On classifying monotone complete algebras of operators

We give a classification of “small” monotone complete C ^*-algebras by order properties. We construct a corresponding semigroup. This classification filters out von Neumann algebras; they are mapped to the zero of the classifying semigroup. We show that there are 2 ^c distinct equivalence classes (where c is the cardinality of the continuum). This remains true when the classification is restricted to special classes of monotone complete C ^*-algebras e.g. factors, injective factors, injective operator systems and commutative algebras which are subalgebras of ℓ^∞. Some examples and applications are given.      

Computational strategy for Russell measure in DEA: Second-order cone programming

In aggregation for data envelopment analysis (DEA), a jointly measured efficiency score among inputs and outputs is desirable in performance analysis. A separate treatment between output-oriented efficiency and input-oriented efficiency is often needed in the conventional radial DEA models. Such radial measures usually need to measure both that a current performance attains an efficiency frontier and that all the slacks are zero on optimality. In the analytical framework of the radial measure, Russell measure is proposed to deal with such a difficulty. A major difficulty associated with the Russell measure is that it is modeled by a nonlinear programming formulation. Hence, a conventional linear programming algorithm, usually applied for DEA, cannot solve the Russell measure. This study newly proposes a reformulation of the Russell measure by a second-order cone programming (SOCP) model and applies the primal–dual interior point algorithm to solve the Russell measure.     

Measurement of returns to scale using a non-radial DEA model: A range-adjusted measure approach

This research theoretically explores the measurement of returns to scale (RTS), using a non-radial DEA (data envelopment analysis) model. A range-adjusted measure (RAM) is used as a representative of such non-radial models. Historically, a type of RTS has been discussed within an analytical framework of radial models. The radial-based RTS measurement is replaced by the non-radial RAM/RTS measurement in this study. When discussing the non-radial RAM/RTS measurement, this study finds a problem of multiple projections that cannot be found in the radial measurement. In this research, a new linear programming approach is proposed to identify all efficient DMUs (decision making units) on a reference set. The important feature of the proposed approach is that it can deal with a simultaneous occurrence of (a) multiple reference sets, (b) multiple supporting hyperplanes and (c) multiple projections. All of the three difficulties are handled by the proposed RAM/RTS measurement. In particular, we discuss both when the three different types of multiple solutions occur on the RAM/RTS measurement and how to deal with such difficulties. Our research results make it possible to measure not only the type of RTS but also the magnitude of RTS in the RAM measurement.     

Enhanced magnetization and ferrimagnetic behavior of normal spinel ZnFe2O4 thin film irradiated with femtosecond laser

We report on spatially selective change of magnetism from paramagnetic to ferrimagnetic-like behaviors in normal spinel ZnFe₂O₄ thin film under irradiation with 780 nm femtosecond laser pulses. The distribution of Zn²⁺ and Fe³⁺ ions in the irradiated region on the film surface becomes disordered because of local heating to high temperatures, and the metastable phase of ZnFe₂O₄ is frozen in by the rapid quenching after irradiation, resulting in the formation of the ferrimagnetic phase. The ferrimagnetic phase reverts to the paramagnetic state by annealing at 800°C. The present technique is useful for two-dimensional patterning of magnetic thin films.     

High preconcentration of ultra-trace metal ions by liquid–liquid extraction using water/oil/water emulsions as liquid surfactant membranes

A high preconcentration method by liquid–liquid extraction using liquid surfactant membranes was developed. The water-in-oil (w/o) emulsion containing dilute hydrochloric acid, 2-ethylhexyl hydrogen 2-ethylhexylphosphonate (PC-88A), liquid paraffin, and kerosene was used for the extraction. In a resulting volume of 1000 cm³ of an aqueous sample solution (pH 5.0) containing less than 1 mg of each metal ion, 2 cm³ of w/o emulsion droplets coated with sorbitan monooleate were dispersed. The analyte metal ions in the outer bulk aqueous phase were extracted into the organic phase to form a complex with PC-88A and successively back-extracted into the inner aqueous phase. The analytes in the resulting inner aqueous phase were determined subsequently by graphite furnace atomic absorption spectrometry applied as a detector. By this procedure, concentration factors of 570, 820, 750, 970, 860, and 880 were achieved for chromium(III), manganese(II), cobalt(II), nickel(II), copper(II), and cadmium(II), respectively, and also the respective detection limits (3σ) of 0.4, 20, 1.2, 18, 18, and 0.7 pg cm⁻³ were obtained.     

