Linear and non-linear optical properties of indeno[2,1-b]fluorene (1) and its structural isomers with 20 π-electrons have been studied using many body methods. As compared to other π electron systems of similar conjugation length, the experimentally measured optical gap (vertical excitation energy) and the singlet-triplet gap of 1 are quite small. The diradical character calculated using the ab...

Abstract. Let L(s,π × π) be the Rankin–Selberg L-function attached to automorphic representations π and π. Let π̃ and π̃ denote the contragredient representations associated to π and π. Under the assumption of certain upper bounds for coefficients of the logarithmic derivatives of L(s,π × π̃) and L(s,π × π̃), we prove a log-free zero-density estimate for L(s,π × π) which generalises a result due to...

Infinitene was synthesized in a previous study 2021, and the molecule showed high strain energy. It not clear how affected aromatic character of molecule. To discuss this problem, properties dodecacene, [12]circulene, infinitene have been studied. The structures these compounds optimized at DFT/B3LYP/6-311G + (d,p) level theory, energy π orbitals has used to determine D’ index aromaticity. D′ f...

Let ∧ : GLn(C) −→ GLN (C), where N = n(n−1) 2 , be the map given by the exterior square. Then Langlands’ functoriality predicts that there is a map from cuspidal representations of GLn to automorphic representations of GLN , which satisfies certain canonical properties. To explain, let F be a number field, and let A be its ring of adeles. Let π = ⊗ v πv be a cuspidal (automorphic) representatio...

We examine a two-dimensional Fermi liquid with a Fermi surface which touches the Umklapp surface first at the 4 points (±π/2, ±π/2) as the electron density is increased. Umklapp processes at the 4 patches near (±π/2, ±π/2) lead the renor-malization group equations to scale to strong coupling resembling the behavior of a 2-leg ladder at half-filling. The incompressible character of the fixed poi...

We examine a two-dimensional Fermi liquid with a Fermi surface which touches the Umklapp surface first at the 4 points (±π/2, ±π/2) as the electron density is increased. Umklapp processes at the 4 patches near (±π/2, ±π/2) lead the renor-malization group equations to scale to strong coupling resembling the behavior of a 2-leg ladder at half-filling. The incompressible character of the fixed poi...

We prove an explicit formula for the conductor of an irreducible, admissible representation of GL(n, F ) twisted by a character of F× where the field F is local and non-archimedean. The components of our formula are analysed, both explicitly and on average, for application to the analytic study of automorphic forms on GL(n). We also demonstrate that “functoriality preserves depth” for such Rank...

The title compound, C20H19IS, features a 1,3-disubstituted azulene involving an ethynylene elongated 4-(tert-butyl-sulfanyl)-phenyl sidearm and an iodine atom as the substituents. The azulene ring system is almost planar (r.m.s. deviation = 0.012 Å) and subtends a dihedral angle of 35.7 (1)° with the benzene ring. As a result of the inherent dipole character of the azulene core, a supra-molecul...

conjugation, c, 5anti-cyclotomic p-adic L-function, L (π), 6Atkin–Serre operator, Θord, 13 canonical pairing, ( ,)A, 23convergent modular form, M(m,K), 14admissible, 15of finite tame level, M[ (m,K), 14stable, M[ (m,K)♥, 14universal, 15 distribution algebraA-related, D(A,K), 25ω-related, D(ω,K), 25π-related, D(π), 4 global Lubin–Tate different...