A group G is called co-Dedekindian if every subgroup of G is invariant under all central automorphisms of G. In this paper we give some necessary conditions for certain finite p-groups with non-cyclic abelian second centre to be co-Dedekindian. We also classify 3-generator co-Dedekindian finite p-groups which are of class 3, having non-cyclic abelian second centre with |\Omega_1(G^p)|=p.

In this paper BP-theory is used to give a proof that there exists a stable homotopy element in \pi _{2^{n+1} - 2}^{S}( {\tf="times-b"R}P^{\infty }) with non-zero Hurewicz image in ju-theory if and only if there exists an element of \pi _{2^{n+1} - 2}^{S}( S{\hskip1}^{0}) that is represented by a framed manifold of Arf invariant one.

In this paper, we consider the dependence of the Dirichlet eigenvalues and eigenspaces of the Laplace operator upon perturbation of the domain of definition. We prove that the dependence of a certain eigenvalue and of the corresponding eigenspace is analytic on the set of perturbations that leave the multiplicity constant.

We construct three p-adic L-functions attached to the symmetric square of a modular elliptic curve. Following a calculation of Perrin-Riou for one of these functions, we compute the derivative of the p-adic L-function associated to the square of the non-unit root of Frobenius at p. This generalises Greenberg's notion of [Lscr ]-invariant to these three-dimensional Galois representions.

We study the moduli space of pluriregular threefolds of general type with K3X=8, 10, 12 and p_g(X)=5 and whose canonical map is a finite morphism onto a smooth quadric Q⊂ ℙ4[Copf].

A Banach space X is said to be an {\cal M}-space if every continuous multilinear form on X is weakly sequentially continuous. We study in this paper the stability properties of the class of {\cal M}-spaces.

A unit speed curve \gamma =\gamma (s) in a Riemannian manifold N is called a circle if there exists a unit vector field Y(s) along \gamma and a positive constant k such that \nabla _s \gamma '(s)=k Y(s),\, \nabla _s Y(s)=-k \gamma '(s). The main purpose of this article is to investigate the fundamental relationships between circles, maximal tori in compact symmetric spaces, and immersions of finite type.

This paper discusses the fractional chromatic number of the direct product of graphs. It is proved that if H is a circulant graph G^k_d, or a Kneser graph, or a direct sum of such graphs, then for any graph G, \chi_f{\hskip1}(G\times H{\hskip1}) = {\text min}\{\chi_f{\hskip1}(G), \chi_f{\hskip1}(H{\hskip1})\}.

In this paper, we obtain an exact formula for the Hausdorff and box dimensions of a class of self-affine sets in two dimensions, namely those with disjoint projections. We prove, in particular, that fractals in this class have a Hausdorff and box dimension that is equal to the maximum Hausdorff and box dimension of one of their projections.

Let \bf{R}_+ be the set of all non-negative real numbers, \bf(I}\in \{ \bf(R}, \bf(R}_+\} and {\cal U}_\bf(I}=\{ U(t, s): t\ge s\in I\} be a strongly measurable and exponentially bounded evolution family of bounded linear operators acting on a Banach space X. Let \phi :\bf(R}_+\to \bf(R}_+ be a strictly increasing function and E be a normed function space over \bf(I} satisfying some properties; see Section 2. We prove that if

\phi \circ (\chi _{[s, \infty )}(\cdot )||U(\cdot , s)x||)

defines an element of the space E for every s\in \bf(I} and all x\in X and if there exists M>0 such that

\sup \limits _{s\in \bf(I}}|\phi \circ (\chi _{[s, \infty )} (\cdot )||U(\cdot , s)x||)|_{E}= M<\infty \quad \forall x\in X\ {\text with}\ ||x||\le 1,

then {\cal U}_\bf(I} is uniformly exponentially stable. In particular if \psi :\bf(R}_+\to \bf(R}_+ is a nondecreasing function such that \psi (t)>0, for all t>0, and if there exists K>0 such that

\sup \limits _{s\in \bf(I}}\int \limits _s^{\infty }\psi (||U(t, s)x||)dt=K <\infty ,\quad \forall x\in X\ \text(with)\ ||x||\le 1, then

{\cal U}_\bf(I} is uniformly exponentially stable. For \bf(I}=\bf(R}_+, \psi continuous and {\cal U}_{\bf(R}_+} strongly continuous this last result is due to S. Rolewicz. Some related results for periodic evolution families are also proved.

It is shown that the creation operator is the only (up to a multiplicative constant) injective weighted shift all of whose translations (or at least one) are still injective weighted shifts regardless of what the weight sequences and the bases are. A similar result is true for the annihilation operator as well as for the Heisenberg and Schrödinger couples.

Compact hyperbolic surfaces of given genus g containing discs of the maximum radius have been studied from various points of view. In this paper we connect these different approaches and observe some properties of the Fuchsian groups uniformizing both compact and punctured extremal surfaces. We also show that extremal surfaces of genera g=2,3 may contain one or several extremal discs, while an extremal disc is necessarily unique for g \ge 4. Along the way we also construct explicit families of extremal surfaces, one of which turns out to be free of automorphisms.

We prove that if X is a real Banach space, with dim X\ge 3, which contains subspace of codimension 1 which is 1-complemented in X and whose group of isometries is almost transitive then X is isometric to a Hilbert space. This partially answers the Banach-Mazur rotation problem and generalizes some recent related results.

We give an example of a finitely generated commutative semigroup that is not automatic.

It is proved that the subalgebra of constants of a derivation on a free associative algebra in prime characteristic is free provided that some constraining conditions are satisfied. As a particular case, it follows that the constants of the partial derivatives on a free algebra form a free subalgebra. The main result is also applied in order to provide a simplified proof of a previous result by the author on extensions of tensor rings.