Parametric decomposition of powers of ideals versus regularity of sequences

Let be an ideal in a Noetherian local ring . Then the sequence is -regular if every is a non-zerodivisor in and if for all integers , where runs over the elements of the set .

     

Polyacrylamides as hydrophilic selectors in non-aqueous capillary electrophoresis

Polyacrylamides (PAAms) were investigated as hydrophilic selectors in non-aqueous capillary electrophoresis (CE). Separation of 10 substituted benzoates and unsubstituted benzoate as model samples was greatly improved by the addition of PAAms in acetonitrile-CE. The migration behavior indicates that the carbonyl moiety of PAAms works as a good hydrogen-accepting site toward hydrogen-donating analytes such as 4-hydroxybenzoate anion (4OH-BA) in acetonitrile. PAAms also serve as electron-accepting agents with its amide proton interacting with the dissociated carboxyl groups of the benzoates. The ion-dipole interaction is useful to control the migration behavior of benzoates without hydrogen-donating substituents. The overall mode of the interaction is similar to that of polyethylene glycol (PEG) 20000 reported previously, but the complex formation constant of poly(N-tert.-butyl)acrylamide (PBAAm) with 40H-BA estimated here was 130-fold larger than that of PEG 20000. This would be ascribed to the strong basicity of the carbonyl oxygen atoms of PBAAm as compared with the ether oxygen atoms of PEG. Furthermore, a copolymer of (N-tert.-butyl)acrylamide-acrylamide [70:30 (in feed)] exhibited a complex formation constant of about fourfold larger toward 4OH-BA than PBAAm, most probably due to decrease in steric hindrance from the tert.-butyl groups. Adrenaline and its six precursors have been separated successfully using the PAAms.     

Good ideals in Gorenstein local rings

Let be an -primary ideal in a Gorenstein local ring (, ) with , and assume that contains a parameter ideal in as a reduction. We say that is a good ideal in if is a Gorenstein ring with . The associated graded ring of is a Gorenstein ring with if and only if . Hence good ideals in our sense are good ones next to the parameter ideals in . A basic theory of good ideals is developed in this paper. We have that is a good ideal in if and only if and . First a criterion for finite-dimensional Gorenstein graded algebras over fields to have nonempty sets of good ideals will be given. Second in the case where we will give a correspondence theorem between the set and the set of certain overrings of . A characterization of good ideals in the case where will be given in terms of the goodness in their powers. Thanks to Kato's Riemann-Roch theorem, we are able to classify the good ideals in two-dimensional Gorenstein rational local rings. As a conclusion we will show that the structure of the set of good ideals in heavily depends on . The set may be empty if , while is necessarily infinite if and contains a field. To analyze this phenomenon we shall explore monomial good ideals in the polynomial ring in three variables over a field . Examples are given to illustrate the theorems.

     

Finite Modules of Finite Injective Dimension Over a Noetherian Algebra

Let R be a commutative Noetherian ring. Let P(R) (respectively,I(R)) be the category of all finite R-modules of finite projective(respectively, injective) dimension. Sharp [9] constructed acategory equivalence between I(R) and P(R) for certain Cohen–Macaulaylocal rings R. Thus many properties about finite modules offinite projective dimension can be connected with those of finiteinjective dimension through this equivalence.     

Reduction of ion thermal diffusivity associated with the transition of the radial electric field in neutral-beam-heated plasmas in the large helical device

Recent large helical device experiments revealed that the transition from ion root to electron root occurred for the first time in neutral-beam-heated discharges, where no nonthermal electrons exist. The measured values of the radial electric field were found to be in qualitative agreement with those estimated by neoclassical theory. A clear reduction of ion thermal diffusivity was observed after the mode transition from ion root to electron root as predicted by neoclassical theory when the neoclassical ion loss is more dominant than the anomalous ion loss.     

Observation of the "self-healing" of an error field island in the large helical device

It was observed that the vacuum magnetic island produced by an external error magnetic field in the large helical device shrank in the presence of plasma. This was evidenced by the disappearance of flat regions in the electron temperature profile obtained by Thomson scattering. This island behavior depended on the magnetic configuration in which the plasmas were produced.     

磁场构型的影响及用于RIKEN的RIBF项目的新型ECR离子源

We measured the main plasma parameters(density of electron,temperature of electron and ion confinement time)and beam intensity of various heavy ions as a function of B_(min).The B_(min) strongly affects the field gradient at the resonance zone,consequently the plasma parameters and beam intensity are changed. Based on these experimental results,we started to construct new 18GHz ECRIS and make a detailed design of the 28GHz SC-ECRIS for RIKEN RI beam factory project.     

Insights into sticking of radicals on surfaces for smart plasma nano-processing

In reactive plasma processing, species produced in the plasma reach the surface of a substrate and cause etching, deposition and surface modification through surface reactions. These reactions are characterized by the densities and energies of species incident on the surfaces. In order to realize nano-scale plasma processing, important species for plasma processing have been identified and characterized, and their behavior, not only in the gas phase, but also on the surface, have been clarified and controlled. One of the most critical parameters for insights into surface reaction kinetics of radicals is sticking and surface loss probability. On the basis of radical densities measured by various methods, the sticking and surface reaction loss probabilities have been compiled, and they enable the quantitative understanding of the kinetics of radicals on the surface in the plasma. In this article, the sticking and surface reaction loss probabilities measured thus far are reviewed focusing on fluorocarbon gas, silane gas and methane gas based plasma processes. The establishment of a smart plasma process and the development of an autonomous production device with control of radicals on the basis of insights into the surface reactions for nano-scale plasma processing are presented.     

Non-aqueous capillary electrophoresis of p-quinone anion radicals.

The electrophoretic detection of two kinds of p-quinone anion radicals arising from the electrolysis of benzoquinone and chloranil was achieved by employing an acetonitrile medium. Sufficient dehydration of a running solution was necessary for the detection of the benzoquinone anion radical. Oxygen in the running solution also caused a serious decrease in the amount of the benzoquinone anion radical during electrophoresis. The addition of methanol as a hydrogen-donor decreased the electrophoretic mobility of the benzoquinone anion radical significantly, while that of the chloranil anion radical was little changed. This result is interpreted in terms of hydrogen-bonding interaction between the p-quinone anion radicals and methanol, reflecting the magnitude of their proton-accepting ability (benzoquinone anion radical > chloranil anion radical).