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# On the Maximal Operators of T Means with Respect to Walsh–Kaczmarz System

Studia Scientiarum Mathematicarum Hungarica
Authors:
Nata Gogolashvili
and

In this paper we prove and discuss some new (Hp, Lp,∞) type inequalities of the maximal operators of T means with monotone coefficients with respect to Walsh–Kaczmarz system. It is also proved that these results are the best possible in a special sense. As applications, both some well-known and new results are pointed out. In particular, we apply these results to prove a.e. convergence of such T means.

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# Sticky Polymatroids on At Most Five Elements

Studia Scientiarum Mathematicarum Hungarica
Author:
László Csirmaz

The sticky polymatroid conjecture states that any two extensions of the polymatroid have an amalgam if and only if the polymatroid has no non-modular pairs of flats. We show that the conjecture holds for polymatroids on five or less elements.

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Mathematica Pannonica
Author:
Péter Berkics

A linear operator on a Hilbert space $ℍ$ , in the classical approach of von Neumann, must be symmetric to guarantee self-adjointness. However, it can be shown that the symmetry could be omitted by using a criterion for the graph of the operator and the adjoint of the graph. Namely, S is shown to be densely defined and closed if and only if $k + l : k , l ∈ G S ∩ G S * = ℍ$ .

In a more general setup, we can consider relations instead of operators and we prove that in this situation a similar result holds. We give a necessary and sufficient condition for a linear relation to be densely defined and self-adjoint.

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# Conceptions of Topological Transitivity on Symmetric Products

Mathematica Pannonica
Authors:
Franco Barragán
,
Sergio Macías
, and
Anahí Rojas

Let X be a topological space. For any positive integer n, we consider the n-fold symmetric product of X, ℱ n (X), consisting of all nonempty subsets of X with at most n points; and for a given function ƒ : XX, we consider the induced functions ℱ n (ƒ): ℱ n (X) → ℱ n (X). Let M be one of the following classes of functions: exact, transitive, ℤ-transitive, ℤ+-transitive, mixing, weakly mixing, chaotic, turbulent, strongly transitive, totally transitive, orbit-transitive, strictly orbit-transitive, ω-transitive, minimal, I N, T T ++, semi-open and irreducible. In this paper we study the relationship between the following statements: ƒM and ℱ n (ƒ) ∈ M.

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# Dual Pairs of Matroids with Coefficients in Finitary Fuzzy Rings of Arbitrary Rank

Mathematica Pannonica
Author:
Walter Wenzel

Infinite matroids have been defined by Reinhard Diestel and coauthors in such a way that this class is (together with the finite matroids) closed under dualization and taking minors. On the other hand, Andreas Dress introduced a theory of matroids with coefficients in a fuzzy ring which is – from a combinatorial point of view – less general, because within this theory every circuit has a finite intersection with every cocircuit. Within the present paper, we extend the theory of matroids with coefficients to more general classes of matroids, if the underlying fuzzy ring has certain properties to be specified.

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# Lower Estimate of Clique Size via Edge Coloring

Mathematica Pannonica
Authors:
Balázs Király
and
Sándor Szabó

In many clique search algorithms well coloring of the nodes is employed to find an upper bound of the clique number of the given graph. In an earlier work a non-traditional edge coloring scheme was proposed to get upper bounds that are typically better than the one provided by the well coloring of the nodes. In this paper we will show that the same scheme for well coloring of the edges can be used to find lower bounds for the clique number of the given graph. In order to assess the performance of the procedure we carried out numerical experiments.

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# Pascal’s Hexagram and Desargues Configurations

Mathematica Pannonica
Author:
Jaydeep Chipalkatti

This paper solves an enumerative problem which arises naturally in the context of Pascal’s hexagram. We prove that a general Desargues configuration in the plane is associated to six conical sextuples via the theorems of Pascal and Kirkman. Moreover, the Galois group associated to this problem is isomorphic to the symmetric group on six letters.

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# The Principal Fibre Bundle on Lorentzian Almost R-para Contact Structure

Mathematica Pannonica
Authors:
Lovejoy S. Das
and

The purpose of this paper is to study the principal fibre bundle (P, M, G, π p ) with Lie group G, where M admits Lorentzian almost paracontact structure (Ø, ξ p , η p , g) satisfying certain condtions on (1, 1) tensor field J, indeed possesses an almost product structure on the principal fibre bundle. In the later sections, we have defined trilinear frame bundle and have proved that the trilinear frame bundle is the principal bundle and have proved in Theorem 5.1 that the Jacobian map π * is the isomorphism.

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# Some Zero-One Linear Programming Reformulations for the Maximum Clique Problem

Mathematica Pannonica
Authors:
Ákos Beke
,
Sándor Szabó
, and
Bogdán Zavalnij

Many combinatorial optimization problems can be expressed in terms of zero-one linear programs. For the maximum clique problem the so-called edge reformulation is applied most commonly. Two less frequently used LP equivalents are the independent set and edge covering set reformulations. The number of the constraints (as a function of the number of vertices of the ground graph) is asymptotically quadratic in the edge and the edge covering set LP reformulations and it is exponential in the independent set reformulation, respectively. F. D. Croce and R. Tadei proposed an approach in which the number of the constraints is equal to the number of the vertices. In this paper we are looking for possible tighter variants of these linear programs.

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# Dispersion’s Uncertainty Principles Associated with the Directional short-time Fourier Transform

Studia Scientiarum Mathematicarum Hungarica
Authors:
Siwar Hkimi
,
Hatem Mejjaoli
, and
Slim Omri

We introduce the directional short-time Fourier transform for which we prove a new Plancherel’s formula. We also prove for this transform several uncertainty principles as Heisenberg inequalities, logarithmic uncertainty principle, Faris–Price uncertainty principles and Donoho–Stark’s uncertainty principles.

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