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Mathematics and statistics journals publish papers on the theory and application of mathematics, statistics, and probability. Most mathematics journals have a broad scope that encompasses most mathematical fields. These commonly include logic and foundations, algebra and number theory, analysis (including differential equations, functional analysis and operator theory), geometry, topology, combinatorics, probability and statistics, numerical analysis and computation theory, mathematical physics, etc.

Mathematics and Statistics

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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

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

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 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

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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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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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.

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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.

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Let be a Schrödinger operator on the Heisenberg group n, where Δn is the sublaplacian on n and the nonnegative potential V belongs to the reverse Hölder class Bq with q[Q/2,+). Here  Q=2n+2 is the homogeneous dimension of n. Assume that {esL}s>0 is the heat semigroup generated byL. 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)sddsesLf(υ)2dυdssQ/2+11/2,

where

Γα(u):={(υ,s)n×(0,+):u1υ<αs},

and

gλ,L*(f)(u):=0nss+u1υ2λsddsesLf(υ)2dυdssQ/2+11/2 ,

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 1p<, the following inequality holds true:

SL;2j(f)LpnC2jQ/2+2jQ/psL(f)Lp(n).

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(n). In this article, the author also introduces a class of Morrey spaces associated with the Schrödinger operator L on n. 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.

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In this paper, a relationship between the zeros and critical points of a polynomial p(z) is established. The relationship is used to prove Sendov’s conjecture in some special cases.

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