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Most cited

This page lists all time most cited articles for this title. Please use the publication date filters on the left if you would like to restrict this list to recently published content, for example to articles published in the last three years. The number of times each article was cited is displayed to the right of its title and can be clicked to access a list of all titles this article has been cited by.

Contents

Page 18 of 123

  • Cited by 13

  • On some functional equations from additive and non-additive measures-I

  • PL Kannappan
  • Published online by Cambridge University Press:
    20 January 2009, pp. 145-150
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  • It is known that while the Shannon and the Rényi entropies are additive, the measure entropy of degree β proposed by Havrda and Charvat (7) is non-additive. Ever since Chaundy and McLeod (4) considered the following functional equation

    which arose in statistical thermodynamics, (1.1) has been extensively studied (1, 5, 6, 8). From the algebraic properties of symmetry, expansibility and branching of the entropy (viz. Shannon entropy Hn, etc.) one obtains the sum representation

    which with the property of additivity yields the functional equation (1.1), (9, 10).

  • Cited by 13

  • On the Critical Fujita Exponent for a Degenerate Parabolic System Coupled Via Nonlinear Boundary Flux

  • Jun Zhou, Chunlai Mu
  • Published online by Cambridge University Press:
    12 December 2008, pp. 785-805
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  • In this paper, we deal with the non-negative solutions of a degenerate parabolic system with nonlinear coupled boundary conditions and non-negative non-trivial compactly supported initial data. The critical Fujita exponents are given and the blow-up rates of the non-global solution are obtained.

  • Cited by 13

  • Domination of the supremum of a bounded harmonic function by its supremum over a countable subset

  • F. F. Bonsall
  • Published online by Cambridge University Press:
    20 January 2009, pp. 471-477
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  • For what sequences {an} of points of the open unit disc D does there exist a constant k such that

    for all bounded harmonic functions f on D?

  • Cited by 13

  • The Approximate Solution of Dual Integral Equations by Variational Methods

  • B. Noble
  • Published online by Cambridge University Press:
    20 January 2009, pp. 115-126
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  • The classic application of dual integral equations occurs in connexion with the potential of a circular disc (e.g. Titchmarsh (9), p. 334). Suppose that the disc lies in z = 0, 0≤ρ≤1, where we use cylindrical coordinates (p, z). Then it is required to find a solution of

    such that on z = 0

    Separation of variables in conjunction with the conditions that ø is finite on the axis and ø tends to zero as z tends to plus infinity yields the particular solution .

  • Cited by 13

  • Existence theory for nonresonant singular boundary value problems

  • Donal O'Regan
  • Published online by Cambridge University Press:
    20 January 2009, pp. 431-447
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  • We present some existence results for the “nonresonant” singular boundary value problem a.e. on [0, 1] with Here μ is such that a.e. on [0, 1] with has only the trivial solution.

  • Cited by 13

  • A CRITERION FOR ERDŐS SPACES

  • Jan J. Dijkstra
  • Published online by Cambridge University Press:
    15 September 2005, pp. 595-601
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  • In 1940 Paul Erdős introduced the ‘rational Hilbert space’, which consists of all vectors in the real Hilbert space $\ell^2$ that have only rational coordinates. He showed that this space has topological dimension one, yet it is totally disconnected and homeomorphic to its square. In this note we generalize the construction of this peculiar space and we consider all subspaces $\mathcal{E}$ of the Banach spaces $\ell^p$ that are constructed as ‘products’ of zero-dimensional subsets $E_n$ of $\mathbb{R}$. We present an easily applied criterion for deciding whether a general space of this type is one dimensional. As an application we find that if such an $\mathcal{E}$ is closed in $\ell^p$, then it is homeomorphic to complete Erdős space if and only if $\dim\mathcal{E}>0$ and every $E_n$ is zero dimensional.

  • Cited by 13

  • Torsion in K0 of unit-regular rings*

  • K. R. Goodearl
  • Published online by Cambridge University Press:
    20 January 2009, pp. 331-341
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  • We construct examples of unit-regular rings R for which K0(R) has torsion, thus answering a longstanding open question in the negative. In fact, arbitrary countable torsion abelian groups are embedded in K0 of simple unit-regular algebras over arbitrary countable fields. In contrast, in all these examples K0(R) is strictly unperforated.

  • Cited by 13

  • Generalised quaternion groups and distributively generated near-rings

  • J. J. Malone
  • Published online by Cambridge University Press:
    20 January 2009, p. 234
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  • In this paper two major questions concerning generalised quaternion groups and distributively generated (d.g.) near-rings are investigated. The d.g. near-rings generated, respectively, by the inner automorphisms, automorphisms, and endomorphisms of the group are described. It is also shown that these morphism near-rings are local near-rings and contain no non-trivial idempotents. Finally, it is demonstrated that exactly 16 d.g. near-rings can be defined on a given generalised quaternion group.

  • Cited by 13

  • A Cyclic Inequality

  • R. A. Rankin
  • Published online by Cambridge University Press:
    20 January 2009, pp. 139-147
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  • For any positive integer n and positive real variables x1, x2, …, xn write

    where xr is defined for all integers r by the relations

    If

    and

    it is known that (1, 3, 4)

    and

  • Cited by 13

  • w. G. Cochran, Sampling Techniques (John Wiley & Sons, 2nd edition, 1963), ix+413 pp., 72s.

  • R. A. Robb
  • Published online by Cambridge University Press:
    20 January 2009, pp. 342-343
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  • Cited by 13

  • Principal train algebras of rank 3 and dimensions≦5

  • R. Costa
  • Published online by Cambridge University Press:
    20 January 2009, pp. 61-70
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  • A commutative algebra A over the field F, endowed with a non-zero homorphism ω:A →F is principal train if it satisfies the identity xr+y1ω(x)xr−1 +… +yr−1ω(x)r−1x=0 where y1,…,yr−1 are fixed elements in F. We present in this paper, after the introduction of the concept of “type” of A, some results concerning the classification in the case r = 3. In particular we describe all these algebras of dimension≦5.

