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## Spanning Trees of a Claw-Free Graph Whose Reducible Stems Have Few Leaves

Studia Scientiarum Mathematicarum Hungarica
Author:
Pham Hoang Ha

Let T be a tree. The reducible stem of T is the smallest subtree that contains all branch vertices of T. In this paper, we first use a new technique of Gould and Shull  to state a new short proof for a result of Kano et al.  on the spanning tree with a bounded number of leaves in a claw-free graph. After that, we use a similar idea to prove a sharp sufficient condition for a claw-free graph having a spanning tree whose reducible stem has few leaves.

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## The Norming Sets of Multilinear Forms on the Plane with a Certain Norm

Mathematica Pannonica
Author:
Sung Guen Kim

Let n ∈ ℕ. An element (x 1, … , xn ) ∈ En is called a norming point of $T ∈ L n E$ if $x 1 = ⋯ = x n = 1$ and $T x 1 , … , x n = T$ , where $L n E$ denotes the space of all continuous symmetric n-linear forms on E. For $T ∈ L n E$ , we define

Norm(T) is called the norming set of T.

Let $ℝ · 2$ be the plane with a certain norm such that the set of the extreme points of its unit ball ext $B ℝ · 2 = ± W 1 , ± W 2$ for some $W 1 ≠ ± W 2 ∈ ℝ · 2$ .

In this paper, we classify Norm(T) for every $T ∈ L n ℝ · 2$ . We also present relations between the norming sets of $L n l ∞ 2$ and $L n l 1 2$ .

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## A Characterization of T 1 Spaces via Limit Sets of Nets

Mathematica Pannonica
Author:
Yu-Lin Chou

This article indicates another set-theoretic formula, solely in terms of union and intersection, for the set of the limits of any given sequence (net, in general) in an arbitrary T 1 space; this representation in particular gives a new characterization of a T 1 space.

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## Completely Multiplicative Functions with Special Properties

Mathematica Pannonica
Authors:
Imre Kátai
and
Bui M. Phong

We give all solutions of completely multiplicative functions ƒ , g, for which the equation Ag(n + 1) = Bƒ (n) + C holds for every n ∈ ℕ. We also study the equation G(p + 1) = F(p − 1) + D and we prove some results concerning it.

Open access

## Batch Scheduling with Time Restriction and Clique Search

Mathematica Pannonica
Author:
Sándor Szabó

We consider a graph whose vertices are legally colored using k colors and ask if the graph contains a k-clique. As it turns out this very special type of k-clique problem is in an intimate connection with constructing schedules. The practicality this clique search based construction of schedules is checked by carrying out numerical experiments.

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## Determinant Inequalities for Positive Definite Matrices via Cartwright–Field’s Result for Arithmetic and Geometric Weighted Means

Mathematica Pannonica
Author:
Silvestru Sever Dragomir

Assume that Aj , j ∈ {1, … , m} are positive definite matrices of order n. In this paper we prove among others that, if 0 < l In Aj , j ∈ {1, … , m} in the operator order, for some positive constant l, and In is the unity matrix of order n, then

$o ≤ 1 2 ∑ k = 1 m P k 1 − P k det 2 A j − l I n − 1 / 2 − 2 ∑ 1 ≤ j < k ≤ m P j P k det A j + A k − l I n − 1 / 2 ≤ ∑ j = 1 m P j det A j − 1 / 2 − det ∑ k = 1 m P k A k − 1 / 2 ,$

where Pk ≥ 0 for k ϵ {1, …, m} and $∑ j = 1 m P j = 1$ .

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## Evolutes of Conics in the Pseudo-Euclidean Plane

Mathematica Pannonica
Author:
Ivana Božić Dragun

The evolute of a conic in the pseudo-Euclidean plane is the locus of centers of all its osculating circles. It’s a curve of order six and class four in general case. In this paper we discuss and compute the order and class of evolutes of different types of conics. We will highlight those cases that have no analogy in the Euclidean plane.

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## On Quasi I-Statistical Convergence of Triple Sequences in Cone Metric Spaces

Mathematica Pannonica
Authors:
Işıl Açık Demırcı
,
Ömer Kışı
, and
Mehmet Gürdal

Fast  is credited with pioneering the field of statistical convergence. This topic has been researched in many spaces such as topological spaces, cone metric spaces, and so on (see, for example [19, 21]). A cone metric space was proposed by Huang and Zhang . The primary distinction between a cone metric and a metric is that a cone metric is valued in an ordered Banach space. Li et al.  investigated the definitions of statistical convergence and statistical boundedness of a sequence in a cone metric space. Recently, Sakaoğlu and Yurdakadim  have introduced the concepts of quasi-statistical convergence. The notion of quasi I-statistical convergence for triple and multiple index sequences in cone metric spaces on topological vector spaces is introduced in this study, and we also examine certain theorems connected to quasi I-statistically convergent multiple sequences. Finally, we will provide some findings based on these theorems.

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## The Lower Bipartite Number of a Graph

Mathematica Pannonica
Authors:
Anna Bachstein
and
Wayne Goddard

For a graph G, we define the lower bipartite number LB(G) as the minimum order of a maximal induced bipartite subgraph of G. We study the parameter, and the related parameter bipartite domination, providing bounds both in general graphs and in some graph families. For example, we show that there are arbitrarily large 4-connected planar graphs G with LB(G) = 4 but a 5-connected planar graph has linear LB(G). We also show that if G is a maximal outerplanar graph of order n, then LB(G) lies between (n + 2)/3 and 2 n/3, and these bounds are sharp.

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## Generalized Forms of an Overconstrained Sliding Mechanism Consisting of Two Congruent Tetrahedra

Studia Scientiarum Mathematicarum Hungarica
Authors:
Endre Makai Jr.
and
Tibor Tarnai

The motions of a bar structure consisting of two congruent tetrahedra are investigated, whose edges in their basic position are the face diagonals of a rectangular parallelepiped. The constraint of the motion is the following: the originally intersecting edges have to remain coplanar. All finite motions of our bar structure are determined. This generalizes our earlier work, where we did the same for the case when the rectangular parallelepiped was a cube. At the end of the paper we point out three further possibilities to generalize the question about the cube, and give for them examples of finite motions.

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