Following an earlier paper by Akinrelere (1981), we consider a laminar boundary layer at low speeds in which density is sensibly constant and frictional heating is neglected. Also following the approach of Goldstein (1948) and Stewartson (1958), a singularity is established at separation for the thermal fields. The heat transfer is determined as a function of ξ = xs – x¼/l where xs is the separation point and l in a characteristic length.

The results are for arbitrary Prandtl number σ. The results of Curle (1979) that the heat transfer near separation varies as σ¼ (at least for the first four terms) are confirmed.

Let S be an inverse semigroup and F a field. It is shown that if F has characteristic 0 and is not algebraic over its prime subfield then the algebra of S over F is semiprimitive (i.e. Jacobson semisimple). This generalises a well-known theorem on group algebras due to Amitsur. Similar results for the case in which F has prime characteristic are obtained under the additional hypotheses that S is completely semisimple or that S is E-unitary with a totally ordered semilattice.

We continue with the work of an earlier paper concerning the use of partial differential equations to prove the uniform convergence of the eigenfunction expansion associated with a left definite two-parameter system of ordinary differential equations of the second order.

In the paper the existence is proved of a solution of a non-linear Goursat problem for a 4th order partial differential equation with the boundary conditions given on four curves emanating from a common point. The problem is reduced to a system of integro-functional equations and then Schauder's fixed point theorem is applied.

We consider the ordinary differential equation [Bu(t)]′ = Au(t) with A and B linear operators with domains in a Banach space X and ranges in a Banach space Y. The initial condition is that the limit as (t → 0 of Bu(t) is prescribed in Y. We study the properties of the “solution operator” S(t) which maps the initial state in Y to the solution u(t) at time t. The notion of infinitesimal generator A of S(t) is introduced and the relationships between S(t), an associated semi-group E(t), the operators A and B and some other operators are studied. In particular a pair of operators Ao and Bo, derived from A and B, determine the family S(t) of operators. These so-called “generating pairs” are characterized. The operators A and B and Ao and Bo need not be closed, but form so-called closed pairs which is a weaker condition. We also discuss two applications of the theory.

Some sufficient conditions are obtained on the coefficient g and the initial values Φ and ψfor the solution ot the non-linear hyperbolic equation

to change sign in the first quadrant. An example is given to show that is not sufficient in the linear case.

We characterize direct products of finite monogenic inverse semigroups; we show that a finite monogenic inverse semigroup which is not a group is directly indecomposable and that a finite semigroup which is decomposable into a direct product of monogenic inverse semigroups which are not groups is uniquely so decomposable. We determine when a finite semigroup can be decomposed into a direct product of non-group monogenic inverse semigroups and show how the direct factors, if they exist, can be found.

The classification of orientable vector bundles over CW-complexes of dimension ≦8 is given in terms of characteristic classes using elementary homotopy theoretic methods and relations among characteristic classes.

In this paper, a formally J-symmetric, linear differential expression of 2nth order, with complex-valued coefficients, is considered. A number of results concerning the location of the essential spectrum of associated operators are obtained. These are extensions of earlier work dealing with complex Strum-Liouville operators, and include results which, in the real case, are due to Birman, Glazman and others. They lead to criteria, for the non-emptiness of the regularity field, of the corresponding minimal operator-a condition which is needed in the theory of J-selfadjoint extensions.

Let A and B be commutative Noetherian local rings, such that B is a finitely generated free A-module. It is shown that if M is a balanced big Cohen–Macaulay A-module (that is, every system of parameters for A is an M-sequence), then M⊗AB is a balanced big Cohen-Macaulay B-module.

Let A be a unital C*-algebra and let B be an abelian C*-subalgebra containing the identity of A. For any pure state h of B let Fh be the set of states of A which restrict to h on B. Necessary and sufficient conditions are given for an element x in A to have the property that, for each h, x is unable to distinguish between distinct elements of Fh. By specializing, this leads to a new proof of a theorem giving necessary and sufficient conditions for Fh to be a singleton for each h.

It is also shown that if A is postliminal and π(B) is a maximal abelian C*-subalgebra of π(B) for each irreducible representation π of A then Fh is a Choquet simplex for each h.

In this paper, we demonstrate an intimate connection between the spectrum of a multiparameter problem and the joint spectrum of an associated set of commuting operators, and show that the spectrum of a multiparameter problem involving bounded operators is non-empty. Multiparameter systems involving compact and self-adjoint operators are considered, and some simplification of results in the literature are noted.

By an inverse transversal of a regular semigroup S we mean an inverse subsemigroup that contains a single inverse of every element of S. A certain multiplicative property (which in the case of a band is equivalent to normality) is imposed on an inverse transversal and a complete description of the structure of S is obtained.

Quasi-differential expressions with matrix-valued coefficients, which generalize those of Shin and Zettl, are considered with regard to equivalence, adjoints and symmetry. The characterization results imply that in the scalar case the class of quasi-differential expressions considered here coincides with that of Shin and is equivalent to that of Zettl. Furthermore polynomials in quasi-differential expressions are defined as expressions of the same kind and shown to coincide with the usual ones. Finally it is indicated that the known general results for the deficiency indices carry over to quasi-differential expressions.

Let J(KG) be the Jacobson radical of the group algebra KG of a finite p-solvable group G over a field K of characteristic p > 0, and let t(G) be the least positive integer t such that J(KG)t = 0. In this paper we determine the structure of G with t(G) = 4 under the assumption that H is abelian, H is metacyclic, or the order of H is not divisible by 3 where H = O2'(G).