An affine manifold is a manifold with a distinguished system of affine coordinates, namely, an open covering by charts which map homeomorphically onto open sets in an affine space E such that on overlapping charts the homeomorphisms differ by an affine automorphism of E. Some, but certainly not all, affine manifolds arise as quotients Ω/Γ of a domain in E by a discrete group Γ of affine transfo...

The folding of RNA sequences into secondary structures is a simple yet biophysically grounded model of a genotype-phenotype map. Its computational and mathematical analysis has uncovered a surprisingly rich statistical structure characterized by shape space covering, neutral networks and plastogenetic congruence. I review these concepts and discuss their evolutionary implications.

The GHS attack is known as a method to map the discrete logarithm problem(DLP) in the Jacobian of a curve C0 defined over the d degree extension kd of a finite field k to the DLP in the Jacobian of a new curve C over k which is a covering curve of C0. Such curves C0/kd can be attacked by the GHS attack and index calculus algorithms. In this paper, we will classify all elliptic curves and hypere...

We study the covering dimension of (positive ) solutions to varoius classes of nonlinear equations based on the nontriviality of the fixed point index of a certain condensing map. Applications to semilinear equations and to nonlinear perturbations of the Wiener-Hopf integral equations are given.

A dense linkage map was constructed for the silkworm, Bombyx mori, containing 1018 genetic markers on all 27 autosomes and the Z chromosome. Most of the markers, covering approximately 2000 cM, were randomly amplified polymorphic DNAs amplified with primer-pairs in combinations of 140 commercially available decanucleotides. In addition, eight known genes and five visible mutations were mapped. ...

Refinement operators for triangular meshes as used in subdivision schemes or remeshing are discussed. A numbering scheme is presented, covering all refinement operators that (topologically) map vertices onto vertices. Using this characterization, some special properties of n-adic and √ 3-subdivision are easy to see.

In this paper, we propose a method to estimate the density of nodes for pedestrians and/or vehicles with information terminals. The method enables us to provide intelligent services which are environmentaware with highly dynamic movement of nodes such as intellectual navigation that tells the user the best route to detour congested regions. In the proposed method, each node is supposed to know ...

Eucommia ulmoides is an economically important tree species for both herbal medicine and organic chemical industry. Effort to breed varieties with improved yield and quality is limited by the lack of knowledge on the genetic basis of the traits. A genetic linkage map of E. ulmoides was constructed from a full-sib family using sequence-related amplified polymorphism, amplified fragment length po...