When a semi-infinite line load moves lengthways, at supersonic velocity, on the plane surface of an elastic solid, the resulting velocity field is conical. There are two characteristic cones, one associated with dilatation effects and the other with shear effects. The propagation process is more complicated than the well-known case of conical flow in supersonic aerodynamics not only because of the presence of two cones of discontinuity but also because the presence of a free surface implies interaction between shear and dilatation effects. It is the interaction process at the free surface which is examined in detail in this paper.

The results of this fundamental problem may be extended by the process of superposition to more general steadily moving loads. In particular by differentiating with respect to time, the potential of a steadily moving point load is obtained explicitly.

Two subgroups ME(G) and MI(G) of the Schur multiplier M(G) of a finite group G are introduced: ME(G) contains those cohomology classes [α] of M(G) for which every element of G is α-regular, and MI(G) consists of those cohomology classes of M(G) which contain a G-invariant cocycle. It is then shown that under suitable circumstances, such as when G has odd order, that each element of MI(G) can be expressed as the product of an element of ME(G) and an element of the image of the inflation homomorphism from M(G/G′) into M(G).

In this article, we prove that for a finite field Fq with even q > 3, any complete mapping polynmial of Fq has reduced degree at most q − 3. This is a solution to a problem of Niederreiter and Robinson about finite fields.;

In this note we investigate lacunarity or ‘thin’ subsets in the dual object of a compact group via different classes of summing operators between Banach spaces. In particular, we give characterisations of Sidon and ∧ (p) sets, 2 < p < ∞

In an extrapolation argument, we prove certain $L^{p}\,(1<p<\infty )$ estimates for nonisotropic Marcinkiewicz operators associated to surfaces under the integral kernels given by the elliptic sphere functions ${\rm\Omega}\in L(\log ^{+}L)^{{\it\alpha}}({\rm\Sigma})$ and the radial function $h\in {\mathcal{N}}_{{\it\beta}}(\mathbb{R}^{+})$. As applications, the corresponding results for parametric Marcinkiewicz integral operators related to area integrals and Littlewood–Paley $g_{{\it\lambda}}^{\ast }$-functions are given.

If ε is an endomorphism of a finitely generated residually finite group onto a subgroup Fε of finite index in F, then there exists a positive integer k such that ε is an isomorphism of Fεk. If K is the kernel of ε, then K is a finite group so that if F is a non trivial free product or if F is torsion free, then ε is an isomorphism on F. If ε is an endomorphism of a finitely generated resedually finite group onto a subgroup Fε (not necessatily of ginite index in F) and if the kernel of ε obeys the minimal condition for subgroups then there exists a positive integer k such that ε is an isomorphism on Fεk.

The most general continuous time and state branching (C.B.) process (Xt) can be constructed as a certain random time transformation of a spectrally positive Levy process. When the generating process is compound Poisson with a superimposed negative linear drift and the C.B. process is not supercritical, then there is a random time T such that Xt+T = e-ctXT where c > 0 is the drift parameter. Thus T is the last epoch of random variation.

The present day theory of finite groups might be regarded as the outgrowth of the algebraic theory of equations. In much the same way one might consider the modern theory of infinite groups as stemming from late nineteenth century topology. The groups that crop up in topology are of a particularly simple type in that they are both finitely generated and finitely related. This means that every element in such a group can be expressed in terms of a finite number of elements and their inverses and every relation is an algebraic consequence of a finite number of relations between these elements. In other words the legacy of topology to group theory is the estate of finitely presented groups. This talk is concerned with the seemingly simplest of the finitely presented groups, the so-called groups with a single defining relator.

Let 𝒳 be a space of homogeneous type in the sense of Coifman and Weiss. In this paper, two weighted estimates related to weights are established for singular integral operators with nonsmooth kernels via a new sharp maximal operator associated with a generalized approximation to the identity. As applications, the weighted Lp(𝒳) and weighted endpoint estimates with general weights are obtained for singular integral operators with nonsmooth kernels, their commutators with BMO (𝒳) functions, and associated maximal operators. Some applications to holomorphic functional calculi of elliptic operators and Schrödinger operators are also presented.

