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.     

The transition from the spin-glass to the ferromagnetic state in the bond-random Ising model in the face-centred cubic lattice

The boundary between the spin-glass state and the ferromagnetic state (p_F-G) of the bond-random (±J) Ising model in the face-centred cubic lattice at T = 0 is calculated by the method of tetrahedron approximation in the simple version. The obtained value is, p_F-G = 0.682, which is a little larger than the triple point p_t = 0.654, and the model shows the reentrant behavior.     

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.     

Infrared laser radar technique using heterodyne detection for range-resolved sensing of air pollutants

An infrared, pulsed heterodyne laser radar using differential absorption technique with tunable lasers is proposed as a practical means of measuring dispersed air pollutants with range resolution. A system analysis shows that this scheme offers an adequate sensitivity for ranges up to several km.     

Sonochemical preparation of composite nanoparticles of Au/gamma-Fe2O3 and magnetic separation of glutathione

We prepared Au/gamma-Fe2O3 composite nanoparticles by sonochemically reducing Au(III) ions employing no stabilizer in the aqueous solution to form stable Au nanoparticles and allowing them to attach onto the surface of gamma-Fe2O3 particles with an average size of 21 nm. Size of the formed Au nanoparticle depended on the initial concentration of Au(III) ions. The number of the Au nanoparticles, supported on each gamma-Fe2O3 particle was controlled by changing the relative amounts of Au(III) ions and gamma-Fe2O3 particles. The composite nanoparticles exhibited a high affinity with glutathione, a tripeptide with mercapto group so that separation and manipulation of glutathione in aqueous solutions could be performed by application of external magnetic field. Because the surfaces of the Au nanoparticles were not shielded by any stabilizers, or naked, sonochemically prepared Au/gamma-Fe2O3 composite nanoparticles seemed to show stronger affinity to the glutathione than those by the radiochemical method.