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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.”

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# 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

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.

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# On Power Integral Bases for Certain Pure Number Fields Defined by x 36 − m

Studia Scientiarum Mathematicarum Hungarica
Author:

Let K = ℚ(α) be a number field generated by a complex root a of a monic irreducible polynomial ƒ (x) = x36 − m, with m ≠ ±1 a square free rational integer. In this paper, we prove that if m ≡ 2 or 3 (mod 4) and m ≠ ±1 (mod 9) then the number field K is monogenic. If m ≡ 1 (mod 4) or m ≡±1 (mod 9), then the number field K is not monogenic.

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# Real Hypersurfaces in ℂP 2 and ℂH 2 with Cyclic Parallel ∗-Ricci Tensor

Studia Scientiarum Mathematicarum Hungarica
Authors:
Yaning Wang
and
Wenjie Wang

In this paper, we prove that the ∗-Ricci tensor of a real hypersurface in complex projective plane ℂP 2 or complex hyperbolic plane ℂH 2 is cyclic parallel if and only if the hypersurface is of type (A). We find some three-dimensional real hypersurfaces having non-vanishing and non-parallel ∗-Ricci tensors which are cyclic parallel.

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# Some Functional Upper Bounds for Fejér’s Sine Polynomial

Studia Scientiarum Mathematicarum Hungarica
Authors:
Jing Quan Chong
,
Xing Chen Huang
,
Tuo Yeong Lee
,
Jing Tao Li
,
Hui Xiang Sim
,
Jing Ren Soh
,
Gabriel Jiaxu Tan
, and
Jay Kin Heng Tai

We prove that

for all integers n ≥ 1 and ɵ ≤ 8 ≤ π. This result refines inequalities due to Jackson (1911) and Turán (1938).

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