We give here a detailed description of the Brill–Noether loci of stable vector bundles of slope 2 on a smooth projective curve, which is assumed to be nonhyperelliptic.

In this paper, the strongly Cohen–Macaulay ideals of second analytic deviation one are characterized in terms of the depth properties of the powers of the ideal in the ‘standard range’. This provides an explanation of the behaviour of certain ideals that have appeared in the literature.

G[Lscr ][Uscr ][Cscr ] is the largest semigroup compactification of the locally compact group G. When G is not compact, given q ∈ G* = G[Lscr ][Uscr ][Cscr ] \ G, there is p ∈ G* such that x [map ] qx is discontinuous at p (Theorem 2). If G is σ-compact, there is one p which will serve for all q (Theorem 1).

In this paper, what is already known about defect 2 blocks of symmetric groups is used to deduce information about the corresponding blocks of Schur algebras. This information includes Ext-quivers and decomposition numbers, as well as Loewy structures of the Weyl modules, principal indecomposable modules and tilting modules.

It is shown that for each compactly generated totally disconnected locally compact group G, there is a finite number of prime numbers, p1, p2, …, pn, such that the scale function s : G → N satisfies s(x) = p1a1(x)p2a2(x)…, pnan(x), where x ∈ G.

The classical Mikhlin–Hörmander multiplier theorem is generalised to the context of discrete groups of polynomial volume growth.

We prove the existence of a power series having radius of convergence 0, whose partial sums have universal approximation properties on any compact set with connected complement that is contained in a finite union of circles centred at 0 and having rational radii, but do not have such properties on any compact set with nonempty interior. This relates to a theorem of A. I. Seleznev.

It is proved that every topologically pure extension of Fréchet algebras 0 → I → A → A/I → 0 such that I is strongly H-unital has the excision property in continuous (co)homology of the following types: bar, naive-Hochschild, Hochschild, cyclic, and periodic cyclic. In particular, the property holds for every extension of Fréchet algebras such that I has a left or right bounded approximate identity.

Let X be a nonsingular real algebraic variety, and let X([Copf ]) be its nonsingular projective complexification. We study the following question: when does the homology class represented by X in the homology group of X([Copf ]) vanish? An application concerning the structure of the set of regular mappings is given.

Let [Gfr ] be a finite-dimensional semisimple Lie algebra over the complex numbers. Let A be the finite-dimensional algebra of a (regular or singular) block of the BGG-category [Oscr ] . By results of Soergel, A has a combinatorial description in terms of a subalgebra C0 of the coinvariant algebra C. König and Mazorchuk have constructed an embedding from C0-mod into the category [Fscr ](Δ) of A-modules having a Verma flag. This is the main tool for the classification of [Fscr ] (Δ) into finite, tame and wild representation types presented here. As a consequence a classification of A-mod into finite, tame and wild representation types is obtained, thus re-proving a recent result of Futorny, Nakano and Pollack.

This paper improves a theorem of Bergweiler on the zeros of functions f ○ g — R with f meromorphic, g entire and R rational. The proof yields a simple inequality for the number of zeros and T(r, g).

We describe a general construction of a module A from a given module B such that Ext(B, A) = 0, and we apply it to answer several questions on splitters, cotorsion theories and saturated rings.

The aim of this paper is to study properties of sequences that are recursively defined by a linear equation and their applications to the truncated moment problem in connection with the problem of subnormal completion of the truncated weighted shifts. Special cases are considered and some classical results due to Stampfli, Curto and Fialkow are recovered using elementary techniques.

Let φ be an analytic function from [ ] to the symmetrized bidisc

(formula here)

We show that if φ(0) = (0,0) and φ(λ) = (s, p) in the interior of Γ, then

(formula here)

Moreover, the inequality is sharp: we give an explicit formula for a suitable φ in the event that the inequality holds with equality. We show further that the inverse hyperbolic tangent of the left-hand side of the inequality is equal to both the Caratheodory distance and the Kobayashi distance from (0,0) to (s, p) in int Γ

It is shown that every ascending HNN extension of a finitely generated free group is Hopfian. An important ingredient in the proof is that under certain hypotheses on the group H, if G is an ascending HNN extension of H, then cd(G) = cd(H) + 1.

An example is constructed of a manifold for which two quadratic forms corresponding to the fourth-order invariant operators are not equivalent.

Let p(n) denote the ordinary partition function. Subbarao conjectured that in every arithmetic progression r (mod t) there are infinitely many integers N ≡ r (mod t) for which p(N) is even, and infinitely many integers M ≡ r (mod t) for which p(M) is odd. We prove the conjecture for every arithmetic progression whose modulus is a power of 2.

It is shown that, for λ > ω, λ-orthogonality classes in locally λ-presentable categories coincide with full subcategories that are closed under limits and under λ-directed colimits. This comes as a surprise, since the statement is known to be false for λ = ω.

We establish the peak point conjecture for uniform algebras generated by smooth functions on two-manifolds: if A is a uniform algebra generated by smooth functions on a compact smooth two-manifold M, such that the maximal ideal space of A is M, and every point of M is a peak point for A, then A = C(M). We also give an alternative proof in the case when the algebra A is the uniform closure P(M) of the polynomials on a polynomially convex smooth two-manifold M lying in a strictly pseudoconvex hypersurface in Cn.

We characterize the extremal functions for Heisenberg type inequalities of the form

(formula here)

The method also yields an alternative and elementary derivation of the sharp constant in Nash's inequality, originally found by Carlen and Loss.