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Volume 28 - October 1983

Contents

Page 2 of 3

Research Article

  • Prolongations of linear connections to the frame bundle

  • Luis A. Cordero, Manuel de Leon
  • Published online by Cambridge University Press:
    17 April 2009, pp. 367-381
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  • In this paper we construct the prolongation of a linear connection Γ on a manifold Μ to the bundle space of its frame bundle, and show that such prolongated connection coincides with the so-called complete lift of Γ to .

  • On two new classes of locally convex spaces

  • Kazuaki Kitahara
  • Published online by Cambridge University Press:
    17 April 2009, pp. 383-392
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  • The purpose of this paper is to introduce two new classes of locally convex spaces which contain the classes of semi-Montel and Montel spaces. Further we give some examples and study some properties of these classes. As to permanence properties, these classes have similar properties to semi-Montel and Montel spaces except strict inductive limits and these classes are not always preserved under their completions. We shall call these two classes as β–semi–Montel and β–Montel spaces. A β–semi–Montel space is obtained by replacing the word “bounded” by “strongly bounded” in the definition of a semi–Montel space. If a β–semi–Montel space is infra-barrelled, we call the space β–Montel.

  • Inverse limit theorem and expansion theorem for cohomological dimension

  • Satya Deo, Subhash Muttepawar
  • Published online by Cambridge University Press:
    17 April 2009, pp. 67-75
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  • For a given ground ring L, let dimL(X) denote the sheaf theoretic cohomological dimension of a space X. In this paper we prove an inverse limit theorem for this dimension function. Then we apply this theorem to show that for a large classs of rings the Freudenthal's expansion theorem, expressing a compact metric space X of dimL(X) as the inverse limit of an system of compact polyhedra Kα of dimL(Kα), is not valid.

  • Varieties with modular subalgebra lattices

  • Trevor Evans, Bernhard Ganter
  • Published online by Cambridge University Press:
    17 April 2009, pp. 247-254
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  • A classification is begun of varieties of algebras with the property that each algebra in the variety has a modular lattice of subalgebras. This turns out to be a very restrictive condition. Such a variety is hamiltonian. If the algebras in it are idempotent, then it is a variety of sets. A variety is subalgebra-modular if and only if it is hamiltonian and satisfies certain conditions on the terms in its three generator free algebras.

  • Twills with bounded float length

  • Janet A. Hoskins, Cheryl E. Praeger, Anne Penfold Street
  • Published online by Cambridge University Press:
    17 April 2009, pp. 255-281
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  • The simple twills on n harnesses can be classified according to their maximum float length. The number of n-harness twills with specified maximum float length is determined both by Burnside enumeration and, for n ≤ 20 , by an adaptation of a sieve algorithm for twills.

  • On convex and starlike univalent functions

  • R.K. Pandey, G.P. Bhargava
  • Published online by Cambridge University Press:
    17 April 2009, pp. 393-400
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  • In this paper we obtain some classical results by using the general integral operators which transform Jakubowski's class K(m, M) into itself and K(μ) × S(m, M) into K(μ). Our results generalize some recent known results due to Causey and Reade, Patil and Thakare.

  • Families of partial functions

  • Kevin P. Balanda
  • Published online by Cambridge University Press:
    17 April 2009, pp. 77-90
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  • The degree of disjunction, δ(F), of a family F of functions is the least cardinal τ such that every pair of functions in F agree on a set of cardinality less than τ.

    Suppose θ, μ, λ, κ are non-zero cardinals with θ ≤ μ ≤ λ. This paper is concerned with functions which map μ-sized subsets of λ into κ. We first show there is always a ‘large’ family F of such functions satisfying δ(F) ≤ θ. Next we determine the cardinalities of families F of such functions that are maximal with respect to δ(F) ≤ θ.

  • Beurling's ordinary value

  • Shinji Yamashita
  • Published online by Cambridge University Press:
    17 April 2009, pp. 91-99
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  • Let n(w, f) be the number of w-points of f meromorphic in D = {|z| < 1}. Beurling defined the quantity and called w an ordinary value of f if < ∞. We shall consider the intermediate quantity ṉ(w, f) in the sense that n(w, f) ≤ ṉ(w, f) , and construct two bounded holo-morphic functions f1 and f2 of finite Dirichlet integrals in D for which

    and

    .

