Biased and Unbiased Two-sided Wilcoxon Tests for Equal Sample Sizes

This paper answers the long-standing question of whether the two-sided Wilcoxon rank test for equal sample sizes is unbiased against a location parameter family of distributions by giving a counterexample. It is also shown that the nonrandomized two-sided Wilcoxon test for equal sample sizes with the least positive significance level is unbiased.     

On the use of nickel foil strain gages at varying temperatures

When a strain gage made of nickel foil attached on the surface of a specimen is subjected to repeated loads, the elastic stress is measured by observing slip-bands in the foil resulting from repeated strain. Calibration studies with rotating-bending tests at various temperatures between room temperature and 350°C are performed on round steel bars with nickel foil. The relation between the threshold stress for the first appearance of slip-bands and the number of stress cycles is examined at varying temperatures, which provides the calibration values of the nickel foil tested at varying temperatures. Assuming that the first appearance of slip-bands is based on the linear cumulative damage law, the calibration values at varying temperatures are calculated from those established by the calibration tests at several constant temperatures. It is found that the calculated calibration values agree well with the results obtained by the calibration tests at varying temperatures and that the calculation applying the linear cumulative damage law is a useful method to presume the calibration values at varying temperatures without performing the experiment.     

MARS: selecting basis functions and knots with an empirical Bayes method

An empirical Bayes method to select basis functions and knots in multivariate adaptive regression spline (MARS) is proposed, which takes both advantages of frequentist model selection approaches and Bayesian approaches. A penalized likelihood is maximized to estimate regression coefficients for selected basis functions, and an approximated marginal likelihood is maximized to select knots and variables involved in basis functions. Moreover, the Akaike Bayes information criterion (ABIC) is used to determine the number of basis functions. It is shown that the proposed method gives estimation of regression structure that is relatively parsimonious and more stable for some example data sets.     

Existence Theorems for Set-valued Operators in Banach Spaces

In this paper, we study the problem of existence of zero points for set-valued operators in Banach spaces. We present a simple condition which can be used to verify that under some conditions, set-valued operators have zero points. Furthermore, we derive the surjectivity result and the Kakutani fixed point theorem by using this condition.      

Optical and Thermal Simulator for Laser-assisted Magnetic Recording

“Laser-assisted magnetic recording”, in which a recording media is heated by a laser beam while writing data, is attracting attention as a technology that enables a recording density of 1 Tb/in.². There exists another technology for media in which the recording layer is constructed with many small projections that enable high magnetic coercivity. This is called “patterned media”. For developing hard disk drives using these methods, we developed a simulator that analyzes the optical intensity distribution from the optical head for laser-assisted recording and the temperature profile on the patterned media. The simulator calculates the optical model using the finite-difference time-domain (FDTD) method. The thermal analysis of the three-dimensional model allows fast calculations using the alternating direction implicit (ADI) method. The heat source distribution data for thermal analysis is calculated in order to use the results of optical analysis. The optical and thermal analyses of the laser-assisted recording model were investigated with the simulator.     

Approximation of fixed points for amenable semigroups of nonexpansive mappings in Banach spaces

The purpose of this paper is to study iterative schemes of Browder and Halpern types for a semigroup of nonexpansive mappings on a compact convex subset of a smooth (and strictly convex) Banach space with respect to a sequence of strongly asymptotic invariant means defined on an appropriate space of bounded real valued functions of the semigroup. Various applications to the additive semigroup of nonnegative real numbers and commuting pairs of nonexpansive mappings are also presented.     

Thermoelectric properties of the AA′3B4O12-type ordered perovskite oxides

The perovskite transition-metal oxide ABO₃ has been extensively studied in various areas in solids. While the B ion determines the electronic properties, e.g., ferroelectricity, ferromagnetism, and superconductivity, the A site has been regarded as a “back-seat player” to change the doping level or the bandwidth. However, in the ordered perovskite oxide AA′₃B₄O₁₂, the A site order is closely related to the peculiar electronic states. In CaMn₃Mn₄O₁₂, the unusually small bandwidth justifies to extrapolate the transport data to the high-temperature limit, and in CaCu₃Ru₄O₁₂, a novel heavy-fermion state is realized through the Cu–O–Ru interaction.     

Direct Imaging of Octahedral Distortion in a Complex Molybdenum Vanadium Mixed Oxide

Complex Mo,V‐based mixed oxides that crystallize in the orthorhombic M1‐type structure are promising candidates for the selective oxidation of small alkanes. The oxygen sublattice of such a complex oxide has been studied by annular bright field scanning transmission electron microscopy. The recorded micrographs directly display the local distortion in the metal oxygen octahedra. From the degree of distortion we are able to draw conclusions on the distribution of oxidation states in the cation columns at different sites. The results are supported by X‐ray diffraction and electron paramagnetic resonance measurements that provide integral details about the crystal structure and spin coupling, respectively.     

Parallel distributed block coordinate descent methods based on pairwise comparison oracle

The aim of this paper is to find the global solutions of uncertain optimization problems having a quadratic objective function and quadratic inequality constraints. The bounded epistemic uncertainties in the constraint coefficients are represented using either universal or existential quantified parameters and interval parameter domains. This approach allows to model non-controlled uncertainties by using universally quantified parameters and controlled uncertainties by using existentially quantified ones. While existentially quantified parameters could be equivalently considered as additional variables, keeping them as parameters allows maintaining the quadratic problem structure, which is essential for the proposed algorithm. The branch and bound algorithm presented in the paper handles both universally and existentially quantified parameters in a homogeneous way, without branching on their domains, and uses some dedicated numerical constraint programming techniques for finding a robust, global solution. Several examples clarify the theoretical parts and the tests demonstrate the usefulness of the proposed method.