A notion of entropy for the non-singular action of finite co-ordinate changes on is introduced. This quantity-average co-ordinate or AC entropy-is calculated for product measures and G-measures. It is shown that the type III classes can be subdivided using AC entropy. An equivalence relation is established for which AC entropy is an invariant.

For an algebraic structure A denote by d(A) the smallest size of a generating set for A, and let d(A)=(d(A),d(A2),d(A3),…), where An denotes a direct power of A. In this paper we investigate the asymptotic behaviour of the sequence d(A) when A is one of the classical structures—a group, ring, module, algebra or Lie algebra. We show that if A is finite then d(A) grows either linearly or logarithmically. In the infinite case constant growth becomes another possibility; in particular, if A is an infinite simple structure belonging to one of the above classes then d(A) is eventually constant. Where appropriate we frame our exposition within the general theory of congruence permutable varieties.

We describe several recursive constructions for designs which use designs with “holes”. As an application, we give a short new proof of the Doyen-Wilson Theorem.

Totally umbilical submanifolds of dimension greater than four in quaternion-space-forms are completely classified.

Individuals in a population which grows according to the rules defining the Markov branching process can mutate into novel allelic forms. We obtain some results about the time of the last mutation and the limiting frequency spectrum. In the present context these results refine certain results obtained in the discrete time case and they answer some conjectures still unresolved for the discrete time case.

This article is devoted to studying maximal π spaces where π = Lindelöf, countably compact, connected, lightly compact or pseudocompact. Necessary and sufficient conditions for Lindelöf or countably compact spaces to be maximal Lindelöf or maximal countably compact have been obtained. On the other hand only necessary conditions for maximal π spaces have been deduced where π = connected, lightly compact or pseudocompact.

In this paper, we study the structure of certain conditional expectation on crossed product C*-algebra. In particular, we prove that the index of a conditional expectation E: B → A is finite if and only if the index of the induced expectation from B ⋊ G onto A ⋊ G is finite where G is a discrete group acting on B.

Every invertible n-by-n matrix over a ring R satisfying the first Bass stable range condition is the product of n simple automorphisms, and there are invertible matrices which cannot be written as the products of a smaller number of simple automorphisms. This generalizes results of Ellers on division rings and local rings.

Loy and Miller [4] have studied tight Riesz groups (G, ≦), without pseudozeros, and with (G, ≼) an l-group. In this paper we study abelian l-groups (G, ≼) on which a tight Riesz order can the defined, such that ⋞ is precisely the associated order. Such an order we call a CTRO (compatible tight Riesz order).

In a survey article [1] Baumslag posed the problem of determining the abelian subgroups of a one-relator group. The solution of this problem was stated but not proved in [5], and partly solved by Moldavanskii [4]. In this paper it will be proved that the centralizer of every non-trivial element in a one-relator group with torsion is cyclic, and that the soluble subgroups of a one-relator groups with torsion are cyclic groups or the infinite dihedral group. That both types of groups may occur as subgroups is easily seen by considering

The author has previously associated to each commutative ring with unit $R$ and étale groupoid $\mathscr{G}$ with locally compact, Hausdorff and totally disconnected unit space an $R$-algebra $R\,\mathscr{G}$. In this paper we characterize when $R\,\mathscr{G}$ is Noetherian and when it is Artinian. As corollaries, we extend the characterization of Abrams, Aranda Pino and Siles Molina of finite-dimensional and of Noetherian Leavitt path algebras over a field to arbitrary commutative coefficient rings and we recover the characterization of Okniński of Noetherian inverse semigroup algebras and of Zelmanov of Artinian inverse semigroup algebras.