In this paper we obtain numerical ranges of composition operators on $l^2$.

A new constructive version of Baire's theorem is given and then applied to two problems in functional analysis. The second of these applications provides a new proof that compactly generated Banach spaces are finite dimensional.

In this paper, we investigate isometric immersions of $P^2(\pmb{H})$ into $\pmb{R}^{14}$ and prove that the canonical isometric imbedding $\pmb{f}_0$ of $P^2(\pmb{H})$ into $\pmb{R}^{14}$, which is defined in Kobayashi [11] is rigid in the following strongest sense:Any isometric immersion $\pmb{f}_1$ of a connected open set $U (\subset P^2(\pmb{H}))$ into $\pmb{R}^{14}$ coincides with $\pmb{f}_0$ up to a euclidean transformation of $\pmb{R}^{14}$, i.e., there is a euclidean transformation $a$ of $\pmb{R}^{14}$ satisfying $\pmb{f}_1=a\pmb{f}_0$ on $U$.

We shall investigate maximal surfaces in Minkowski 3-space with singularities.Although the plane is the only complete maximal surface without singular points,there are many other complete maximal surfaces with singularities and we show that they satisfy an Osserman-type inequality.

It is shown that the spatial Sobolev norms of regular global solutions of the (2 + 1), (3 + 1) and (4 + 1)-dimensional Klein-Gordon-Schr\"odinger system and the (2+1) and (3+1)-dimensional Zakharov system grow at most polynomially with a bound depending on the regularity class of the data. The proof uses the Fourier restriction norm method.

A global semianalytic subset of a real analytic manifold is a finite union of finite intersections of the solutions of equations and inequalities of real analytic functions on the manifold. Is a union of connected components of a global semianalytic set again global semianalytic? We consider a two-dimensional global semianalytic set such that the normalization of the Zariski closure of it is affine. We show that a union of connected components of it is again global semianalytic. We also give some partial results on connected components of global semianalytic subset of a three-dimensional analytic manifold.

Let $H$ be a $2$-group with faithful irreducible characters all which are algebraically conjugate to each other, and $\phi$ be any faithful irreducible character of $H$. We are interested in $2$-group $G$ with the normal subgroup $H$ such that induced character $\phi^G$ is irreducible. For example, for $2$-groups $H$ that are the cyclic groups, the dihedral groups $D_n$ and the generalized quaternion groups $Q_n$, all of such $2$-groups $G$ was determined ([3]-[5]). In paticular, we showed that such a $2$-group $G$ for $H=D_n$ or $Q_n$ is uniquely determined. Let $G_t(D_n)$ and $G_t(Q_n)$ be those $2$-groups, respectively. The purpose of this paper is to determine all $2$-groups $G$ for $H=G_t(D_n)$ and $G_t(Q_n)$ and faithful irreducible characters $\phi$ of $H$. In this paper we determine the character tables of $G_t(D_n)$ and $G_t(Q_n)$ in order to show that these groups have faithful irreducible characters all which are algebraically conjugate to each other. As result it is shown that these $2$-groups have identical character tables.

The purpose of this paper is to introduce the space of sequences that are strongly almost $(V,\lambda) (\Delta ^{r})$-$summable with respect to an Orlicz function. We give some relations related to these sequence spaces. We also show that the space }$[ \hat{V},\lambda ,M] (\Delta ^{r})\cap \ell _{\infty}(\Delta ^{r})$ may be represented as a $\hat{s}_{\lambda}(\Delta ^{r})\cap $ $\ell _{\infty }(\Delta ^{r})$ space.

Here we investigate asymptotic behavior of positive solutions of an initial value problem of the second order nonlinear differential equation written in the title. This is done from obtaining analytical expressions of the solution valid in the neighborhoods of both end points of its domain.

We study singular integrals associated with the variable surfaces of revolution. We treat the rough kernel case where the singular integral is defined by an $H^1$ kernel function on the sphere $S^{n-1}$. We prove the $L^p$ boundedness of the singular integral for $1<p\leq 2$ assuming that a certain lower dimensional maximal operator is bounded on $L^s$ for all $s>1$. We also study the $(L^p,L^r)$ boundedness for fractional integrals associated with surfaces of revolution.

In this paper the KKT system of a general variational inequality problem (denoted by VIP(X,F)) is reformulated as a constrained optimization problem. A sufficient condition, which ensures a stationary point of the optimization problem being a solution of the KKT system of VIP(X,F), is analyzed. A projection-type method for solving the KKT system of VIP(X,F) with closed convex set $X$ is presented. The new algorithm has nice properties such as retaining feasibility, easy computation if the region $X$ is a box or a ball, and strongly global and local convergence. Numerical examples show that the new algorithm is promising.