Admissibility and minimaxity of generalized Bayes estimators for spherically symmetric family

We give a sufficient condition for admissibility of generalized Bayes estimators of the location vector of spherically symmetric distribution under squared error loss. Compared to the known results for the multivariate normal case, our sufficient condition is very tight and is close to being a necessary condition. In particular, we establish the admissibility of generalized Bayes estimators with respect to the harmonic prior and priors with slightly heavier tail than the harmonic prior. We use the theory of regularly varying functions to construct a sequence of smooth proper priors approaching an improper prior fast enough for establishing the admissibility. We also discuss conditions of minimaxity of the generalized Bayes estimator with respect to the harmonic prior.     

An application of fragment interaction analysis based on local MP2

We have developed a method named ‘fragment interaction analysis based on local MP2’ (abbreviated as FILM). This method enables us to decompose the interaction energy associated with dispersion interactions into contributions of localized occupied orbitals. In this study, the basis set dependence of the results derived from FILM was examined. The results suggested that the individual ratio of pair correlation energies of selected orbital pairs to the total dispersion interaction was almost independent of the basis set size. As an illustrative example, detailed analysis was performed on the human immunodeficiency virus type 1 protease complexed with lopinavir molecule.     

First-principles energy band calculation for undoped and N-doped InTaO4 with layered wolframite-type structure

The electronic structures of undoped and N-doped InTaO₄ with optimized structures are calculated within the framework of the density functional theory. Calculated lattice constants are in excellent agreement with experimental values, within a difference of 2%. The valence band maximum (VBM) is located near the middle point on the ZD line and the conduction band minimum (CBM) near the middle point on the DX line. This means that InTaO₄ is an indirect-gap material and a minimum theoretical gap between VBM and CBM is ca. 3.7 eV. The valence band in the range from −6.0 to 0 eV mainly consists of O 2p orbitals, where In 4d5s5p and Ta 5d orbitals are slightly hybridized with O 2p orbitals. On the other hand, the conduction band below 5.5 eV is mainly composed of the Ta 5d orbitals and the contributions of In and O orbitals are small. The band gap of N-doped InTaO₄ decreases by 0.3 eV than that of undoped InTaO₄, because new gap states originating from N 2p orbitals appear near the top of the valence band. This result indicates that doping of N atoms into metal oxides is a useful method to develop photocatalysts sensitive to visible light.     

Localization and completion of nilpotent groups of automorphisms

We study nilpotent subgroups of automorphism groups in the category of groups and the homotopy category of spaces. We establish localization and completion theorems for nilpotent groups of automorphisms of nilpotent groups. We then apply these algebraic theorems to prove analogous results for certain groups of self-homotopy equivalences of spaces.     

Energy transfer in hyperthermal Xe-graphite surface scattering

The scattering of a hyperthermal Xe from a graphite (0001) surface has been studied using a molecular beam-surface scattering technique and molecular dynamics (MD) simulations. The angular and velocity distributions of scattered Xe atoms were measured at incidence energies from 0.45 to 3.5 eV, three incidence angles of 15°, 35° and 60° and the surface temperatures of 300 K and 550 K. The observed time-of-flight spectra exhibit a sharp velocity distribution with only one velocity component, which is ascribed to the direct inelastic scattering process. The angle-resolved energy ratios of the mean final translational energy over the mean incidence energy E_f/E_i agree well with those predicted based on the assumption of the conservation of the momentum parallel to the surface. The Hard-Cube model, where the mass of the cube is approximately 310 u, has reproduced the angle-resolved flux distributions of scattered Xe atoms. In the Hard-Cube model almost 80% of the normal component of the incidence translational energy is found to be lost in collision. The MD simulations reproduce well the experimental results by using the Brenner potential for intralayer C atoms and a Lennard-Jones potential for interlayer C–C pair interactions.     

Graphene Oxide Nanosheets Modified with Single‐Domain Antibodies for Rapid and Efficient Capture of Cells

Peripheral blood can provide valuable information on an individual’s immune status. Cell‐based assays typically target leukocytes and their products. Characterization of leukocytes from whole blood requires their separation from the far more numerous red blood cells. 1 Current methods to classify leukocytes, such as recovery on antibody‐coated beads or fluorescence‐activated cell sorting require long sample preparation times and relatively large sample volumes. 2 A simple method that enables the characterization of cells from a small peripheral whole blood sample could overcome limitations of current analytical techniques. We describe the development of a simple graphene oxide surface coated with single‐domain antibody fragments. This format allows quick and efficient capture of distinct WBC subpopulations from small samples (～30 μL) of whole blood in a geometry that does not require any specialized equipment such as cell sorters or microfluidic devices.     

Experimental determination of transverse vibration modes of thin I-shaped plates

The natural frequencies and the corresponding mode shapes of clamped thin I-shaped plates were experimentally determined by time-averaged holographic interferometry. The test plate was shaped as shown in Fig. 1, and eight kinds of plates were tested by taking a dimensionless length parameter ξ as a parameter. The natural-vibration modes exceeding 200 were identified using the real-time method. The corresponding natural frequencies ranged from 172 to 5606 Hz. In addition, in the case of a rectangular plate, the experimental results were shown to be good agreement with the theoretical ones.     

Synthesis of unsymmetrically substituted pyrene derivatives through (6-bromo-3,8-dibutylpyren-1-yl)trimethylsilane

A straightforward route to unsymmetrically functionalized pyrene derivatives is described involving the synthesis of key precursor (6-bromo-3,8-dibutylpyren-1-yl)trimethylsilane 1. In a first step bromide 1 was successful in Suzuki-Miyaura, Sonogashira, and Buchwald-Hartwig cross-coupling reactions. Subsequent transformation of the trimethylsilyl group to bromide enabled the introduction of a second variable functional group onto the pyrene skeleton.