A Numerical Method for Determining the Parameters of Schwarz-Christoffel Transformation

In the present paper we construct a numerical method for determining the unknown parameters that appear in the Schwarz-Christoffel transformation. For the polygon on the upper half domain with two cuts, we introduce some integrals and their derivatives and obtain the integral formulae which can be easily computed by the numerical quadratures. We show the numerical computations in the cases of d = 1/4, 1/8, 1/12, 1/16 (2d is the distance between two cuts)

Psychophysical Threshold Estimates in Logistic Regression Using the Bootstrap Resampling

We propose the non-parametric bootstrap resampling algorithm for the problem of psychophysical threshold estimates. We use the logistic regression with guessing rate and the log-likelihood ratio test statistics of two samples for testing the hypothesis by using the bootstrap resampling. We apply our algorithm to the visual acuity test, and show that the bootstrap resampling is useful for the problem of the two-sample test when the numbers of observations are not identical between the two samples. We also propose the bootstrap algorithm for one-sample testing to certify the values of parameters and threshold obtained by logistic regression

The Parametric and Non-parametric Bootstrap Resamplings for the Visual Acuity Measurement

We propose a useful tool for the visual acuity measurement from the results of parametric and non-parametric bootstrap algorithms in the logistic regression model. We present the kurtosis and the variance of deviance residuals to estimate the efficiency of bootstrap resampling. We applied our parametric and non-parametric algorithms to the problem of the visual acuity measurement and obtained the efficiency measures for the comparison of the parametric and non-parametric bootstrap resamplings

A statistical modelling of the visual acuity measurement and its multiple test procedure

To establish the computer assisted system of the visual acuity test, we propose a statistical modelling of the visual acuity measurement and its multiple test procedure. The psychometric functions for individual patients are produced by the logistic regression combined with the guessing rate. We adopt test statistics based on (i) psychometric functions (the Cochran-Mantel-Haenszel method) and (ii) psychophysical thresholds (the delta method). The multiple comparisons are performed by the step-down procedure with Ryan-Einot-Gabriel-Welsch (REGW) significance levels. To show the practical effectiveness of our system, we present a numerical example of four patient groups

リーマン面上の有限要素法

Contents / p2 Introduction / p1 Chapter 1. Triangulation / p6 　§1.1. Collection Φ of local parameters / p6 　§1.2. Triangulation K associated to Φ / p7 　§1.3. Normal subdivision of triangulation K / p10 　§1.4. Naturalized triangulation / p11 　§1.5. Parametrization of lunar domains / p13 　§1.6. Area of lune / p14 Chapter 2. Spaces of differentials / p16 　§2.1. Subspace Λ of Γc / p16 　§2.2. Space Λ' / p17 　§2.3. Finite element interpolations / p19 　§2.4. Harmonic differentials on a lune / p19 　§2.5. Difference of norms of σh and σ'h / p20 Chapter 3. Finite element approximations / p24 　§3.1. Formulation of problems / p24 　§3.2. Finite element approximation ψh in Λ / p26 　§3.3. Finite element approximation ω'h in Λ' / p28 　§3.4. Lemma of Bramble and Zlámal / p29 　§3.5. Pointwise estimate / p29 　§3.6. Smoothness of ω on Ω / p31 　§3.7. Approximation by ψh / p33 　§3.8. Approximation by ω'h / p36 　§3.9. Estimate of ||ω'h - ω̂'|| / p39 Chapter 4. Determination of the periodicity moduli of Riemann surfaces / p41 　§4.1. Periodicity moduli of Riemann surfaces / p41 　§4.2. Calculation of periodicity moduli / p42 　§4.3. Numerical example 1(the case of a ciosed Riemann sueface) / p43 　§4.4. Numerical example 2(the case of acompact bordered Rimann surface) / p51 Chapter 5. Determination of the modulus of quadrilaterals / p60 　§5.1. Quadrilateral on a Riemann surface / p60 　§5.2. Formulation of problems / p60 　§5.3. Numerical example 3(the case of Gaier's example) / p62 　§5.4. Numerical example 4(the case of a riemann surface) / p68 　§5.5. Numerical example 5(the case of an unbounded domain) / p75 　§5.6. Numerical example 6(the case of a curvilinear domain) / p77 References / p81広島大学(Hiroshima University)博士(学術)Sciencedoctora