  • Cited by 13

  • Harmonic functions and ends of graphs

  • Massimo A. Picardello, Wolfgang Woess
  • Published online by Cambridge University Press:
    13 July 2011, pp. 457-461
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  • In this note we discuss extensions of results [5], where transient random walks are considered, whose transition matrix is compatible with a tree-structure of the underlying discrete state space. Notation is generally as in [5], with the exception that instead of a tree T we consider an arbitrary graph Γ, which is locally finite, connected, and whose vertex set S is infinite. The edge set E is unoriented, there are no multiple edges. We consider a transition operator P, given by a stochastic matrix (p(u, v))u, v ∈ S, which gives rise to a transient Markov chain (“random walk”), related to the graph structure by:

    (i) if p(u, v)>0 then [u, v] ∈ E,

    (ii) there is an M>0 such that p(k)(u, v)>0 for some k=k(u, v)≦M whenever [u, v]∈E (“uniform irreducibility”).

  • Cited by 13

  • POSITIVE SOLUTIONS OF HIGHER-ORDER BOUNDARY-VALUE PROBLEMS

  • Lingju Kong, Qingkai Kong
  • Published online by Cambridge University Press:
    23 May 2005, pp. 445-464
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  • We consider a class of even-order boundary-value problems with nonlinear boundary conditions and an eigenvalue parameter $\lambda$ in the equations. Sufficient conditions are obtained for the existence and non-existence of positive solutions of the problems for different values of $\lambda$.

  • Cited by 13

  • Two Proofs of the 6Ψ6 Summation Theorem

  • L. J. Slater, A. Lakin
  • Published online by Cambridge University Press:
    20 January 2009, pp. 116-121
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  • The 6Ψ6 summation theorem was first proved by Bailey1, who deduced it indirectly from a transformation of a well-poised 8Φ7 series into two 4Φ3 series. No direct proof of the theorem has been published, and, since it has interesting applications in the proofs of various identities which occur in combinatory analysis, for example the A series of Rogers2 and some elegant identities due to Ramanujan3, we give two new proofs of the theorem in this paper.

  • Cited by 13
  • Cited by 13

  • ZT-subgroups of sharply 3-transitive groups

  • Heinrich Wefelscheid
  • Published online by Cambridge University Press:
    20 January 2009, pp. 9-14
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  • A permutation group G operating on a set M is called a ZT-group (Zassenhaus transitive group) if G has the properties (i) and (ii):

    (i) G operates 2-transitively on M;

    (ii) Ga,b≠{id} and Ga,b,c = {id} for distinct elements a,b,c ∈ M.

    Here Ga,b = {α ∈ G | α(a) = a and α(b) = b} denotes the stabilizer of {a, b}, and Ga,b,c the stabilizer of {a, b, c}, respectively.

  • Cited by 13

  • THE BEST-CONSTANT PROBLEM FOR A FAMILY OF GAGLIARDO–NIRENBERG INEQUALITIES ON A COMPACT RIEMANNIAN MANIFOLD

  • Christophe Brouttelande
  • Published online by Cambridge University Press:
    27 January 2003, pp. 117-146
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  • The best-constant problem for Nash and Sobolev inequalities on Riemannian manifolds has been intensively studied in the last few decades, especially in the compact case. We treat this problem here for a more general family of Gagliardo–Nirenberg inequalities including the Nash inequality and the limiting case of a particular logarithmic Sobolev inequality. From the latter, we deduce a sharp heat-kernel upper bound.

    AMS 2000 Mathematics subject classification: Primary 58J05

  • Cited by 13

  • Lamé Equation, Quantum Euler Top and Elliptic Bernoulli Polynomials

  • M.-P. Grosset, A. P. Veselov
  • Published online by Cambridge University Press:
    12 December 2008, pp. 635-650
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  • A generalization of the odd Bernoulli polynomials related to the quantum Euler top is introduced and investigated. This is applied in order to compute the coefficients of the spectral polynomials for the classical Lamé operator.

  • Cited by 13

  • Strongly E-reflexive inverse semigroups

  • L. O'Carroll
  • Published online by Cambridge University Press:
    20 January 2009, pp. 339-354
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  • Let S be an inverse semigroup with semilattice of idempotents E. We denote by σ the minimum group congruence on S (6), and by τ the maximum idempotent-determined congruence on S (2). (Recall that the congruence η on S is called idempotent-determined if (e, x)∈ η and e ∈ E imply that x ∈ E.) In general τ ⊆ σ.

  • Cited by 13

  • BEST POSSIBLE COMPACTNESS RESULTS OF LIONS–PEETRE TYPE

  • Fernando Cobos, Michael Cwikel, Pedro Matos
  • Published online by Cambridge University Press:
    20 January 2009, pp. 153-173
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  • If $T:A_{0}\rightarrow B$ boundedly and $T:A_{1}\rightarrow B$ compactly, then a result of Lions–Peetre shows that $T:A\rightarrow B$ compactly for a certain class of spaces $A$ which are intermediate with respect to $A_{0}$ and $A_{1}$. We investigate to what extent such results can hold for arbitrary intermediate spaces $A$. The ‘dual’ case of an operator $S$ such that $S:X\rightarrow Y_{0}$ boundedly and $S:X\rightarrow Y_{1}$ compactly, is also considered, as well as similar questions for other closed operator ideals.

    AMS 2000 Mathematics subject classification: Primary 46B70; 47D50

Page 18 of 123