Remarks on unit indices of imaginary abelian number fields II

Satz 41 in Hasse's monograph [4] is modified because of the incorrectness of Satz 29. We investigate unit indices of imaginary abelian number fields of type (2,2) and (2,2, 2), some of which give counterexamples to Satz 41. We moreover give a relation between unit indices of certain imaginary fields of type (2,2²) and those of their real cyclic subfields.     

Covering vertices of a graph by k disjoint cycles

Let d, k and n be three integers with k3, d4k−1 and n3k. We show that if d(x)+d(y)d for each pair of nonadjacent vertices x and y of a graph G of order n, then G contains k vertex-disjoint cycles converting at least min{d,n} vertices of G.     

Gamma-ray spectroscopy of the neutron-rich Ni region through heavy-ion deep-inelastic collisions

Nuclei in the neutron-rich Ni region have been studied by γ-ray spectroscopy. Gamma-rays emitted from isomers, with T _1/2 > 1 ns, produced in heavy-ion deep-inelastic collisions were measured with an isomer-scope. The nuclear structure of the doubly magic ⁶⁸Ni and its neighbor ^69,71Cu is discussed on the basis of the shell model. Future experiments for more neutron-rich Ni nuclei are also viewed. Received: 1 May 2001 / Accepted: 4 December 2001     

Outflow refreshment angiography: A bright blood, bright static tissue technique

A new “bright blood” strategy, outflow refreshment imaging, is introduced in which a number of overlapping slices are excited in rapid succession. Flowing spins that refresh each overlapped slice portion contribute a bright signal. Additionally, static tissue in each non-overlapped slice portion also yields a bright signal. However, the flow/static contrast is comparable to that produced in inflow refreshment images, and angiograms can be generated by conventional maximum intensity projection processing. The dual ability to visualize angiograms and static tissue images is a major benefit of the strategy. Computer simulations of flow sensitivities and in vivo results are presented which compare the outflow and inflow refreshment imaging strategies.     

Anisotropic giant magnetoresistance originating from the π-d interaction in a molecule

We synthesized TPP[Fe^III(Pc)(CN)₂]₂, PTMA_x[Fe^III(Pc)(CN)₂]·y(MeCN), and PXX [Fe^III(Pc)(CN)₂], a new series of charge-transfer salts containing the axially-substituted phthalocyanine (Pc), [Fe^III(Pc)(CN)₂]⁻. In this molecular unit, the π conduction electron derived from the Pc-ring coexists with the d electron which is a potential source of a local magnetic moment. Therefore various phenomena associated with the interplay between local magnetic moments and conduction electrons are expected. We observed the giant negative magnetoresistance (GNMR) in all the three salts. The GNMR is highly anisotropic for the magnetic-field direction, and reflects the g-tensor anisotropy of the local magnetic moment in the [Fe^III(Pc)(CN)₂]⁻ unit. This indicates that the GNMR in these salts originates from the strong π-d interaction in the [Fe^III(Pc)(CN)₂]⁻ unit.     

Buchsbaum homogeneous algebras with minimal multiplicity

In this paper we first give a lower bound on multiplicities for Buchsbaum homogeneous k-algebras A in terms of the dimension d, the codimension c, the initial degree q, and the length of the local cohomology modules of A. Next, we introduce the notion of Buchsbaum k-algebras with minimal multiplicity of degree q, and give several characterizations for those rings. In particular, we will show that those algebras have linear free resolutions. Further, we will give many examples of those algebras.     

Some Recent Progress and Applications in Graph Minor Theory

In the core of the seminal Graph Minor Theory of Robertson and Seymour lies a powerful theorem capturing the ``rough' structure of graphs excluding a fixed minor. This result was used to prove Wagner's Conjecture that finite graphs are well-quasi-ordered under the graph minor relation. Recently, a number of beautiful results that use this structural result have appeared. Some of these along with some other recent advances on graph minors are surveyed. Research partly supported by Japan Society for the Promotion of Science, Grant-in-Aid for Scientific Research, Grant number 16740044, by Sumitomo Foundation, by C & C Foundation and by Inoue Research Award for Young Scientists Supported in part by the Research Grant P1–0297 and by the CRC program On leave from: IMFM & FMF, Department of Mathematics, University of Ljubljana, Ljubljana, Slovenia     

Validation of a method for predicting the precision, limit of detection and range of quantitation in competitive ELISA.

The mathematical model for predicting the precision, limit of detection (LOD) and range of quantitation (ROQ) in a competitive enzyme-linked immunosorbent assay (ELISA) proposed by Hayashi et al. (Anal. Chem., 2004, 76, 1295) was validated. The model describes the relative standard deviation (RSD) of concentration estimates by the RSDs of pipetting volumes of analyte, enzyme-conjugated antigen, antibody and substrate solutions, and the standard deviation (SD) of inherent absorbances between the wells in an ELISA plate. For 6 kinds of direct competitive ELISA kits, the LOD and ROQ predicted by the model agreed well with those obtained by experiments with real samples. It was also confirmed that the model is applicable to the prediction of uncertainty that depends on the pipetting error of the viscous antiserum solution. The model was demonstrated to be useful for estimating the LOD and ROQ of competitive ELISA.