Let F be a nonarchimedean field of characteristic zero, let q be the order of the residue class field of F , let χ be a quasi-character of F×, and let n be a positive integer. Let π ∈ Irr(Sp(n, F )). Just as for representations of the general linear group [GodementJacquet, 1972], [Jacquet, 1979] zeta integrals have been defined for π [Piatetski-Shapiro, Rallis, 1986, 1987a, 1987b]. Associated t...

The excitation spectra of linear atomic chains of silver and gold with various sizes have been calculated using time-dependent density functional theory. Silver chains show longitudinal and transverse peaks as well as a low-intensity d-band. The longitudinal peak, corresponding to the HOMO-LUMO transition (along the main axis of the chain), shifts linearly to the red as the length of the system...

We report on results of computational studies of the interaction of slow electrons with the purine and pyrimidine bases of DNA, as well as with their associated nucleosides and nucleotides. The calculations focus on characterisation of the π∗ resonances associated with the bases and also provide general information on the scattering of slow electrons by these targets. High-level studies of the ...

stability of the π-π stacking interactions in the ben||substituted-coronene and hfben||substituted-coronene complexes was studied using the computational quantum chemistry methods (where ben and hfben are benzene and hexaflourobenzene, || denotes π-π stacking interaction, substituted-coronene is coronene molecule which substituted with four x groups, and x= nh2, ch3, oh, h, f, cf3, cn and no). ...

In this work, two different classes of polyaromatic hydrocarbon (PAH) systems have been investigated in order to characterize the amount of polyradical character and to localize the specific regions of chemical reactivity: (a) the non-Kekulé triangular structures phenalenyl, triangulene and a π-extended triangulene system with high-spin ground state and (b) PAHs based on zethrenes, p-quinodimet...

We show the consistency of statement: “the set of regular cardinals which are the character of some ultrafilter on ω is not convex”. We also deal with the set of π-characters of ultrafilters on ω.

Let k be a non-Archimedean local field of characteristic 0. Let D be a division algebra with center k and index n. The group D∗ is a locally compact group which is compact modulo the center. Its complex irreducible representations are finite dimensional. If π is an irreducible representation of D∗ which is self-dual, i.e., if π∨ denotes the dual of π, π∨ ∼= π, then there exists a D∗-invariant, ...

We show that the A-polynomial A(L,M) of a 2-bridge knot b(p, q) is irreducible if p is prime, and if (p − 1)/2 is also prime and q , 1 then the L-degree of A(L,M) is (p−1)/2. This shows that the AJ conjecture relating the A-polynomial and the colored Jones polynomial holds true for these knots, according to work of the second author. We also study relationships between the A-polynomial of a 2-b...

Let K/Q be a number field. Let π and π′ be cuspidal automorphic representations of GLd(AK) and GLd′(AK), and suppose that either both d and d′ are at most 2 or at least one of π and π′ is self-dual. We prove an effective log-free zero density estimate for the Rankin-Selberg L-function L(s, π ⊗ π′,K) when at least one of L(s, π,K) and L(s, π′,K) satisfies the generalized Ramanujan conjecture. Wi...

Let π be a Poisson structure on Rn vanishing at 0. It leads to a Kontsevich type star product ⋆π on C∞(Rn)[[ǫ]]. We show that 1. The evaluation map at 0 ev0 : C ∞(Rn) → C can in general not be quantized to a character of (C∞(Rn)[[ǫ]], ⋆π). 2. A given Poisson structure π vanishing at zero can in general not be extended to a formal Poisson structure πǫ also vanishing at zero, such that ev0 can be...