A direct approach to convergence of multivariate,nonhomogeneous, Padé approximants

We present a direct approach for proving convergence in measure/product capacity of multivariate, nonhomogeneous, Padé approximants. Previous approaches have involved projection onto Padé-type approximation in one variable, and only yielded convergence in (Lebesgue) measure.     

Logarithmic Sobolev Inequalities for Pinned Loop Groups

LetGbe a connected compact type Lie group equipped with anAd_G-invariant inner product on the Lie algebra ofG. Given this data there is a well known left invariant “H¹-Riemannian structure” on =(G)—the infinite dimensional group of continuous based loops inG. Using this Riemannian structure, we define and construct a “heat kernel”ν_T(g₀, ·) associated to the Laplace–Beltrami operator on (G). HereT>0,g₀∈(G), andν_T(g₀,·) is a certain probability measure on (G). For fixedg₀∈(G) andT>0, we use the measureν_T(g₀,·) and the Riemannian structure on (G) to construct a “classical” pre-Dirichlet form. The main theorem of this paper asserts that this pre-Dirichlet form admits a logarithmic Sobolev inequality.     

Kinetic and thermodynamic preferences in aryl vs benzylic C-H bond activation with cationic Pt(II) complexes

Anhydrous cationic Pt(II) complexes [(NN)Pt(CH3)(CF3CD2OD)]+ (1, NN = ArN=C(Me)-C(Me)=NAr), which are obtained by reaction of (NN)Pt(CH3)2 with B(C6F5)3 in CF3CD2OD, activate C-H bonds of benzene and methylbenzenes, with enhanced reactivity compared to the previously prepared equilibrium mixtures with the (thermodynamically favored) aquo complexes. For methylbenzenes (toluene, p-xylene, mesitylene), activation at the aromatic and benzylic positions are kinetically competitive, but the product of the latter is strongly favored thermodynamically. This unusual trend is attributed to formation of eta3-benzyl structures, which can be observed spectroscopically for 1,4-diethylbenzene activation.     

Naphthalin und Naphthalinderivate

Ohne Zusammenfassung     

Bounds for extreme zeros of some classical orthogonal polynomials

We use mixed three term recurrence relations typically satisfied by classical orthogonal polynomials from sequences corresponding to different parameters to derive upper (lower) bounds for the smallest (largest) zeros of Jacobi, Laguerre and Gegenbauer polynomials.