[1,3]-Dipolar cycloaddition of N-aryl sydnones to benzothiophene 1,1-dioxide, 1-cyclopropylprop-2-yn-1-ol and 1-(prop-2-ynyl)-1H-indole

[1,3]-Dipolar cycloadditions of N-aryl sydnones to benzothiophene 1,1-dioxide, 1-cyclopropylprop-2-yn-1-ol and 1-(prop-2-ynyl)indole gave fused pyrazole derivatives when carried out in refluxing toluene. While the first two dipolarophiles gave single regioisomers, this indolic derivative gave mixtures, the ratios of which appeared to be controlled by the phenyl substituents. Their structures were identified in the usual manner, supported by single crystal X-ray diffraction measurements.     

Group homomorphisms inducing isomorphisms in cohomology

In this article, we call a ring R right generalized semiregular if for any a ∈ R there exist two left ideals P, L of R such that lr(a) = P⊕ L, where P ? Ra and Ra ∩ L is small in R. The class of generalized semiregular rings contains all semiregular rings and all AP-injective rings. Some properties of these rings are studied and some results about semiregular rings and AP-injective rings are extended. In addition, we call a ring R semi-π-regular if for any a ∈ R there exist a positive integer n and e ² = e ∈ a ⁿ R such that (1 ? e)a ⁿ  ∈ J(R), the Jacobson radical of R. It is shown that a ring R is semi-π-regular if and only if R/J(R) is π-regular and idempotents can be lifted modulo J(R).     

Large core, multimode, chalcogenide glass fibre coupler by side-polishing

A novel method for obtaining a multimode optical coupler in chalcogenide glass fibre is described. The fibres used had a large $\text{ Ge }_{17}\text{ As }_{18}\text{ Se }_{65}$ Ge 17 As 18 Se 65 core comprising about 74 % of the total cross-sectional area with an optical cladding of $\text{ Ge }_{17}\text{ As }_{18}\text{ Se }_{62}\text{ S }_{3}$ Ge 17 As 18 Se 62 S 3 . A single arc-shaped U-groove was formed in each of two silicate glass blocks. A length of fibre was embedded into each groove and glued in place. The centre of each fibre length was subsequently side-polished. Finally two such embedded fibres were glued together in close contact to form the coupler, whilst monitoring the coupling ratio at the output.     

Mixing-driven equilibrium reactions in multidimensional fractional advection–dispersion systems

We study instantaneous, mixing-driven, bimolecular equilibrium reactions in a system where transport is governed by a multidimensional space fractional dispersion equation. The superdiffusive, nonlocal nature of the system causes the location and magnitude of reactions that take place to change significantly from a classical Fickian diffusion model. In particular, regions where reaction rates would be zero for the Fickian case become regions where the maximum reaction rate occurs when anomalous dispersion operates. We also study a global metric of mixing in the system, the scalar dissipation rate and compute its asymptotic scaling rates analytically. The scalar dissipation rate scales asymptotically as t^−(d+α)/α$t^{-(d+\alpha )/\alpha }$, where d$d$ is the number of spatial dimensions and α$\alpha$ is the fractional derivative exponent.     

Highly efficient design of spectrally engineered whispering-gallery-mode microlaser resonators

We present an accurate, reliable and versatile method for studying the effect of deformations on the characteristics of the high-Q whispering gallery (WG) modes supported by two-dimensional dielectric resonators (DR). An eigenvalue problem is formulated in terms of contour integral equations and further discretised with the method of analytical regularisation. Such a procedure significantly reduces the number of unknowns whilst providing high and controllable accuracy. Natural frequencies, Q-factors and field patterns of elliptical, flower- and egg-shaped DRs are calculated. Methods to enhance the Q-factors, provide directional light output, and parasitic mode suppression are discussed. The identification of WG modes is simplified by the symmetrical/asymmetrical mode separation included into the formulation of the problem and solution algorithm.     

Continuous Modular Design Problem: Analysis and Solution Algorithms

This article studies the continuous modular design (MD) problem. First, the article presents duality results for problem (MD) based upon the Wolfe duality theory for nonlinear programming. From these results, an optimality test for problem (MD) is derived that consists of solving a single, balanced transportation problem. Second, the article shows that two well-known optimization approaches, the generalized Benders decomposition and the separable programming approach of linear programming, each have the potential to solve efficiently large instances of problem (MD).This research was supported by a Summer Research Grant from the Warrington College of Business Administration, University of Florida, Gainesville, Florida. The author is indebted to Panos Pardalos for introducing the topic to him.     

Three-step Harmonic Solvmanifolds

The Lichnerowicz conjecture asserted that every harmonic Riemannian manifold is locally isometric to a two-point homogeneous space. In 1992, E. Damek and F. Ricci produced a family of counter-examples to this conjecture, which arise as abelian extensions of two-step nilpotent groups of type-H. In this paper we consider a broader class of Riemannian manifolds: solvmanifolds of Iwasawa type with algebraic rank one and two-step nilradical. Our main result shows that the Damek–Ricci spaces are the only harmonic manifolds of this type.     

A Strong Schottky Lemma for Nonpositively Curved Singular Spaces

Motivated by the question of faithfulness of the four-dimensional Burau representation, we study a generalization of the Schottky Lemma which is useful for studying actions on affine buildings.     

Analytic-numerical approach to non-linear problems in dielectric waveguides

A combined analytic-numerical approach is presented for investigations of electromagnetic signal propagation in dielectric waveguides containing a non-linear medium. The approach is based on the resolvent method for the Volterra integral equation describing an electromagnetic process. The proposed algorithm uses the exact expression for the solution to the integral equation for the electromagnetic field in the planar waveguide with time jump changing of the medium properties. In the case of a non-linear dielectric as the waveguide core the continuous change of the medium parameters is replaced by jump changes of the latter. This is the only approximation made in the algorithm. The resolvents that are constructed give the exact solution on each jump step. The results from some example numerical calculations are presented.     

Using concave envelopes to globally solve the nonlinear sum of ratios problem

This article presents a branch and bound algorithm for globally solving the nonlinear sum of ratios problem (P). The algorithm works by globally solving a sum of ratios problem that is equivalent to problem (P). In the algorithm, upper bounds are computed by maximizing concave envelopes of a sum of ratios function over intersections of the feasible region of the equivalent problem with rectangular sets. The rectangular sets are systematically subdivided as the branch and bound search proceeds. Two versions of the algorithm, with convergence results, are presented. Computational advantages of these algorithms are indicated, and some computational results are given that were obtained by globally solving some sample problems with one of these algorithms.