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1

Flat structure and potential vector fields related with algebraic solutions to Painleve VI equation

Kato M., Mano T., Sekiguchi J.

Opuscula Mathematica

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2018

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Vol. 38, no. 2

201--252

EN

A potential vector field is a solution of an extended WDVV equation which is a generalization of a WDVV equation. It is expected that potential vector fields corresponding to algebraic solutions of Painleve VI equation can be written by using polynomials or algebraic functions explicitly. The purpose of this paper is to construct potential vector fields corresponding to more than thirty non-equivalent algebraic solutions.

2

Weak nearly uniform smoothness of the ψ-direct sums (X1 O…O XN)ψ

Kato M., Tamura T.

Commentationes Mathematicae

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2012

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Vol. 52, [Z] 2

171--198

EN

We shall characterize the weak nearly uniform smoothness of the ψ-direct sum (X1 O…O XN)ψof N Banach spaces X1,..., XN, where ψ is a convex function satisfying certain conditions on the convex set [formula]. To do this, a class of convex functions which yield l1-like norms will be introduced. We shall apply our result to the fixed point property for nonexpansive mappings (FPP). In particular, an example which indicates that there are plenty of Banach spaces with FPP failing to be uniformly non-square will be presented.

3

Uniform non l -ness of l∞-sums of Banach spaces

Kato M., Tamura T.

Commentationes Mathematicae

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2009

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Vol. 49, [Z] 2

179-187

EN

We shall characterize the uniform non-l {...} -ness of `l∞-sums of Banach spaces (X1 ⊕ź ź ź⊕Xm)1. As applications, some results on super-reflexivity and the fixed point property for nonexpansive mappings will be presented.

4

Uniform non-ln1-ness of l_1-sums of Banach spaces

Kato M., Tamura T.

Annales Societatis Mathematicae Polonae. Seria 1: Commentationes Mathematicae

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2007

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Vol. 47, [Z] 2

161-169

EN

We shall characterize the uniform non-`n1-ness of the `1-sum (X1 +ź ź ź + X_m)_1 of a finite number of Banach spaces X_1, ź ź ź ,X_m. Also we shall obtain that (X_1 +ź ź ź +X_m)_1 is uniformly non-lm+1 if and only if all X_1, . . . ,X_m are uniformly non-square (note that (X_1 + ź ź ź +X_m)_1 is not uniformly non-lm1). Several related results will be presented.

5

Weak nearly uniform soothness and worth property of [fi]-direct sums of Banach spaces

Kato M., Tamura T.

Annales Societatis Mathematicae Polonae. Seria 1: Commentationes Mathematicae

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2006

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Vol. 46, [Z] 1

113-129

EN

We shall characterize the weak nearly uniform smoothness of the fi-direct sum X Y of Banach spaces X and Y . The Schur and WORTH properties will be also characterized. As a consequence we shall see in the [...]-sums of Banach spaces there are many examples of Banach spaces with the fixed point property which are not uniformly non-square.

6

The Effects of Local Cooling on Thermophysiological Response in Participants Wearing Dust-Free Garments

Kwon O. K., Kwon A. H., Kato M., Hayashi C., Tokura H.

International Journal of Occupational Safety and Ergonomics

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1998

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Vol. 4, No. 1

57--67

EN

This study was designed to find the effects of two kinds of dust-free garments with (A) and without (B) frozen gel strip (FGS), and half-naked clothing (brassiere and shorts; C) on thermophysiological parameters and on temperature and humidity within clothing. The heart rate, rectal, and skin temperatures as well as sweat rate and clothing microclimate were measured during 140 min in 9 healthy females. Inquiries were also made into the subjective rating of thermal, humidity, and comfort sensations. The main findings in our experiments are as follows: (a) Physiological parameters such as rectal and skin temperatures (chest and forehead), heart rate, and sweat rate were clearly lowest in garb C, intermediate in garb A, and highest in garb B throughout the experiment; (b) Temperature and humidity within clothing were lower in garb A than in garb B; (c) More than half of the 9 participants decreased thermal sensation by wearing garb A. These results suggest that the usage of FGS could improve the heat load in lightly working participants wearing dust-free garments.