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Volume 35 - February 1987

Contents

Page 2 of 3

Research Article

  • Semigroups of composition operators in Bergman spaces

  • Aristomenis G. Siskakis
  • Published online by Cambridge University Press:
    17 April 2009, pp. 397-406
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  • Semigroups consisting of composition operators are considered on weighted Bergman spaces. They are strongly continuous, and their infinitesimal generators are identified. One specific semigroup is used to obtain information on an averaging operator.

  • Nonlinear integral operators and chaos in Banach spaces

  • Phil Diamond
  • Published online by Cambridge University Press:
    17 April 2009, pp. 275-289
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  • Sufficient conditions are given for chaotic behaviour of continuous transformations on Banach spaces. The conditions avoid the requirement that mappings be expanding on compact sets and are probably easier to verify for many classes of operator equations than existing criteria. Two classes of integral operators on C[0, 1] are considered in the light of these results: one nonlinear but compact, the second noncompact.

  • Lattice coverings and the diagonal group

  • G. Ramharter
  • Published online by Cambridge University Press:
    17 April 2009, pp. 407-414
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  • Let M be any bounded set in n-dimensional Euclidean space. Then almost all n-dimensional lattices L with determinant 1 have the following property: There exists a diagonal transformation D with determinant 1 (depending on L) such that L does not cover space with DM. Moreover, if M has non-empty interior, the exceptional (null-) set contains at least enumerably many diagonally non-equivalent lattices.

  • Metric spaces with nice closed balls and distance functions for closed sets

  • Gerald Beer
  • Published online by Cambridge University Press:
    17 April 2009, pp. 81-96
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  • A metric space 〈X,d〉 is said to have nice closed balls if each closed ball in X is either compact or the entire space. This class of spaces includes the metric spaces in which closed and bounded sets are compact and those for which the distance function is the zero-one metric. We show that these are the spaces in which the relation F = Lim Fn for sequences of closed sets is equivalent to the pointwise convergence of 〈d (.,Fn)〉 to d (.,F). We also reconcile these modes of convergence with three other closely related ones.

  • Finite soluble groups have large centralisers

  • John Cossey
  • Published online by Cambridge University Press:
    17 April 2009, pp. 291-298
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  • We say that a finite group G has a large centraliser if G contains a non-central element x with |CG (x)| > |G|½. We prove that every finite soluble group has a large centraliser, confirming a conjecture of Bertram and Herzog.

  • A note on convex cones in topological vector spaces

  • Alicia Sterna-Karwat
  • Published online by Cambridge University Press:
    17 April 2009, pp. 97-109
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  • The aim of the present note is an independent study of a class of convex cones, which is the largest possible with regard to existence of cone-maximal points in abstract vector optimization problems.

  • Asymptotic equivalence of ordinary and operator-differential equations

  • P. S. Simeonov, D. D. Bainov
  • Published online by Cambridge University Press:
    17 April 2009, pp. 415-425
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  • The paper considers problems connected with the asymptotic equivalence of the system of ordinary differential equations

    and the system of operator differential equations

    The generality of the operator At guarantees a number of its important implementations. By a specific choice of the operator At the system (2) can be one of the concentrated delay, a system of distributed delay, a system with maxima, etcetera.

  • N-th root rings

  • Henry Heatherly, Altha Blanchet
  • Published online by Cambridge University Press:
    17 April 2009, pp. 111-123
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  • A ring for which there is a fixed integer n ≥ 2 such that every element in the ring has an n-th in the ring is called an n-th root ring. This paper gives numerous examples of diverse types of n-th root rings, some via general construction procedures. It is shown that every commutative ring can be embedded in a commutative n-th root ring with unity. The structure of n-th root rings with chain conditions is developed and finite n-th root rings are completely classified. Subdirect product representations are given for several classes of n-th root rings.

  • Homomorphisms of distributive p-algebras with countably many minimal prime ideals

  • M. E. Adams, V. Koubek, J. Sichler
  • Published online by Cambridge University Press:
    17 April 2009, pp. 427-439
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  • According to a result of Lee, varieties of pseudocomplemented distributive lattices form an ω+1 chain in which is the trivial variety and is the variety of Boolean algebras. In the present paper it is shown that the variety contains an almost universal subcategory B in which the members of Hom(B,B') associated with minimal prime ideals of B form a countably infinite set for any B,B' ∈ B. In particular, B3contains arbitrarily large algebras whose nontrivial endomorphisms form the countably infinite right zero semigroup. Our earlier results concerning categorical properties of varieties of pseudocomplemented distributive lattices show that no further reduction of the right zero count is possible.

