We generalise the existence result for harmonic maps obtained by Hildebrandt-Kaul-Widman to the case where the domain manifold is complete noncompact.

Using the equivariant Ljusternik-Schnirelmann theory and the estimate of the upper bound of the critical value and lower bound for the collision solutions, we obtain some new results in the large concerning multiple geometrically distinct periodic solutions of fixed energy for a class of planar N-body type problems.

Let K be a one variable function field of genus g defined over an algebraically closed field k of characteristic p > 0. Let E/K be a non-constant elliptic curve. Denote by MK the set of places of K and let S ⊂ MK be a non-empty finite subset.

Mason in his paper “Diophantine equations over function fields” Chapter VI, Theorem 14 and Voloch in “Explicit p-descent for elliptic curves in characteristic p” Theorem 5.3 proved that the number of S-integral points of a Weiertrass equation of E/K defined over RS is finite. However, no explicit upper bound for this number was given. In this note, under the extra hypotheses that E/K is semi-stable and p > 3, we obtain an explicit upper bound for this number for a certain class of Weierstrass equations called S-minimal.

Using Padé approximations of the q-logarithmic series we obtain new approximation measures for values of q-logarithms and for the series , k = 1, 2, …, where (un) is a recurrence sequence, satisfying

Following Dwork's indications, in this work we give a further elaboration and a list of corrections for the article “G-fonctions et cohomologie des hypersurfaces singulières”. Moreover we extend the contents of that work to quasi-homogeneous polynomials.

An investigation of representation of Abel type infinite sums in closed form will be presented in this paper. An arbitrary order forced differential-difference equation will be analysed from which sums will be generated. Identities of resulting infinite sums will be proved.

New fixed point theorems are given which have applications in the theory of abstract economies.

We prove that certain square function operators in the Littlewood-Paley theory defined by the kernels without any regularity are bounded on , 1 < p < ∞, w ∈ Ap (the weights of Muckenhoupt). Then, we give some applications to the Carleson measures on the upper half space.

Let Mn be the “polygon space” introduced by Kirwan and Klyachko. In this paper, we give new results on the topology of Mn for odd n. We determine πq(Mn) (q ≤ n − 3). Then we describe Mn in the oriented cobordism ring . We also give new and elementary proofs of the result on the ring structure of H*(Mn/Sn; Q), where Sn denotes the symmetric group acting naturally on Mn.

A Fréchet lattice E is an AL-space if its topology can be defined by a family of lattice seminorms that are additive in the positive cone of E. Grothendieck proved that AL-Banach spaces have the Dunford-Pettis property. This result was recently extended by Fernández and Naranjo to AL-Fréchet spaces with a continuous norm and weak order unit. In this note we show how to remove both hypotheses.

In this paper we give the n-th derivative criterion for functions belonging to recently defined function spaces Qp and Qp, 0. For a special parameter value p = 1 this criterion is applied to BMOA and VMOA, and for p > 1 it is applied to the Bloch space and the little Bloch space . Further, a Carleson measure characterisation is given to Qp, and in the last section the multiplier space from Hq into Qp is considered.

Using the compactness of an imbedding for weighted Sobolev spaces (that is, a Hardy-type inequality), it is shown how the assumption of monotonicity can be weakened still guaranteeing the pseudo-monotonicity of certain nonlinear degenerated or singular elliptic differential operators. The result extends analogous assertions for elliptic operators.

For a p-compact group G and G-space X, we prove the finite generation of the equivariant cohomology and give the form of the Poincaré series of .

A twisted group algebra kσP on a free Abelian group P with finite rank and a Poisson structure on kP are studied. As an application, the primitive spectrum of , the coordinate ring of quantum Euclidean space, is described and a Poisson algebra A is constructed so that there is a bijection between the primitive spectrum of and the symplectic spectrum of R.

If standard central difference formulas are used to compute second or third order derivatives from measured data even quite precise data can lead to totally unusable results due to the basic instability of the differentiation process. Here an averaging procedure is presented and analysed which allows the stable computation of low order derivatives from measured data. The new method first averages the data, then samples the averages and finally applies standard difference formulas. The size of the averaging set acts like a regularisation parameter and has to be chosen as a function of the grid size h.

We apply the theory of monotone operators to study farthest points in closed bounded subsets of real Banach spaces. This new approach reveals the intimate connection between the farthest point mapping and the subdifferential of the farthest distance function. Moreover, we prove that a typical exception set in the Baire category sense is pathwise connected. Stronger results are obtained in Hilbert spaces.

Suitable normalisation of time-homogeneous rotation-invariant random walks on unit spheres Sd ⊂ ℝd+1 for d ≥ 2 leads to a central limit theorem with a Gaussian limit measure. This paper is devoted to an associated Edgeworth expansion with respect to the total variation norm. This strong type of convergence is different from the classical case. The proof is performed in the more general setting of Jacobi-type hypergroups on an interval.

We use a Betti number estimate of Freedman-Hain-Teichner to show that the maximal torsion-free nilpotent quotient of the fundamental group of a 3-manifold with boundary is either Z or Z ⊕ Z. In particular we reobtain the Evans-Moser classification of 3-manifolds with boundary which have nilpotent fundamental groups.

Weighted sums of products of independent normal random variables arise naturally as distributional limits for various statistics. This note investigates the rate at which the tail probability of these sums approaches zero.

For m and k positive integers, define a k-term hm-progression to be a sequence of positive integers {x1,…,xk} such that for some positive integer d, xi + 1 − xi ∈ {d, 2d,…, md} for i = 1,…, k - 1. Let hm(k) denote the least positive integer n such that for every 2-colouring of {1, 2, …, n} there is a monochromatic hm-progression of length k. Thus, h1(k) = w(k), the classical van der Waerden number. We show that, for 1 ≤ r ≤ m, hm(m + r) ≤ 2c(m + r − 1) + 1, where c = ⌈m/(m − r)⌉. We also give a lower bound for hm(k) that has order of magnitude 2k2/m. A precise formula for hm(k) is obtained for all m and k such that k ≤ 3m/2.