and δj = sin 2 π k+2 / sin π(j+1) k+2 . They were first proved by Kirillov and Reshetikhin [1]. The right hand side of this identity is equal to π 2 6 times the central charge of an integrable level k representation of the affine Kac-Moody Lie algebra ŝl2. This number appears in the asymptotics of the character of such a representation. Following the general approach taken in our previous work ...

Let F be a local non-archimedian field and let ψ : F → C be a nontrivial additive character of F . To this data one associates a meromorphic function γψ : π 7→ γψ(π) on the set of irreducible representations of the group GL(n, F ) in the following way. Consider the invariant distribution Φψ := ψ(tr(g))| det(g)|n|dg| on GL(n, F ), where |dg| denotes a Haar distribution on GL(n, F ). Although the...

A portfolio of photochemical transformations found in a variety areas can be rationalized through consideration either gain 4nπ-electron aromaticity or relief (4n+2) π-electron antiaromaticity excited states ππ* character. These back-of-an-envelope tools provided by Baird's rule serve as compass for excursions electronically states. More information the Review H. Ottosson and co-workers (DOI: 1...

In the mol-ecule of 3-chloro-2-(4-methyl-phen-yl)-2H-pyrazolo-[3,4-b]quinoline, C17H12ClN3, (I), the dihedral angle between the planes of the pyrazole ring and the methyl-ated phenyl ring is 54.25 (9)°. The bond distances in the fused tricyclic system provide evidence for 10-π delocalization in the pyrazolo-pyridine portion of the mol-ecule, with diene character in the fused carbocyclic ring. I...

The optoelectronic nature of two-dimensional sheets of sp(2)-hydridized carbons (for example, graphenes and nanographenes) can be dramatically altered and tuned by altering the degree of π-extension, shape, width and edge topology. Among various approaches to synthesize nanographenes with atom-by-atom precision, one-shot annulative π-extension (APEX) reactions of polycyclic aromatic hydrocarbon...

In this paper, we consider the homogeneous one-dimensional wave equation on [0, π] with Dirichlet boundary conditions, and observe its solutions on a subset ω of [0, π]. Let L ∈ (0, 1). We investigate the problem of maximizing the observability constant, or its asymptotic average in time, over all possible subsets ω of [0, π] of Lebesgue measure Lπ. We solve this problem by means of Fourier ser...