On Swan conductors for Brauer groups of curves over local fields

For an element of the Brauer group of a curve over a local field, we define the ``Swan conductor' of , which measures the wildness of the ramification of . We give a relation between and Swan conductors for Brauer groups of henselian discrete valuation fields defined by Kato.

     

G. Martens′ Dimension Theorem for Curves of Odd Gonality

For a smooth projective irreducible algebraic curve C of odd gonality, the maximal possible dimension of the variety of special linear systems W _d ^r (C) is d-3r by a result of M. Coppens et al. Furthermore it is known that if the maximum dimension of W(C) for a curve C of odd gonality is attained then C is of very special type of curves by the recent progress made by G. Martens. The purpose of this paper is to chase an extension of the result of G. Martens; if dim W(C)=d-3r-1 for a curve C of odd gonality for some dg-4 and r1, then C must be either a smooth plane sextic, a pentagonal curve of bounded genus or a smooth plane octic.     

Nonlinear effects of electrolyte diodes and transistors in a polymer gel medium

The polarization curve of an acid-base interface in a hydrogel medium has a diode characteristic. Two of each such electrolyte diodes can be combined to give an electrolyte transistor. When a salt is added to the alkaline or to the acidic part of a reverse biased electrolyte diode, the current response is highly nonlinear. If the salt is added to the acidic side, even bistability can be observed. This bistability can generate complex oscillations in a base-acid-base electrolyte transistor. These nonlinear effects are studied experimentally and theoretically. While the nonlinear salt effect can be explained with the Nernst-Planck equations, to understand the bistable behavior further investigations are necessary. (c) 1999 American Institute of Physics.     

Variable-priority queue and doughnut routing

This paper proposes a new data structure called a variable-priority queue. The queue supports, in addition to the ordinary queue operations, an operation MIN to find an item of minimum key and three operations to change keys of items. Any sequence of these m operations can be processed in O(m) time. Furthermore, as its application, this paper presents two efficient algorithms for network problems. The first finds multicommodity flows in cycles in linear time. The second, using the first, finds edge-disjoint paths connecting terminal pairs in a doughnut-shaped grid. The grid is bounded by two nested rectangles, and terminals are specified on the two rectangular boundaries outside the four corners. If there are k terminal pairs and all the terminals are ordered in clockwise order around rectangles, then the algorithm decides in O(k) time whether there are edge-disjoint paths connecting terminals in the grid, and actually finds edge-disjoint paths in O(k log k) time.     

Fundamental constants and higher-dimensional universe

In order to study the origin of the fundamental constants and Dirac's large number, a cosmological solution in vacuum is presented in a seven-dimensional universe which is defined by adding extra three coordinates (e ² G/c ⁴)^1/2, (hG/c ³)^1/2 and (Gm/c ²) to the four-dimensional spacetime coordinates. It has common features with Chodos-Detweiler's solution. The parameters appearing in this theory are estimated to meet the conditions required by the cosmological first-order phase transition and Dirac's large number hypothesis.     

A novel cyclodimerization of 3-methyl-3-butenenitrile. An efficient synthesis of 4-cyanoisophorone

Dimerization of 3-methyl-3-butenenitrile (1) by lithium dialkylamide gave selectively 3,5,5-trimethyl-1-amino-4-cyanocyclohexa-1,3-diene (2), which was easily hydrolyzed by aqueous acid to afford 4-cyanoisophorone (3,5,5-trimethyl-4-cyano-cyclohex-2-enone) (3) quantitatively.     

Magneto-volume effect and invar phenomena in ferromagnetic metals

The magneto-volume effect is discussed in terms of the recent unified theory of ferromagnetic metals based on general spin fluctuations. Explanations are given for the large negative thermal expansion observed in weakly ferromagnetic metals and for the invar effect in some f.c.c. alloys. Large thermal expansion in nearly ferromagnetic metals is also pointed out.     

Extremal graphs of diameter at most 6 after deleting any vertex

Suppose G is a graph of n vertices and diameter at most d having the property that, after deleting any vertex, the resulting subgraph has diameter at most 6. Then G contains at least max{n, (4n - 8)/3} edges if 4 ≤ d ≤ 6.