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This paper is concerned with the existence of solutions to a class of p(x)-Kirchhoff-type equations with Robin boundary data as follows:

Where

The major aim of the note is to give new brief proofs of the results in the paper “The influence of weakly *H* -subgroups on the structure of finite groups” [Studia Scientiarum Mathematicarum Hungarica, 51 (1), 27–40 (2014)].

In this paper we prove and discuss some new (H_{p}, L_{p,∞}) 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.

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.

A linear operator on a Hilbert space *S* is shown to be densely defined and closed if and only if

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.

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*:

*X*→

*X*, 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:

*ƒ*∈

*M*and ℱ

*(*

_{n}*ƒ*) ∈

*M*.

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.

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.

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.

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.