  • On degenerate fully nonlinear elliptic equations in balls

  • Neil S. Trudinger
  • Published online by Cambridge University Press:
    17 April 2009, pp. 299-307
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  • We establish derivative estimates and existence theorems for the Dirichlet and Neumann problems for nonlinear, degenerate elliptic equations of the form F (D2u) = g in balls. The degeneracy arises through the possible vanishing of the function g and the degenerate Monge-Ampère equation is covered as a special case.

  • Holomorphic curves in the complex quadric

  • Gary R. Jensen, Marco Rigoli, Kichoon Yang
  • Published online by Cambridge University Press:
    17 April 2009, pp. 125-148
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  • A local theory of holomorphic curves in the complex hyperquadric is worked out using the method of moving frames. As a consequence a complete global characterization of totally isotropic curves is obtained.

Abstracts of Australasian Ph.D. Theses

  • Nondifferentiable programming and duality with modified convexity

  • V. Jeyakumar
  • Published online by Cambridge University Press:
    17 April 2009, pp. 309-313
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Research Article

  • On the area of planar convex sets containing many lattice points

  • P. R. Scott
  • Published online by Cambridge University Press:
    17 April 2009, pp. 441-454
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  • A classical theorem of van der Corput gives a bound for the volume of a symmetric convex set in terms of the number of lattice points it contains. This theorem is here generalized and extended for a large class of non-symmetric sets in the plane.

  • Extensions of continuous functions: reflective functors

  • W. N. Hunsaker, S. A. Naimpally
  • Published online by Cambridge University Press:
    17 April 2009, pp. 455-470
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  • The purpose of this paper is to develop a general technique for attacking problems involving extensions of continuous functions from dense subspaces and to use it to obtain new results as well as to improve some of the known ones. The theory of structures developed by Harris is used to get some general results relating filters and covers. A necessary condition is derived for a continuous function f: X → Y to have a continuous extension : λx → λy where λZ denotes a given extension of the space Z. In the case of simple extensions, is continuous and in the case of strict extensions is θ-continuous. In the case of strict extensions, sufficient conditions for uniqueness of are derived. These results are then applied to several extensions considered by Banaschewski, Fomin, Kattov, Liu-Strecker, Blaszczyk-Mioduszewski, Rudölf, etc.

Abstracts of Australasian Ph.D. Theses

  • The generation of water waves by travelling pressure disturbances

  • F. Viera
  • Published online by Cambridge University Press:
    17 April 2009, pp. 315-316
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Abstracts of Australian Ph.D. Theses

  • Micro-local analysis of operators with non-involutive characteristics

  • Baliganahalli Raja Iyengar Nagaraj
  • Published online by Cambridge University Press:
    17 April 2009, pp. 149-151
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Research Article

  • A note on a space Hp, a of holomorphic functions

  • H. O. Kim, S. M. Kim, E. G. Kwon
  • Published online by Cambridge University Press:
    17 April 2009, pp. 471-479
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  • For 0 < p < ∞ and 0 ≤a; ≤ 1, we define a space Hp, a of holomorphic functions on the unit disc of the complex plane, for which Hp, 0 = H∞, the space of all bounded holomorphic functions, and Hp, 1 = Hp, the usual Hardy space. We introduce a weak type operator whose boundedness extends the well-known Hardy-Littlewood embedding theorem to Hp, a, give some results on the Taylor coefficients of the functions of Hp, a and show by an example that the inner factor cannot be divisible in Hp, a.

Abstracts of Australian Ph.D. Theses

  • Some aspects of the critical problem for matroids

  • Geoffrey P. Whittle
  • Published online by Cambridge University Press:
    17 April 2009, pp. 153-154
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Abstracts of Australasian Ph.D. Theses

  • The gravitational lens effect of galaxies and black holes

  • Igor Bray
  • Published online by Cambridge University Press:
    17 April 2009, pp. 317-318
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Abstracts of Australian Ph.D. Theses

  • Boundary integral methods for the Laplace equation

  • William McLean
  • Published online by Cambridge University Press:
    17 April 2009, pp. 155-158
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Page 2 of 3