Chamber behavior of double Hurwitz numbers in genus 0

We study double Hurwitz numbers in genus zero counting the number of covers CP¹→CP¹ with two branching points with a given branching behavior. By the recent result due to Goulden, Jackson and Vakil, these numbers are piecewise polynomials in the multiplicities of the preimages of the branching points. We describe the partition of the parameter space into polynomiality domains, called chambers, and provide an expression for the difference of two such polynomials for two neighboring chambers. Besides, we provide an explicit formula for the polynomial in a certain chamber called totally negative, which enables us to calculate double Hurwitz numbers in any given chamber as the polynomial for the totally negative chamber plus the sum of the differences between the neighboring polynomials along a path connecting the totally negative chamber with the given one.     

Vortex–antivortex states in nanostructured superconductor–ferromagnet hybrids

The formation of vortex–antivortex states in a superconducting film with a square array of magnetic dipoles magnetized perpendicularly to the film is investigated in the framework of the time-dependent Ginzburg–Landau equations. It is shown that a possible route to obtain equilibrium states is obtained following an experimentally realizable field-cooling procedure. The states thus obtained demonstrate a rich variety of phases, depending on magnetic moment intensity and dipole array-to-superconducting film distance. For instance, in the region of the phase diagram where each dipoles is able to generate N = 2 vortex–antivortex pairs, the antivortices induced by the negative stray fields of the dipoles undergo two transitions before ultimately merging into doubly-quantized giant antivortices. For N = 4, a state consisting on a three-quanta giant vortex below each dipole and an interstitial vortex–antivortex molecule was observed. Such state is thermodynamically stable and is induced by the fourfold symmetry of the dipole array, similar to symmetry-induced vortex–antivortex molecules found in mesoscopic superconductors.     

Some identities between basic hypergeometric series deriving from a new Bailey-type transformation

We prove a new Bailey-type transformation relating WP-Bailey pairs. We then use this transformation to derive a number of new 3- and 4-term transformation formulae between basic hypergeometric series.     

线性空间偶的运动公式

本文研究了线性空间偶的运动公式．利用活动标架法．在获得相交线性空间偶的运动密度公式的基础上，得到一系列有关相交线性空间偶的运动公式．     

一维p-Laplacian方程边值问题多解的存在性

利用Clark定理，研究了一维p-Laplacian方程边值问题多解的存在性，得到了这类边值问题至少有n对非平凡解的充分条件．     

II. Ionic association and mobility in propylene carbonate

Conductance data are reported for Ph₄AsPic, Ph₄PPic, Ph₄SbPic, Hex₄NPic, Bu₄PPic, Et₄NSbCl₆ in propylene carbonate at 25°C in the concentration range 1×10^–4 to 15×10^–4 M. The data were analyzed by the Justice modification of the Fuoss-Hsia equation and all salts studied were found to be associated and to form solvent separated ion pairs. Application of the Barthel-Bjerrum model of ion association permitted calculation of the non coulombic portion of the potentials of mean force, W_±. Ionic limiting equivalent conductances of six ions were calculated using known values of R₄N⁺, and Pic^– ions. Walden products of ions in propylene carbonate were examined in the light of modern ion mobility theories, including Boyd-Zwanzig, Hubbard-Onsager, and Hubbard-Kayser models of ion solvent interactions.     

Historical perspectives on living anionic polymerization

A brief overview of the role that Dr. Michael Szwarc has played in unraveling the mechanism of living anionic polymerization is presented. Emphasis is placed on the different ionic species that control the propagation reaction in ether-type solvents. © 2002 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 40: 2101–2107, 2002