This paper deals with the problems of formulating and testing the hypotheses of redundancy of some variables in correspondence analysis for a two-way contingency table. The testing problems are examined under the assumption that the contingency table is multinomial or independent multinomial. The asymptotic properties of the MLE's and the test statistics under the null hypotheses are also examined.

We give asymptotic forms of positive solutions of second-order quasilinear ordinary differential equations. We obtain further the uniqueness of positive decaying solutions.

In this paper we generalize Bôcher's theorem for polyharmonic functions $u$. In fact, if $u$ is polyharmonic outside the origin and satisfies a certain integral condition, then it is shown that $u$ is written as the sum of partial derivatives of the fundamental solution and a polyharmonic function near the origin.

We give a simultaneous study of $A$-Radon-Nikodym sets and $A$-Pettis sets for nonempty bounded subsets $A$ of Banach spaces with comparable characterizations of these two classes of sets by various properties, using certain weak*-measurable functions.

We extend two stability theorems due to Howard and Okayasu to the case of $F$-harmonic maps. In fact we show that every stable $F$-harmonic map into sufficiently pinched simply-connected Riemannian manifold is constant.