A loop group method for minimal surfaces in the three-dimensional Heisenberg group

We characterize constant mean curvature surfaces in the three-dimensional Heisenberg group by a family of flat connections on the trivial bundle \D \times \GL over a simply connected domain $\mathbb{D}$ in the complex plane. In particular for minimal surfaces, we give an immersion formula, the so-called Sym-formula, and a generalized Weierstrass type representation via the loop group method.Comment: 40 pages, v2: The argument for branch points has been fixed and the references have been updated. v3: The argument for canonical examples has been fixed and the classification for homogeneous surfaces has been added v4: Some typos are fixed and Remark 5.4 (3) is adde

Minimal surfaces with non-trivial topology in the three-dimensional Heisenberg group

We study symmetric minimal surfaces in the three-dimensional Heisenberg group $\mathrm{Nil}_3$ using the generalized Weierstrass type representation, the so-called loop group method. In particular, we will discuss how to construct minimal surfaces in $\mathrm{Nil}_3$ with non-trivial topology. Moreover, we will classify equivariant minimal surfaces given by one-parameter subgroups of the isometry group $\mathrm{Iso}_{\circ}(\mathrm{Nil}_3)$ of $\mathrm{Nil}_3$.Comment: 49 page

New Spectrophotometric Determination of Chromium and Cobalt with Disodium Ethylenediaminetetraacetate

The light absorptions of complexes between EDTA and various metallic ions were measured by using Beckmann model DU spectrophotometer and it was found that a new double complex consisting of EDTA, Cr_2O_7^ and Co_ had strong absorbancy. Utilizing the nature of this complex spectrophotometric determinations of chromium and cobalt were investigated and 5～30γ/ml of chromium and 10～80γ/ml of cobalt could be determined under certain conditions. The composition of this complex was suggested to be (Co-EDTA)_7Cr_2O_7

Polynomial-Time Algorithm for Controllability Test of a Class of Boolean Biological Networks

<p/> <p>In recent years, Boolean-network-model-based approaches to dynamical analysis of complex biological networks such as gene regulatory networks have been extensively studied. One of the fundamental problems in control theory of such networks is the problem of determining whether a given substance quantity can be arbitrarily controlled by operating the other substance quantities, which we call the controllability problem. This paper proposes a polynomial-time algorithm for solving this problem. Although the algorithm is based on a sufficient condition for controllability, it is easily computable for a wider class of large-scale biological networks compared with the existing approaches. A key to this success in our approach is to give up computing Boolean operations in a rigorous way and to exploit an adjacency matrix of a directed graph induced by a Boolean network. By applying the proposed approach to a neurotransmitter signaling pathway, it is shown that it is effective.</p

Open-architecture Implementation of Fragment Molecular Orbital Method for Peta-scale Computing

We present our perspective and goals on highperformance computing for nanoscience in accordance with the global trend toward "peta-scale computing." After reviewing our results obtained through the grid-enabled version of the fragment molecular orbital method (FMO) on the grid testbed by the Japanese Grid Project, National Research Grid Initiative (NAREGI), we show that FMO is one of the best candidates for peta-scale applications by predicting its effective performance in peta-scale computers. Finally, we introduce our new project constructing a peta-scale application in an open-architecture implementation of FMO in order to realize both goals of highperformance in peta-scale computers and extendibility to multiphysics simulations.Comment: 6 pages, 9 figures, proceedings of the 2nd IEEE/ACM international workshop on high performance computing for nano-science and technology (HPCNano06