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# Hankel Determinant of Second Order for Some Classes of Analytic Functions

Mathematica Pannonica
Authors:
and
Nikola Tuneski

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

# Circles of Curvature at Points of Parabola in Isotropic Plane

Mathematica Pannonica
Authors:
,
Marija Šimić Horvath
, and
Ema Jurkin

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

# A Combinatorial Approach to the Stirling Numbers of the First Kind with Higher Level

Studia Scientiarum Mathematicarum Hungarica
Authors:
Takao Komatsu
,
José L. Ramírez
, and
Diego Villamizar

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.

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# Corrigendum: Ideals of Residuated Lattices

Studia Scientiarum Mathematicarum Hungarica
Authors:
Liviu-Constantin Holdon
and
Arsham Borumand Saeid
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# A Corson Compact Space is Countable if the Complement of its Diagonal is Functionally Countable

Studia Scientiarum Mathematicarum Hungarica
Author:

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.

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# Criterion for the Coincidence of Strong and Weak Orlicz Spaces

Studia Scientiarum Mathematicarum Hungarica
Authors:
Maria Rosaria Formica
and
Eugeny Ostrovsky

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.

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# Heegaard Floer Homology, Degree-One Maps and Splicing Knot Complements

Studia Scientiarum Mathematicarum Hungarica
Authors:
Narges Bagherifard
and
Eaman Eftekhary

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.

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# The “k = 1” Case of a Problem of Greene and Kleitman from 1976: Join-Irreducible Elements in the Lattice of Sperner 1-Families

Mathematica Pannonica
Author:
Jonathan David Farley

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.”

Open access

# Localization Operators and Uncertainty Principles for the Hankel Wavelet Transform

Studia Scientiarum Mathematicarum Hungarica
Authors:
Saifallah Ghobber
,
Siwar Hkimi
, and
Slim Omri

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.

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# A Note on Generating a Power Basis over a Dedekind Ring

Studia Scientiarum Mathematicarum Hungarica
Authors:
Abdulaziz Deajim
and