It is conjectured that a hyperbolic knot complement does not contain a closed embedded totally geodesic surface. In this paper, we show that there are no such surfaces in the complements of hyperbolic 3-bridge knots and double torus knots. Some topological criteria for a closed essential surface failing to be totally geodesic are given. Roughly speaking, sufficiently ‘complicated’ surfaces cannot be totally geodesic.

Let E be a real Banach space ordered by a closed, normal and generating cone. Suppose also that the order induced on E has the Riesz decomposition property. It is shown that if T:E → E is a positive linear operator with the property that y, z, a ∈ E with a ≧ Ty, Tz implies there is x ∈ E with x ≧ y, z and a ≧ Tx then the approximate point spectrum and spectrum of T are cyclic subsets of the complex plane. That is, if α = |α|γ lies in one of these sets then so does |α|γk for all integers k.

It is shown, given any positive real number λ and any point (x1, x2, x3) of R3 and any lattice λ R3; that there exists a point (z1, z2, z3) of λ for which

which generalizes a theorem due to Remak.

Let $p_{n}(x)=\int _{0}^{\infty }J_{0}(xt)[J_{0}(t)]^{n}xt\,dt$ be Kluyver’s probability density for $n$-step uniform random walks in the Euclidean plane. Through connection to a similar problem in two-dimensional quantum field theory, we evaluate the third-order derivative $p_{5}^{\prime \prime \prime }(0^{+})$ in closed form, thereby giving a new proof for a conjecture of J. M. Borwein. By further analogies to Feynman diagrams in quantum field theory, we demonstrate that $p_{n}(x),0\leq x\leq 1$ admits a uniformly convergent Maclaurin expansion for all odd integers $n\geq 5$, thus settling another conjecture of Borwein.

The object of this note is to show that under suitable restrictions some results on the wreath product of groups can be carried over to topological groups. We prove in particular the following analogue of the well-known theorem of Krasner and Kaloujnine (see for example [2] Theorem 3.5): Theorem. Let A and B be two locally compact topological groups, and let (C, ε) be an extension of A by B. If there exists a continuous left inverseof ε, that is to say a continuous mapping τ: B → C such that re is the identity on B, then there exists a continuous monomorphism of C into the topological standard wreath product of A by B.

For each complex reductive dual pair introduced by R. Howe, this paper presents a formula for the central elements of the universal enveloping algebras given by I. M. Gelfand. This formula provides an explicit description of the correspondence between the ‘centers’ of the two universal enveloping algebras.

In this paper, we review the parametrized strict deformation quantization of C*-bundles obtained in a previous paper, and give more examples and applications of this theory. In particular, it is used here to classify H3-twisted noncommutative torus bundles over a locally compact space. This is extended to the case of general torus bundles and their parametrized strict deformation quantization. Rieffel’s basic construction of an algebra deformation can be mimicked to deform a monoidal category, which deforms not only algebras but also modules. As a special case, we consider the parametrized strict deformation quantization of Hilbert C*-modules over C*-bundles with fibrewise torus action.

There exists a natural notion of convexity in the space of all compact convex sets in D. Thus, we may consider the space of all bounded closed convex families of compact convex sets. We present here a strange generic extremal behaviour of the elements of this space.

The Boolean ring B{M} universal over a meet semilattice M is examined. It is the vector space over the two element field Z2 with base M\{0}. The Z2 linear independence of a meet subsemilattice of a Boolean ring is characterized in order theoretic terms and some ramifications of this on B[M] are considered. The space (ℱpM) of proper filters of M is shown homeomorphic to the Stone space S(B[M]) of B[M] if M has no least element, with ℱP(M) ∪ {M} and S(B[M]) homeomorphic otherwise. The congruence lattice θ(M) of M is compared to the ideal lattice ℱ(B [M]) of B [M] with best results coming if M is a tree with zero when θ (M) = ℐ (B [M]).

This paper presents some properties of continuous complex-valued mean periodic functions of a single real variable. The theory of these functions is due mainly to Schwartz [7] and they have also been considered by Kahane [4, 5]. Most of the properties outlined here are also shared by the continuous meanperiodic functions on a half line introduced by Koosis [6].

The operators K, k, T and t are defined on the lattice of congruences on a Rees matrix semigroup S as follows. For ρ ∈ (S), ρK and ρk (ρT and ρt) are the greatest and the least congruences with the same kernel (trace) as ρ, respectively. We determine the semigroup generated by the operators K, k, T and t as they act on all completely simple semigroups. We also determine the network of congruences associated with a congruence ρ ∈ (S) and the lattice generated by it. The latter is then represented by generators and relations.

Bijective correspondences are established between the radical classes R (in a variety W of rings) with the property that a ring A is in R exactly when its finitely generated subrings are all in R, and certain filters of ideals in a free W-ring. It follows that such classes are determined by the polynomial identities satisfied by the finite subsets of their members. Analogous considerations are applied to radical classes R which, for a fixed integer n, have the property that a ring is in R if and only if its subrings generated by at most n elements are in R.

In a recent paper [1] Adati and Miyazawa studied conformally recurrent spaces, that is, Riemannian spaces defined by where is the conformal curvature tensor: λi is a non-zero vector and comma denotes covariant differentiation with respect to the metric tensor gij.

We consider two related classes of groups. For any group G of the first of these — the smallest class containing all finitely generated free groups and closed under cyclic amalgamations — we show that for any U, W ∈ G we can “effectively describe” the set of all x and y with U* and W* conjugate in G. For the second class, which consists of all groups obtained from the first class through cyclic HNN constructions, we solve the conjugacy and power-conjugacy problems.

Let N be a direct summand of a module which is a direct sum of modules of torsion-free rank one over a discrete valuation ring. Then there is a torsion module T such that N⊕T is also a direct sum of modules of torsion-free rank one.

A quasi-permutation group of degree n was defined in [3] to be a finite group with a faithful representation of degree n whose character has only non-negative rational integral values. If G is such a group, then the following simple properties of permutation groups of degree n were proved to hold also for G:

(i) the order of G is a divisor of the order of the symmetric group Sn of degree n; and (ii) if G is a p-group and n < p2, then G has exponent at most p and derived length at most 1 (i.e. G is elementary Abelian).

If we consider any particular topological semigroup S it may seem reasonable to ask for a characterization of all additions on S which make it a topological semiring. We are interested here in this problem when

(i) S is an (I)-semigroup;

(ii) S is [0, ∞) and the multiplication on S is such that 0 and 1 are Zero and identity respectively.

A commutative complex unital Banach algebra can be represented as a space of continuous complex-valued functions on a compact Hausdorff space via the Gelfand transform. However, in general it is not possible to represent a commutative real unital Banach algebra as a space of continuous real-valued functions on some compact Hausdorff space, and for this to happen some additional conditions are needed. In this note we represent a commutative real Banach algebra on a part of its state space and show connections with representations on the maximal ideal space of the algebra (whose existence one has to prove first).

We prove that a continuous map $\phi $ defined on the set of all $n\times n$ Hermitian matrices preserving order in both directions is up to a translation a congruence transformation or a congruence transformation composed with the transposition.

We compute the kernel of cup product of 1-dimensional cohomology classes for a group G acting trivially on Z or F2, by means of the naturality of cup product and the 5-term exact sequence of low degree of a suitable LHS spectral sequence. We determine thereby when cup product is injective, and when it is null.