Influence of the configuration of the amine nitrogen atom on the efficiency of fluorescence of 4-aminonaphthalimide derivatives

The fluorescence properties of 4-aminonaphthalimide were studied in relation to the size of the heterocycle incorporating the amine nitrogen atom, the temperature, and the polarity of the medium. Increases in the temperature, polarity of the medium, and heterocycle size increase the efficiency of the nonradiative deactivation and insignificantly affect the fluorescence rate. The low efficiency of fluorescence of 4-aminonaphthalimides in polar solvents is associated with formation of a nonfluorescing charge-transfer state. The efficiency of fluorescence of 4-aminonaphthalimides is directly associated with the inversion barrier of the amine nitrogen atom, which, in turn, is determined by the structure of the heterocyclic amine substituent.Translated from Zhurnal Obshchei Khimii, Vol. 74, No. 11, 2004, pp. 1858–1863.Original Russian Text Copyright © 2004 by Mednykh, Manaev, Volchkov, Uzhinov.This revised version was published online in April 2005 with a corrected cover date.     

The volume of the Lambert cube in spherical space

Mathematical Notes - We study multipoint rational approximations with free poles for the beta function. The denominators of the approximations satisfy orthogonality relations with variable weight...     

Enumeration of maps regardless of genus: Geometric approach

We use the conceptual idea of “maps on orbifolds” and the theory of the non-Euclidean crystallographic groups (NEC groups) to enumerate rooted and unrooted maps (both sensed and unsensed) on surfaces regardless of genus. As a consequence we deduce a formula for the number of chiral pairs of maps. The enumeration principle used in this paper is due to Mednykh (2006) [15], it counts the number of conjugacy classes of subgroups in NEC groups which are in one-to-one correspondence with unrooted (sensed or unsensed) maps.     

Classification up to equivalence of the holomorphic mappings of riemann surfaces of low genus

We give a complete classification up to equivalence of the holomorphic mappings of a Riemann surface of genus 3 onto a Riemann surface of genus 2. Also we establish that every Riemann surface of genus 3 has at most three holomorphic images of genus 2.     

Twofold unbranched coverings of genus two 3-manifolds are hyperelliptic

A closed 3-dimensional manifold is hyperelliptic if it admits an involution such that the quotient space of the manifold by the action of the involution is homeomorphic to the 3-sphere. We prove that a twofold unbranched covering of a genus two 3-manifold is hyperelliptic. This result is reminiscent of a theorem, which seems to have first appeared in a paper by Enriques and which has been reproved more recently by Farkas and Accola, which states that a twofold unbranched covering of a Riemann surface of genus two is hyperelliptic.     

Harmonic morphisms of graphs and the Riemann–Hurwitz theorem

Several versions of the Riemann–Hurwitz theorem for branched coverings of graphs are presented. A larger class of graphs which may have not only multiple edges but also loops and darts is considered. This makes it possible to render the class of graphs closed with respect to morphisms arising as quotient maps for actions of finite groups.     

Spherical coxeter groups and hyperelliptic 3-manifolds

Reflection groups of Coxeter polyhedra in three-dimensional Thurston geometries are examined. For a wide class of Coxeter groups, the existence of subgroups of finite index that uniformize hyperelliptic 3-manifolds is established. Translated fromMatematicheskie Zametki, Vol. 66, No. 2, pp. 173–177, August, 1999.