Browse

You are looking at 61 - 70 of 11,138 items for :

  • Mathematics and Statistics x
  • Refine by Access: All Content x
Clear All

Let ƒ be analytic in the unit disk B and normalized so that ƒ (z) = z + a2z2 + a3z3 +܁܁܁. In this paper, we give upper bounds of the Hankel determinant of second order for the classes of starlike functions of order α, Ozaki close-to-convex functions and two other classes of analytic functions. Some of the estimates are sharp.

Open access

The authors have studied the curvature of the focal conic in the isotropic plane and the form of the circle of curvature at its points has been obtained. Hereby, we discuss several properties of such circles of curvature at the points of a parabola in the isotropic plane.

Open access

In this paper, we investigate a generalization of the classical Stirling numbers of the first kind by considering permutations over tuples with an extra condition on the minimal elements of the cycles. The main focus of this work is the analysis of combinatorial properties of these new objects. We give general combinatorial identities and some recurrence relations. We also show some connections with other sequences such as poly-Cauchy numbers with higher level and central factorial numbers. To obtain our results, we use pure combinatorial arguments and classical manipulations of formal power series.

Restricted access
Restricted access

A space X is called functionally countable if ƒ (X) is countable for any continuous function ƒ : X → Ø. Given an infinite cardinal k, we prove that a compact scattered space K with d(K) > k must have a convergent k+-sequence. This result implies that a Corson compact space K is countable if the space (K × K) \ ΔK is functionally countable; here ΔK = {(x, x): x ϵ K} is the diagonal of K. We also establish that, under Jensen’s Axiom ♦, there exists a compact hereditarily separable non-metrizable compact space X such that (X × X) \ ΔX is functionally countable and show in ZFC that there exists a non-separable σ-compact space X such that (X × X) \ ΔX is functionally countable.

Restricted access

We provide necessary and sufficient conditions for the coincidence, up to equivalence of the norms, between strong and weak Orlicz spaces. Roughly speaking, this coincidence holds true only for the so-called exponential spaces.

We also find the exact value of the embedding constant which appears in the corresponding norm inequality.

Restricted access

Suppose that K and K' are knots inside the homology spheres Y and Y', respectively. Let X = Y (K, K') be the 3-manifold obtained by splicing the complements of K and K' and Z be the three-manifold obtained by 0 surgery on K. When Y' is an L-space, we use the splicing formula of [1] to show that the rank of H Y ^ (X ) is bounded below by the rank of H Y ^ (Y ) if τ(K 2) = 0 and is bounded below by rank( H Y ^ (Z)) − 2 rank( H Y ^ (Y)) + 1 if τ(K') ≠ 0.

Restricted access

Let k ≥ 1. A Sperner k-family is a maximum-sized subset of a finite poset that contains no chain with k + 1 elements. In 1976 Greene and Kleitman defined a lattice-ordering on the set Sk (P) of Sperner k-families of a fifinite poset P and posed the problem: “Characterize and interpret the join- and meet-irreducible elements of Sk (P),” adding, “This has apparently not been done even for the case k = 1.”

In this article, the case k = 1 is done.

Open access

The aim of this paper is to prove some uncertainty inequalities for the continuous Hankel wavelet transform, and study the localization operator associated to this transformation.

Restricted access

In this note, we show that the result [1, Proposition 5.2] is inaccurate. We further give and prove the correct modification of such a result. Some applications are also given.

Restricted access