By a linear canonical system we mean a system of linear differential equations of the form where J is an invertible skew-Hermitian matrix and H(t) is a continuous Hermitian matrix valued function. We reserve the name Hami1tonia for real canonical systems with where Ik denotes the k × k unit matrix. In recent years the stability properties of Hamiltonian systems whose coefficient matrix H(t) is periodic have been deeply investigated, mainly by Russian authors ([2], [3], [5], [7]). An excellent survey of the literature is given in [6]. The purpose of the present paper is to extend this theory to canonical systems. The only work which we know of in this direction is a paper by Yakubovič [9].

Matching theorems, fixed point theorems and minimax inequalities are obtained in H-spaces which generalize the corresponding results of Bae-Kim-Tan, Browder, Fan, Horvath, Kim, Ko-Tan, Shih-Tan, Takahashi, Tan and Tarafdar to non-compact and/or non-convex settings.

Our title has become something of a misnomer, however we retain it since drafts of this note have been quoted with it.

Let Gbe a primitive permutation group on a finite set Ω. We investigate the subconstitutents of G, that is the permutation groups induced by a point stabilizer on its orbits in Ω, in the cases where Ghas a diagonal action or a product action on Ω. In particular we show in these cases that no subconstituent is doubly transitive. Thus if G has a doubly transitive subconstituent we show that G has a unique minimal normal subgroup N and either N is a nonabelian simple group or N acts regularly on Ω: we investigate further the case where N is regular on Ω.

We introduce perfect effect algebras and we show that every perfect algebra is an interval in the lexicographical product of the group of all integers with an Abelian directed interpolation po-group. To show this we introduce prime ideals of effect algebras with the Riesz decomposition property (RDP). We show that the category of perfect effect algebras is categorically equivalent to the category of Abelian directed interpolation po-groups. Moreover, we prove that any perfect effect algebra is a subdirect product of antilattice effect algebras with the RDP.

In this paper, we investigate the properties of locally univalent and multivalent planar harmonic mappings. First, we discuss coefficient estimates and Landau’s theorem for some classes of locally univalent harmonic mappings, and then we study some Lipschitz-type spaces for locally univalent and multivalent harmonic mappings.

This paper shows that every lattice group G can be densely embedded in a unique laterally complete lattice group H (the lateral completion of G). All reasonable structure properties of G are inherited by H and we have the following relationships between the ideal radical L(G), the distributive radical D(G) and the radical R(G) of G and the corresponding radicals of H. .

The purpose of this paper is to provide a detailed treatment of the behaviour of essential spectra of closed densely defined linear operators subjected to additive perturbations not necessarily belonging to any ideal of the algebra of bounded linear operators. If A denotes a closed densely defined linear operator on a Banach space X, our approach consists principally in considering the class of A-closable operators which, regarded as operators in ℒ(XA, X) (where XA denotes the domain of A equipped with the graph norm), are contained in the set of A-Fredholm perturbations (see Definition 1.2). Our results are used to describe the essential spectra of singular neutron transport equations in bounded geometries.

We extend an uncertainty principle due to Cowling and Price to Euclidean spaces, Heisenberg groups and the Euclidean motion group of the plane. This uncertainty principle is a generalisation of a classical result due to Hardy. We also show that on the real line this uncertainty principle is almost equivalent to Hardy's theorem.

A relationship between symplectic geometry and information geometry is studied. The square of a dually flat space admits a natural symplectic structure that is the pullback of the canonical symplectic structure on the cotangent bundle of the dually flat space via the canonical divergence. With respect to the symplectic structure, there exists a moment map whose image is the dually flat space. As an example, we obtain a duality relation between the Fubini–Study metric on a projective space and the Fisher metric on a statistical model on a finite set. Conversely, a dually flat space admitting a symplectic structure is locally symplectically isomorphic to the cotangent bundle with the canonical symplectic structure of some dually flat space. We also discuss nonparametric cases.

Paterson showed how to construct an étale groupoid from an inverse semigroup using ideas from functional analysis. This construction was later simplified by Lenz. We show that Lenz’s construction can itself be further simplified by using filters: the topological groupoid associated with an inverse semigroup is precisely a groupoid of filters. In addition, idempotent filters are closed inverse subsemigroups and so determine transitive representations by means of partial bijections. This connection between filters and representations by partial bijections is exploited to show how linear representations of inverse semigroups can be constructed from the groups occurring in the associated topological groupoid.

The purpose of this paper is to show that the various differentiability conditions for the norm of a normed linear space can be characterised by continuity conditions for a certain mapping from the space into its dual. Differentiability properties of the norm are often more easily handled using this characterisation and to demonstrate this we give somewhat more direct proofs of the reflexivity of a Banach space whose dual norm is strongly differentiable, and the duality of uniform rotundity and uniform strong differentiability of the norm for a Banach space.

The main result of this paper is the theorem in the title. Only special cases of it seem to be known so far. As an application, we obtain a result on the unique extension of Galois connexions. As a matter of fact, it is only by the use of Galois connexions that we obtain the main result, in its present generality.

If (X, ) is a set X with topology we shall say that is connected if (X, ) is a connected topological space. We shall investigate the existence of and the properties of maximal connected topologies.

Methods from the theory of orthogonal polynomials are extended to L-polynomials . By this means the authors and W. B. Jones (J. Math. Anal. Appl. 98 (1984), 528–554) solved the strong Hamburger moment problem, that is, given a double sequence , to find a distribution function ψ(t), non-decreasing, with an infinitenumber of points of increase and bounded on −∞ < t < ∞, such that for all integers . In this article further menthods such as analogues of the Lioville-Ostrogradski formula and of the Christoffel-Darboux formula are developed to investigated When the moment porblem has a unique solution. This will be the case if and only if a sequence of nested disks associated with the sequence has only a point as its intersection (the so called limit point case).

We develop a concrete Fourier transform on a compact Lie group by means of a symbol calculus, or *-product, on each integral co-adjoint orbit. These *-products are constructed by means of a moment map defined for each irreducible representation. We derive integral formulae for these algebra structures and discuss the relationship between two naturally occurring inner products on them. A global Kirillov-type character is obtained for each irreducible representation. The case of SU(2) is treated in some detail, where some interesting connections with classical spherical trigonometry are obtained.

A subspace of a Banach space is called an operator range if it is the continuous linear image of a Banach space. Operator ranges and operator ideals with fixed range space are investigated. Properties of strictly singular, strictly cosingular, weakly sequentially precompact, and other classes of operators are derived. Perturbation theory and closed semi-Fredholm operators are discussed in the final section.

The family (R) of all endomorphisms of a ring R is a semigroup under composition. It follows easily that if R and T are isomorphic rings, then (R) and (T) are isomorphic semigroups. We devote ourselves here to the converse question: ‘If (R) and (T) are isomorphic, must R and T be isomorphic?’ As one might expect, the answer is, in general, negative. For example, the ring of integers has precisely two endomorphisms – the zero endomorphism and the identity automorphism. Since the same is true of the ring of rational numbers, the two endomorphism semigroups are isomorphic while the rings themselves are certainly not.

The actions, anomalies and quantization conditions allow the M2-brane and the M5-brane to support, in a natural way, structures beyond spin on their world-volumes. The main examples are twisted string structures. This also extends to twisted stringc structures which we introduce and relate to twisted string structures. The relation of the C-field to Chern–Simons theory suggests the use of the string cobordism category to describe the M2-brane.

We consider a single-server queueing system with first-come first-served queue discipline in which (i) customers arrive at the instants 0 = A0 < A1 < A2 < …, with time interval between the mth and (m+1)th arrivals