The Angle Defect for Odd-Dimensional Simplicial Manifolds

In a 1967 paper, Banchoff stated that a certain type of polyhedral curvature, that applies to all finite polyhedra, was zero at all vertices of an odd-dimensional polyhedral manifold; one then obtains an elementary proof that odd-dimensional manifolds have zero Euler characteristic. In a previous paper, the author defined a different approach to curvature for arbitrary simplicial complexes, based upon a direct generalization of the angle defect. The generalized angle defect is not zero at the simplices of every odd-dimensional manifold. In this paper we use a sequence based upon the Bernoulli numbers to define a variant of the angle defect for finite simplicial complexes that still satisfies a Gauss-Bonnet-type theorem, but is also zero at any simplex of an odd-dimensional simplicial complex K (of dimension at least 3), such that χ(link(ηⁱ, K)) = 2 for all i-simplices ηⁱ of K, where i is an even integer such that 0 ≤ i ≤ n – 1. As a corollary, an elementary proof is given that any such simplicial complex has Euler characteristic zero.     

The role of the pion cloud in the interpretation of the valence light-cone wavefunction of the nucleon

The pion cloud renormalises the light-cone wavefunction of the nucleon which is measured in hard, exclusive photon-nucleon reactions. We discuss the leading twist contributions to high-energy exclusive reactions taking into account both the pion cloud and perturbative QCD physics. The nucleon’s electromagnetic form-factor at high Q² is proportional to the bare nucleon probability Z and the cross-sections for hard (real at large angle or deeply virtual) Compton scattering are proportional to Z². Our present knowledge of the pion-nucleon system is consistent with Z = 0.7 ± 0.2. If we apply just perturbative QCD to extract a light-cone wavefunction directly from these hard exclusive cross-sections, then the light-cone wavefunction that we extract measures the three valence quarks partially screened by the pion cloud of the nucleon. We discuss how this pion cloud renormalisation effect might be understood at the quark level in terms of the (in-)stability of the perturbative Dirac vacuum in low energy QCD.     

A new technique for spatially resolved thermal lensing measurements

A new method is presented for spatially resolved thermal lensing measurements using multiple narrow probe beams and a two-dimensional array detector. The method is applied to an Er, Tm, Ho: YAG laser rod. No significant deviation from a parabolic temperature profile has been found although there is extraordinarily strong thermal lensing in the crystal. Thermo-optical constants of the material are reported.     

On a theorem of Shchepin and Repovš concerning the smoothness of compacta

We show that a theorem of Shchepin and Repovš concerning the smoothness of compacta follows from the theory of semicontinuous relations.     

(α-Nitroalkyl)-ONN-azoxysulfones and some of their transformations

A regioselective method for the synthesis of [(-nitroalkyl)-ONN-azoxy]alkyl- and-arylsulfones by oxidative condensation of pseudonitroles with aliphatic and aromatic sulfamides under the action of dibromoisocyanurate (DBI) was proposed. The behavior of the azoxysulfones obtained toward acids and bases as well as futher transformations of the products of acid hydrolysis into salts and halo-derivatives of nitroalkylazoxysulfones were investigated.Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 7, pp. 1267–1270, July, 1994.     

Immanant positivity for Catalan-Stieltjes matrices

We give some sufficient conditions for the nonnegativity of immanants of square submatrices of Catalan-Stieltjes matrices and their corresponding Hankel matrices. To obtain these sufficient conditions, we construct new planar networks with a recursive nature for Catalan-Stieltjes matrices. As applications, we provide a unified way to produce inequalities for many combinatorial polynomials, such as the Eulerian polynomials, Schröder polynomials, and Narayana polynomials.     

Evidence for a two-step mechanism in electronically selective single-walled carbon nanotube reactions

Covalent and noncovalent chemistries that are selective to single-walled carbon nanotubes of a particular electronic type have become increasingly important for electronic structure separation and on-chip modification of nanoelectronic devices. By monitoring transient Raman spectroscopy and photoluminescence (PL) during a reaction with 4-chlorobenzene diazonium in aqueous solution, evidence for a characteristic two-step mechanism with two distinct time constants is uncovered. A long-lived intermediate selectively and noncovalently binds and partially dopes the nanotube surface (tau = 2.4 min). A slower, covalent reaction is tracked using the time-dependent increase in the disorder mode in Raman (tau = 73 min). The transient Raman and PL data are well described using a series of two first-order reactions. The covalent bonding step can be deactivated by changing the structure of the surfactant adsorbed phase, further supporting the mechanism.