁺, B⁺, Na⁺, Al⁺, and K⁺ form -type complexes whereas H⁺, F⁺, and Cl⁺ form -type complexes. It was concluded that the driving force to form the -type complex is chemical bonding, and that for metal cations to form -type complexes is non-covalent interaction.     

Tetraaryl-methane analogues in group 14—V. Distortion of tetrahedral geometryin terms of through-space π–π and π–σ interactions andNMR sagging in terms of π–σcharge transfer

44 members of thecompound series Ph_4−nMR_n (M=Si, Ge, Sn, Pb; R=o-, m-, p-Tol; n=0–4) were synthesized (15 newcompounds). The crystal structures of Ph₃Sn (o-Tol) and PhSn (o-Tol)₃ were determined and compared to 16 known structures. Subject to the distanced (M–C), an interplay between through-space π–π repulsion and π–σ attraction leads to either elongated or compressed tetrahedral geometry. ²⁹ Si-, ¹¹⁹ Sn- and ²⁰⁷ Pb-NMR chemical shifts were determined in solution and in the solid state. ⁷³ Ge chemical shifts were measured only in solution. Anupfield or downfield sagging of the chemical shifts along each series is rationalized in terms of a π–σcharge transfer which is constrained by torsion of the aromatic groups.     

Study of pure and semileptonic decays of Ds meson within R-parity violating supersymmetric model

We present the comaprative study of semileptonic and leptonic decays of Ds, D±and D0meson（D →M l＋-αl-β, D → l＋αlβ, D → l＋αvα;α,β=e,μ） within the framework of R-parity violating the（ Rp） Minimal Supersymmetric Standard Model（MSSM）. The comparison shows that combination and product couplings,（λβiα λ＊ ij qor λβqkλ＊αj k）contribution to the branching fractions of the said processes（under consideration） is consistent with or comparable to the experimental measurements in most of the cases. However, some cases exist where these contributions are highly suppressed. We identify such cases in our analysis and single out the important ones suitable for exploring in the future and current experiments.     

Halogen Bonding: An Interim Discussion

Halogen bonding is a noncovalent interaction that is receiving rapidly increasing attention because of its significance in biological systems and its importance in the design of new materials in a variety of areas, for example, electronics, nonlinear optical activity, and pharmaceuticals. The interactions can be understood in terms of electrostatics/polarization and dispersion; they involve a region of positive electrostatic potential on a covalently bonded halogen and a negative site, such as the lone pair of a Lewis base. The positive potential, labeled a σ hole, is on the extension of the covalent bond to the halogen, which accounts for the characteristic near‐linearity of halogen bonding. In many instances, the lateral sides of the halogen have negative electrostatic potentials, allowing it to also interact favorably with positive sites. In this discussion, after looking at some of the experimental observations of halogen bonding, we address the origins of σ holes, the factors that govern the magnitudes of their electrostatic potentials, and the properties of the resulting complexes with negative sites. The relationship of halogen and hydrogen bonding is examined. We also point out that σ‐hole interactions are not limited to halogens, but can also involve covalently bonded atoms of Groups IV–VI. Examples of applications in biological/medicinal chemistry and in crystal engineering are mentioned, taking note that halogen bonding can be “tuned” to fit various requirements, that is, strength of interaction, steric factors, and so forth.     

Super strong nuclear force caused by migrating K? mesons - Revival of the Heitler-London-Heisenberg scheme in kaonic nuclear clusters

We have studied the structure of K⁻pp comprehensively by solving this threebody system in a variational method, starting from the Ansatz that the Λ(1405) resonance (≡Λ^*) is a K⁻p bound state. The structure of K⁻pp reveals a molecular feature, namely, the K⁻ in Λ^* as an “atomic center” plays a key role in producing strong covalent bonding with the other proton. We point out that strongly bound $\bar{K}$ nuclear systems are formed by “super strong” nuclear force due to migrating real bosonic particles $\bar{K}$ a la Heitler-London-Heisenberg, whereas the normal nuclear force is caused by mediating virtual mesons. We have shown that the elementary process, p + p → K⁺ + Λ^* + p, which occurs in a short impact parameter and with a large momentum transfer, leads to unusually large self-trapping of Λ^* by the involved proton, since the Λ^*-p system exists as a compact doorway state propagating to K⁻pp.