# Browse

## You are looking at 51 - 60 of 11,089 items for :

• Mathematics and Statistics
• Refine by Access: All Content
Clear All

# 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.

Open access

# 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.

Open access

# 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.

Open access

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

Mathematica Pannonica
Authors: Lovejoy S. Das and Mohammad Nazrul Islam Khan

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, ηp, 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.

Open access

# 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.

Open access

# 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.

Restricted access

# The Extended Beta Generator of Distributions: Properties and Applications

Studia Scientiarum Mathematicarum Hungarica
Authors: Gauss M. Cordeiro, Thiago G. Ramires, Edwin M. M. Ortega, and Rodrigo R. Pescim

We deﬁne the extended beta family of distributions to generalize the beta generator pioneered by Eugene et al. [10]. This paper is cited in at least 970 scientiﬁc articles and extends more than ﬁfty well-known distributions. Any continuous distribution can be generalized by means of this family. The proposed family can present greater ﬂexibility to model skewed data. Some of its mathematical properties are investigated and maximum likelihood is adopted to estimate its parameters. Further, for different parameter settings and sample sizes, some simulations are conducted. The superiority of the proposed family is illustrated by means of two real data sets.

Restricted access

# Extended Cauchy–Schwarz Inequality and its Application for the two-Class Fisher Discriminant Analysis

Studia Scientiarum Mathematicarum Hungarica
Authors: Maciej Sablik and Katarzyna Stapor

We present the sufficient condition for a classical two-class problem from Fisher discriminant analysis has a solution. Actually, the solution was presented up to our knowledge with a necessary condition only. We use an extended Cauchy–Schwarz inequality as a tool.

Restricted access

# Morrey Spaces Related to Schrödinger Operators with Certain Nonnegative Potentials and Littlewood–Paley–Stein Functions on the Heisenberg groups

Studia Scientiarum Mathematicarum Hungarica
Author: Hua Wang

Let be a Schrödinger operator on the Heisenberg group $ℍn$, where $Δℍn$ is the sublaplacian on $ℍn$ and the nonnegative potential V belongs to the reverse Hölder class $Bq$ with $q∈[Q/2,+∞)$. Here is the homogeneous dimension of $ℍn$. Assume that ${e−sL}s>0$ is the heat semigroup generated by$L$. The Lusin area integral $SL;α$ and the Littlewood–Paley–Stein function $gλ,L*$ associated with the Schrödinger operator $L$ are deﬁned, respectively, by

$SL;α(f)(u):=∬Γα(u)sddse−sLf(υ)2dυdssQ/2+11/2,$

where

$Γα(u):={(υ,s)∈ℍn×(0,+∞):u−1υ<αs},$

and

Where $λ∈(0,+∞)$ is a parameter. In this article, the author shows that there is a relationship between $SL;α$ and the operator $gλ,L*$ and for any $1≤p<∞$, the following inequality holds true:

$SL;2j(f)Lpℍn≤C2jQ/2+2jQ/psL(f)Lp(ℍn).$

Based on this inequality and known results for the Lusin area integral $SL;1$, the author establishes the strong-type and weak-type estimates for the Littlewood–Paley–Stein function $gλ,L*$ on $Lp(ℍn)$. In this article, the author also introduces a class of Morrey spaces associated with the Schrödinger operator $L$ on $ℍn$. By using some pointwise estimates of the kernels related to the nonnegative potential V, the author establishes the boundedness properties of the operator $gλ,L*$ acting on the Morrey spaces for an appropriate choice of $λ>0$. It can be shown that the same conclusions hold for the operator $gλ,L*$ on generalized Morrey spaces as well.

Restricted access

# Some Classes of Polynomials Satisfying Sendov’s Conjecture

Studia Scientiarum Mathematicarum Hungarica