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.     

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.     

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.     

Energy band and electron-vibration coupling in organic thin films: photoelectron spectroscopy as a powerful tool for studying the charge transport

This article describes the origins of the width of the highest occupied molecular orbital (HOMO) state observed in the ultraviolet photoemission spectra (UPS) of thin organic semiconductor films. Although much research has been performed on the electrical properties of organic devices, a lot of crucial problems still remain. Among these problems, the charge mobility in organic semiconductor systems is one the most important subjects to be elucidated. In order to discuss the mobility, it is essential to understand both the intermolecular interaction and the electron-molecular vibration coupling. Experimental measurements of the energy band dispersion give information about the intermolecular interaction, and experimental detection of the HOMO hole-vibration coupling is indispensable to comprehend impacts of the electron-vibration coupling on the hole transport. Since most of the information is hidden behind the finite bandwidth of the HOMO, only careful UPS measurements can provide information on these important phenomena related to charge carrier dynamics. In this article, we summarize our recent challenges on UPS measurements of organic thin films, which give the band dispersion of the HOMO and the HOMO hole-vibration coupling, and discuss the origins of the UPS bandwidth that relates to the charge carrier dynamics.     

Cross patterning on MgO based on dislocations using femtosecond laser irradiation

We show a unique technique to form dense dislocations locally inside a MgO single crystal with a rock-salt type structure using femtosecond (fs) laser irradiation. Cross-shaped patterns of micrometer size, originating from densely introduced dislocations, are formed spontaneously around the focal point. We controlled the three-dimensional propagation of the dislocations by adjusting the pulse energy of the fs laser and NA of objective lens. The technique may open up a new field of dislocation technology for optical applications.     

Sheet-beam geometry for in vivo fluorescent x-ray computed tomography: proof-of-concept experiment in molecular imaging

We propose a fluorescent x-ray computed tomography method using an array of detectors with an incident sheet beam, aimed at providing molecular imaging with high sensitivity and good spatial resolution. In this study, we prove the feasibility of this concept and investigate its imaging properties, including spatial and contrast resolutions and quantitativeness, by imaging an acrylic phantom and a normal mouse brain using a preliminary imaging system with monochromatic synchrotron x rays.     

Emergent organization of oscillator clusters in coupled self-regulatory chaotic maps

Here we introduce a model of parametrically coupled chaotic maps on a one-dimensional lattice. In this model, each element has its internal self-regulatory dynamics, whereby at fixed intervals of time the nonlinearity parameter at each site is adjusted by feedback from its past evolution. Additionally, the maps are coupled sequentially and unidirectionally, to their nearest neighbor, through the difference of their parametric variations. Interestingly we find that this model asymptotically yields clusters of superstable oscillators with different periods. We observe that the sizes of these oscillator clusters have a power-law distribution. Moreover, we find that the transient dynamics gives rise to a 1/f power spectrum. All these characteristics indicate self-organization and emergent scaling behavior in this system. We also interpret the power-law characteristics of the proposed system from an ecological point of view.      

OPENCORE NMR: open-source core modules for implementing an integrated FPGA-based NMR spectrometer

A tool kit for implementing an integrated FPGA-based NMR spectrometer [K. Takeda, A highly integrated FPGA-based nuclear magnetic resonance spectrometer, Rev. Sci. Instrum. 78 (2007) 033103], referred to as the OPENCORE NMR spectrometer, is open to public. The system is composed of an FPGA chip and several peripheral boards for USB communication, direct-digital synthesis (DDS), RF transmission, signal acquisition, etc. Inside the FPGA chip have been implemented a number of digital modules including three pulse programmers, the digital part of DDS, a digital quadrature demodulator, dual digital low-pass filters, and a PC interface. These FPGA core modules are written in VHDL, and their source codes are available on our website. This work aims at providing sufficient information with which one can, given some facility in circuit board manufacturing, reproduce the OPENCORE NMR spectrometer presented here. Also, the users are encouraged to modify the design of spectrometer according to their own specific needs. A home-built NMR spectrometer can serve complementary roles to a sophisticated commercial spectrometer, should one comes across such new ideas that require heavy modification to hardware inside the spectrometer. This work can lower the barrier of building a handmade NMR spectrometer in the laboratory, and promote novel and exciting NMR experiments.     

The simple and selective synthesis of 3-amino-2,2-difluorocarboxylic esters and difluoro-β-lactams using ethyl bromodifluoroacetate in the presence of rhodium catalyst

Treatment of imines (5) with ethyl bromodifluoroacetate (1) and Et₂Zn in the presence of RhCl(PPh₃)₃ in anhydrous medium gave difluoro-β-lactams (7) in good to excellent yields, while 3-amino-2,2-difluorocarboxylic esters (6) were obtained in good yields by adding MgSO₄·7H₂O to the reaction medium.     

A new and known cytotoxic aryltetralin-type lignans from stems of Bursera graveolens

A new 4alpha-aryltetralin-type lignan called burseranin (1) and a known analogous lignan picropolygamain (2) were isolated along with known triterpenes, lupeol and epi-lupeol from the methanol extract of stems of Bursera graveolens, which showed a remarkable inhibitory activity against human HT1080 fibrosarcoma cells. The whole structure of 1 was established based on combined spectral studies and the absolute structure for 2 was first confirmed by CD spectral evidence. In addition, cytotoxic activities of the stem (methanol) extract and its components are evaluated in this paper.