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## Polynomial Interpolation on Sequences

Mathematica Pannonica
Authors:
Francesc Tugores
and
Laia Tugores

This short note deals with polynomial interpolation of complex numbers verifying a Lipschitz condition, performed on consecutive points of a given sequence in the plane. We are interested in those sequences which provide a bound of the error at the first uninterpolated point, depending only on its distance to the last interpolated one.

Open access

## A Property of Lattices of Sublattices Closed Under Taking Relative Complements and Its Connection to 2-Distributivity

Mathematica Pannonica
Author:
Gábor Czédli

For a lattice L of finite length n, let RCSub(L) be the collection consisting of the empty set and those sublattices of L that are closed under taking relative complements. That is, a subset X of L belongs to RCSub(L) if and only if X is join-closed, meet-closed, and whenever {a, x, b} ⊆ S, yL, xy = a, and xy = b, then yS. We prove that (1) the poset RCSub(L) with respect to set inclusion is lattice of length n + 1, (2) if RCSub(L) is a ranked lattice and L is modular, then L is 2-distributive in András P. Huhn’s sense, and (3) if L is distributive, then RCSub(L) is a ranked lattice.

Open access

## On Derivations and Lie Ideals of Semirings

Mathematica Pannonica
Authors:
and
Neelam

In this paper, centralizing (semi-centralizing) and commuting (semi-commuting) derivations of semirings are characterized. The action of these derivations on Lie ideals is also discussed and as a consequence, some significant results are proved. In addition, Posner’s commutativity theorem is generalized for Lie ideals of semirings and this result is also extended to the case of centralizing (semi-centralizing) derivations of prime semirings. Further, we observe that if there exists a skew-commuting (skew-centralizing) derivation D of S, then D = 0. It is also proved that for any two derivations d 1 and d 2 of a prime semiring S with char S ≠ 2 and x d 1 x d 2 = 0, for all xS implies either d 1 = 0 or d 2 = 0.

Open access

## In Memoriam István Győri

Mathematica Pannonica
Authors:
Ferenc Hartung
and
Mihály Pituk
Open access

## On a Special Gini Mean

Mathematica Pannonica
Author:
József Sándor

We offer new properties of the special Gini mean S(a, b) = aa /( a + b )bb /( a + b ), in connections with other special means of two arguments.

Open access

## Distance Domination in Vertex Partitioned Graphs

Mathematica Pannonica
Authors:
Allan Frendrup
,
Zsolt Tuza
, and
Preben Dahl Vestergaard

We treat a variation of graph domination which involves a partition (V 1, V 2,..., Vk ) of the vertex set of a graph G and domination of each partition class V i over distance d where all vertices and edges of G may be used in the domination process. Strict upper bounds and extremal graphs are presented; the results are collected in three handy tables. Further, we compare a high number of partition classes and the number of dominators needed.

Open access

## Proof of a Conjecture of Proctor and Scoppetta Related to d-Complete Posets

Mathematica Pannonica
Author:
Jonathan David Farley

Proctor and Scoppetta conjectured that

• (1) there exists an infinite locally finite poset that satisfies their conditions VT and NTC but not SIS;

• (2) there exists an infinite locally finite poset satisfying their conditions D3-C and D3MF but not both VT and FT; and

• (3) there exists an infinite locally finite poset satisfying their conditions D3-C and D3MD but not NCC.

In this note, the conjecture of Proctor and Scoppetta, which is related to d-complete posets, is proven.

Open access

## Hamilton Triangle of a Triangle in the Isotropic Plane

Mathematica Pannonica
Authors:
Zdenka Kolar-Begović
and

In this paper we introduce the concept of the Hamilton triangle of a given triangle in an isotropic plane and investigate a number of important properties of this concept. We prove that the Hamilton triangle is homological with the observed triangle and with its contact and complementary triangles. We also consider some interesting statements about the relationships between the Hamilton triangle and some other significant elements of the triangle, like e.g. the Euler and the Feuerbach line, the Steiner ellipse and the tangential triangle.

Open access

## Menon-Type Identities Concerning Subsets of the Set {1, 2,..., n}

Mathematica Pannonica
Author:
László Tóth

We prove certain Menon-type identities associated with the subsets of the set {1, 2,..., n} and related to the functions f, fk , Ф and Ф k , defined and investigated by Nathanson.

Open access

## On the Almost Sure Central Limit Theorem Along Subsequences

Mathematica Pannonica
Authors:
István Berkes
and
Endre Csáki

Generalizing results of Schatte [11] and Atlagh and Weber [2], in this paper we give conditions for a sequence of random variables to satisfy the almost sure central limit theorem along a given sequence of integers.

Open access