Here we give a partial classification of varieties X ⊂ Pn such that any two general zero-dimensional linear sections are projectively equivalent. They exist (with deg(X) > codim(X) + 2) only in positive characteristic.

It is proved that the summability of a series by the Borel-type summability method (B,α,β) together with a certain Tauberian condition implies its summability by the Riesz method (R, log(n + l),p).

We provide general results on the behaviour of the Krasnoselski-Mann iteration process for nonexpansive mappings in a variety of normed settings.

We discuss [2] of the same title and offer an alternative example. This example is a subalgebra of the ortholattice of closed subspaces of separable real Hilbert space.

We give a simple description of boundary sets which may be ignored in calculating the maximum of subharmonic or plurisubharmonic functions.

Let D be the unit disc in the complex plane. It is shown that

(i) for 0 < p < 2, there exists an analytic function f ∊ BMOA for which

and

(ii) for 2 < p < ∞, there exists an analytic function f ∉ BMOA for which

This settles the question of Stroethoff [5] on BMOA.

Suppose u is a harmonic function on a domain D and x, x' are in D. We estimate |u(x) — u(x')| using two Brownian motions started at x and x' and killed on exiting a cube Q ⊂ D. By selecting appropriate versions of the two Brownian motions, a classical gradient estimate for u is easily derived.

Let E be a Banach ideal space and X be a Banach space. The Banach function space E(X) does not contain a copy of C0 if and only if neither E nor X contains a copy of c0. Some extensions of this result are also noted.

We consider the self-adjoint second-order scalar difference equation (1) Δ(rnΔxn) +pnXn+1 = 0 and the matrix system (2) Δ(RnΔXn) + PnXn+1 = 0, where are seQuences of real numbers (d x d Hermitian matrices) with rn > 0(Rn > 0). The oscillation and nonoscillation criteria for solutions of (1) and (2), obtained in [3, 4, 10], are extended to a much wider class of equations by Riccati and averaging techniques.

We explicitly identify the possible probability entrance laws for a class of measure-valued processes that are constructed by taking a particular measure-valued Markov branching process and conditioning it to stay away from the zero measure trap. The set of extreme points of the entrance space is larger than the state space of the conditioned process, and contains elements which correspond to starting the conditioned process at the zero measure.

For any X and any q > 0, one has natural inclusions where the groups S1 and S3 act on S4q-1 in the standard way and are the G-invariant homotopy subsets, G = S1 or G = S3 . It is proved here that for any space X of the homotopy type of a CW-complex and for π4q-1 (X) in the c3 cl stable range, the inclusion is m fact an equality when localized away from the prime 2.

It is proved that a compact subset of a finite product of Brelot harmonic spaces is multipolar if it is a locally multipolar set.

We consider a piecewise monotonie and piecewise continuous map T on the interval. If T has a derivative of bounded variation, we show for an ergodic invariant measure μ with positive Ljapunov exponent λμ that the Hausdorff dimension of μ equals hμ / λμ.

It is shown that if a solvable group is not locally finite, then the group algebra over a field of characterisitc 0 has no nonzero algebraic ideals.

The annihilating polynomials for trace forms, as discovered recently by Conner, are shown to also annihilate many other classes of positive quadratic forms over a field F provided that F satisfies suitable conditions.

In this article we investigate the average order of the arithmetical function

where p1(t), p2(t) are polynomials in Z [t], of equal degree, positive and increasing for t ≥ 1. Using the modern method for the estimation of exponential sums ("Discrete Hardy-Littlewood Method"), we establish an asymptotic result which is as sharp as the best one known for the classical divisor problem.

A unique factorisation theorem is obtained for tensor products of finite lattices of commuting projections in a factor. This leads to unique tensor product factorisations for reflexive subalgebras of the hyperfinite II1 factor which have irreducible finite commutative invariant projection lattices. It is shown that the finite refinement property fails for simple approximately finite C*-algebras, and this implies that there is no analogous general result for finite lattice subalgebras in this context.

For a prime ring R and σ ∊ Aut(R), we determine the group of Rstabilizing automorphisms of the skew polynomial ring R[x; σ]. In the case where R is simple, we characterize the X-inner automorphisms of R[x; σ]. We also provide necessary and sufficient conditions for a σ -commuting derivation of a prime ring R to extend to a derivation of R[x; σ].

It is shown that each commutative Artin local ring having each of its ideals generated by two elements is the homomorphic image of a one-dimensional local complete intersection ring which also has each of its ideals generated by two elements. It is indicated how this can be applied to show that the property that each ideal is projective over its endomorphism ring does not pass to homomorphic images, and in determining the commutative group rings with the two-generator property.

This paper deals with the Stefan-type problem with a zone of coexistence of both phases. We formulate the problem in the enthalpy form and show that the interfaces between the liquid and the mushy, the mushy and the solid phase are smooth. Our approach is to study the structures of the level sets of the solution via Sard's Lemma and the implicit function theorem.