Renormalization-Group Method for Reduction of Evolution Equations; Invariant Manifolds and Envelopes

The renormalization group (RG) method as a powerful tool for reduction of evolution equations is formulated in terms of the notion of invariant manifolds. We start with derivation of an exact RG equation which is analogous to the Wilsonian RG equations in statistical physics and quantum field theory. It is clarified that the perturbative RG method constructs invariant manifolds successively as the initial value of evolution equations, thereby the meaning to set t₀=t is naturally understood where t₀ is the arbitrary initial time. We show that the integral constants in the unperturbative solution constitutes natural coordinates of the invariant manifold when the linear operator A in the evolution equation is semi-simple, i.e., diagonalizable; when A is not semi-simple and has a Jordan cell, a slight modification is necessary because the dimension of the invariant manifold is increased by the perturbation. The RG equation determines the slow motion of the would-be integral constants in the unperturbative solution on the invariant manifold. We present the mechanical procedure to construct the perturbative solutions hence the initial values with which the RG equation gives meaningful results. The underlying structure of the reduction by the RG method as formulated in the present work turns out to completely fit to the universal one elucidated by Kuramoto some years ago. We indicate that the reduction procedure of evolution equations has a good correspondence with the renormalization procedure in quantum field theory; the counter part of the universal structure of reduction elucidated by Kuramoto may be Polchinski's theorem for renormalizable field theories. We apply the method to interface dynamics such as kink–anti-kink and soliton–soliton interactions in the latter of which a linear operator having a Jordan-cell structure appears.     

Ferroelectric porous molecular crystal, [Mn3(HCOO)6](C2H5OH), exhibiting ferrimagnetic transition

A porous molecular crystal with guest ethanol molecules, [Mn3(HCOO)6](C2H5OH), was found to be a new type of multifunctional molecular system, which exhibits a ferroelectric transition at 165 K and a ferrimagnetic transition at 8.5 K. [Mn3(HCOO)6](C2H5OH) will give a hint to design "multiferroic" molecular materials where ferroelectric and ferromagnetic orders coexist.     

Existence and Stability of Time Periodic Solution to the Compressible Navier–Stokes–Korteweg System on $${\mathbb{R}^3}$$

The compressible Navier–Stokes–Korteweg system is considered on \({\mathbb{R}^3}\) when the external force is periodic in the time variable. The existence of a time periodic solution is proved for a sufficiently small external force by using the time-T-map related to the linearized problem around the motionless state with constant density and absolute temperature. The spectral properties of the time-T-map is investigated by a potential theoretic method and an energy method in some weighted spaces. The stability of the time periodic solution is proved for sufficiently small initial perturbations. It is also shown that the \({L^\infty}\) norm of the perturbation decays as time goes to infinity.     

Partially unstable attractors in networks of forced integrate-and-fire oscillators

The asymptotic attractors of a nonlinear dynamical system play a key role in the long-term physically observable behaviors of the system. The study of attractors and the search for distinct types of attractor have been a central task in nonlinear dynamics. In smooth dynamical systems, an attractor is often enclosed completely in its basin of attraction with a finite distance from the basin boundary. Recent works have uncovered that, in neuronal networks, unstable attractors with a remote basin can arise, where almost every point on the attractor is locally transversely repelling. Herewith we report our discovery of a class of attractors: partially unstable attractors, in pulse-coupled integrate-and-fire networks subject to a periodic forcing. The defining feature of such an attractor is that it can simultaneously possess locally stable and unstable sets, both of positive measure. Exploiting the structure of the key dynamical events in the network, we develop a symbolic analysis that can fully explain the emergence of the partially unstable attractors. To our knowledge, such exotic attractors have not been reported previously, and we expect them to arise commonly in biological networks whose dynamics are governed by pulse (or spike) generation.