It is proved that if is a formal power series with algebraic p-adic coefficients which satisfies an algebraic differential equation, then a constant y4 > 0 and a constant integer h1 ≧ 0 exist such that .

It is shown that the complex semigroup algebra of a free monoid of rank at least two is *-primitive, where * denotes the involution on the algebra induced by word-reversal on the monoid.

We generalise the approximation theory described in Mahier's paper “Perfect Systems” to linked simultaneous approximations and prove the existence of nonsingular approximation and of transfer matrices by generalising Coates' normality zig-zag theorem. The theory sketched here may have application to constructions important in the theory of diophantine approximation.

In this paper we describe the moduli spaces of degree d branched superminimal immersions of a compact Riemann surface of genus g into S4. We prove that when d ≥ max {2g, g + 2}, such spaces have the structure of projectivzed fibre products and are path-connected quasi projective varieties of dimension 2d − g + 4. This generalizes known results for spaces of harmonic 2-spheres in S4.

A λ-graph system is a labeled Bratteli diagram with shift transformation. It is a generalization of finite labeled graphs and presents a subshift. In Doc. Math. 7 (2002) 1–30, the author constructed a C*-algebra O£ associated with a λ-graph system £ from a graph theoretic view-point. If a λ-graph system comes from a finite labeled graph, the algebra becomes a Cuntz-Krieger algebra. In this paper, we prove that there is a bijective correspondence between the lattice of all saturated hereditary subsets of £ and the lattice of all ideals of the algebra O£, under a certain condition on £ called (II). As a result, the class of the C*-algebras associated with λ-graph systems under condition (II) is closed under quotients by its ideals.

We give a partial answer to the following questions: Given an additive category and a class of sequences, under what conditions is the universal functor to the abelian category faithful and what other sequences are taken to exact sequences?

The “answers” to these questions appear as theorems 2.2 and 3.2 respectively and amount to a weakening of the condition that there be enough relative projectives.

We then characterize those additive categories with exactness which have the property that all relative exact sequences are determined by a small set of functors into the category of abelian groups.

In this paper, we consider contact metric three-manifolds $(M;\unicode[STIX]{x1D702},g,\unicode[STIX]{x1D711},\unicode[STIX]{x1D709})$ which satisfy the condition $\unicode[STIX]{x1D6FB}_{\unicode[STIX]{x1D709}}h=\unicode[STIX]{x1D707}h\unicode[STIX]{x1D711}+\unicode[STIX]{x1D708}h$ for some smooth functions $\unicode[STIX]{x1D707}$ and $\unicode[STIX]{x1D708}$, where $2h=\unicode[STIX]{x00A3}_{\unicode[STIX]{x1D709}}\unicode[STIX]{x1D711}$. We prove that if $M$ is conformally flat and if $\unicode[STIX]{x1D707}$ is constant, then $M$ is either a flat manifold or a Sasakian manifold of constant curvature $+1$. We cannot extend this result for a smooth function $\unicode[STIX]{x1D707}$. Indeed, we give such an example of a conformally flat contact three-manifold which is not of constant curvature.

It is shown that if {Gn: n = 1, 2,…} is a countable family of Hausdorff kω-topological groups with a common closed subgroup A, then the topological amalgamated free product *AGn exists and is a Hausdorff kω-topological group with each Gn as a closed subgroup. A consequence is the theorem of La Martin that epimorphisms in the category of kω-topological groups have dense image.

This paper is a contribution to the problem of characterizing the ℵ0-categorical Stone algebras. If the dense set is either finite or a chain, the problem is solved by reducing it to the ℵ0-categoricity of the skeleton and the dense set, solutions for these being known. If the dense set is a Boolean algebra, we show that this type of reduction works for certain subclasses but not for all such algebras. For generalized Post algebras the characterization problem is solved completely.

Let Ω[x1, x2, …, xn] denote the algebra of polynomials in variables x1, x2, …, xn with coefficients from a fixed field Ω of characteristic zero, where n = 1, 2,…. There exists a natural projection which maps xn onto 0 and all the other variables onto themselves, for n = 1, 2, …. This enables one to construct the corresponding inverse limit which we here denote by Ω[x]. The algebra Ω[x] has a natural degree function defined on it.

In this article we consider whether, for integrable functions on the unit ball of ℂn, the mean-value property implies (α,β)-harmonicity. We find that the answer is affirmative when 0<n+α+β≤ρ0, but is negative when n+α+β>ρ0. Here ρ0 is a constant between 11.025 and 11.069.

The series is said to be summable |Eα| (0 < α < 1) if where Sv = a0 + a1 … + av, and . Since (see [2]), (1) is equivalent to .

If a property P of ring elements satisfies conditions (a)-(d), then the largest homomorphically closed class having no non-zero P-element is a dual radical in the sense of Andrunakievič, and every dual radical can be obtained in this way. Also properties defined by polynomials are considered and as an application we get various characterizations of the Behrens radical.

In this paper it is proved that the principal series of representations of Γ = Z2*…*Z2 may be analytically continued to give uniformly bounded representations on the same Hilbert space, and that these representations are irreducible. Further, the reducibility of the restrictions to Γ ⊂ SL(2, Qp) of the irreducible unitary representations of SL(2, Qp) is examined.

Recently, we have introduced the notion of stable permutations in a Latin rectangle L(r×c) of r rows and c columns. In this note, we prove that the set of all stable permutations in L (r×c) forms a distributive lattice which is Boolean if and only if c ≤ 2.

We give algebraic proofs of some results of Wang on homomorphisms of nonzero degree between aspherical closed orientable 3-manifolds. Our arguments apply to PDn-groups which are virtually poly-Z or have a Kropholler decomposition into parts of generalized Seifert type, for all n.

Let ${\mathcal{A}}$ be a complex unital Banach algebra, let $a$ be an element in it and let $0<\unicode[STIX]{x1D716}<1$. In this article, we study the upper and lower hemicontinuity and joint continuity of the condition spectrum and its level set maps in appropriate settings. We emphasize that the empty interior of the $\unicode[STIX]{x1D716}$-level set of a condition spectrum at a given $(\unicode[STIX]{x1D716},a)$ plays a pivotal role in the continuity of the required maps at that point. Further, uniform continuity of the condition spectrum map is obtained in the domain of normal matrices.

In this paper we discuss the existence of an are of minimal length joining two arbitrary, yet fixed points in a complete metric space, where the metric is restricted only by the properties (A) and (B) given below. It is shown that under these conditions an arc of least length joining any two fixed points exists, and is unique. In addition, its length is shown to be equal to the metrie distance between the points.

An infinite subset of ω is monotone (1–1) if every recursive function is eventually monotone on it (eventually constant on it or eventually 1–1 on it). A recursively enumerable set is co-monotone (co-1–1) just if its complement is monotone (1–1). It is shown that no implications hold among the properties of being cohesive, monotone, or 1–1, though each implies r-cohesiveness and dense immunity. However it is also shown that co-monotone and co-1–1 are equivalent, that they are properly stronger than the conjunction of r-maximality and dense simplicity, and that they do not imply maximality.

The quotient bounded and the universally bounded elements in a calibrated locally convex algebra are defined and studied. In the case of a generalized B*-algebra A, they are shown to form respectively b* and B*-algebras, both dense in A. An internal spatial characterization of generalized B*-algebras is obtained. The concepts are illustrated with the help of examples of algebras of measurable functions and of continuous linear operators on a locally convex space.