  • A connected metric space without an equally spaced chain of points

  • J. Arias de Reyna
  • Published online by Cambridge University Press:
    17 April 2009, pp. 283-285
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  • We construct a connected subspace M of the euclidean plane R2 containing two points A and B such that, for every pair of points {P, Q} of M\{A, B}, the three real numbers d(A, P), d(P, Q) and d(Q, B) are not the same. This solves a question posed by Väisälä.

  • On complete reducibility of module bundles

  • G. Prema, B.S. Kiranagi
  • Published online by Cambridge University Press:
    17 April 2009, pp. 401-409
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  • We prove the local triviality of module bundles over semisimple Lie algebra bundles and using this result we establish the complete reducibility of module bundles over semisimple Lie algebra bundles.

  • On approximation in spaces of continuous functions

  • Heinz H. Gonska
  • Published online by Cambridge University Press:
    17 April 2009, pp. 411-432
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  • This paper deals with approximation of certain operators defined on the space C(X) of real-valued continuous functions on an arbitrary compact metric space (X, d). In particular the problem of giving quantitative Korovkin type theorems for approximation by positive linear operators is solved. This is achieved by using a smoothing approach and the least concave majorant of the modulus of continuity of a function f in C(X). Several new estimates are given as applications, including such for Shepard's method of metric interpolation.

Abstracts of Australasian PhD theses

  • Permutation polynomials in one and several variables

  • Rex W. Matthews
  • Published online by Cambridge University Press:
    17 April 2009, pp. 287-289
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Research Article

  • On groups with small Engel depth

  • Rolf Brandl
  • Published online by Cambridge University Press:
    17 April 2009, pp. 101-110
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  • Every finite group G satisfies a law [x, ry] = [x, sy] for some positive integers r < s. The minimal value of r is called the depth of G. It is well known that groups of depth 1 are abelian. In this paper we prove the following. Let G be a finite group of depth 2. Then G/F(G) is supersoluble, metabelian and has abelian Sylow p-subgroups for all odd primes p. Moreover, lp(G) ≤ 1 for p odd and l2(G2) ≤ 1.

  • A radius of convexity problem

  • K.S. Padmanabhan, M.S. Ganesan
  • Published online by Cambridge University Press:
    17 April 2009, pp. 433-439
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  • The authors determine the sharp radius of convexity for functions analytic in the unit disc having power series representation of the form f(z) = z + an+1zn+1 + an+2zn+2 + … where an+1 is fixed and such that zf′(z)/f(x) = (1 + Aw(z))/(1 + Bw(z)), −1 ≤ B < 0 < A ≤ 1 where w(z) is an analytic function satisfying the conditions of Schwarz's lemma, in the case A + B ≥ 0. The estimate obtained is an improvement over the corresponding result obtained by Mogra and Juneja for functions analytic and starlike in the unit disc, with missing coefficients where the initial non-vanishing coefficient is fixed.

  • The difference operators and extended Laguerre polynomials

  • B.P. Parashar
  • Published online by Cambridge University Press:
    17 April 2009, pp. 111-119
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  • A new set of polynomials in powers of xh (h > 0) which are related to the Laguerre polynomials , have been defined by a Rodrigues type formula involving the forward difference operator Δh of increment h. Besides obtaining shift operator formulae for , a definition of fractional power of Δh has been given. The definition has been illustrated by establishing known relations of the confluent hypergeometric function.

Abstracts of Australasian PhD theses

  • On modular representation algebras of cyclic p-groups

  • John Charles Renaud
  • Published online by Cambridge University Press:
    17 April 2009, pp. 291-292
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Abstracts of Australian PhD thesis

  • Controlled Markov processes and related semigroups of operators

  • Volf Frishling
  • Published online by Cambridge University Press:
    17 April 2009, pp. 441-442
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Abstracts of Australasian PhD theses

  • Combining information in linear and log-linear analyses

  • Matthew William Knuiman
  • Published online by Cambridge University Press:
    17 April 2009, pp. 293-294
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Research Article

  • Subordination theorems for p-valent functions with initial gaps

  • Prem Singh, A.V.V. Satyanarayana
  • Published online by Cambridge University Press:
    17 April 2009, pp. 121-129
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  • In the present note we prove some results for p-valent functions with initial gaps by means of N-subordination.

Abstracts of Australian PhD thesis

  • Topics in the theory of latin squares

  • Bohdan Peter Smetaniuk
  • Published online by Cambridge University Press:
    17 April 2009, pp. 443-444
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Page 2 of 3