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Applying certain convexity arguments we investigate the existence of a classical solution for a Dirichlet problem for which the Euler action functional is not necessarily differentiable in the sense of Gâteaux.

The aim of this paper is to investigate the semifields of order *q*
^{4} over a finite field of order *q*, *q* an odd prime power, admitting a Klein 4-group of automorphisms.

The main aim of this paper is to investigate (*H*
_{p}, *L*
_{p}) and (*H*
_{p}, *L*
_{p,∞}) type inequalities for maximal operators of Riesz logarithmic means of one-dimensional Vilenkin—Fourier series.

*u*have the bound

*u*in ℝ

^{n}.

In the following text we prove that in a generalized shift dynamical system (*X*
^{Г}, *σ*
_{φ}) for infinite countable Г and discrete *X* with at least two elements the following statements are equivalent:

- the dynamical system (
*X*^{Г},*σ*_{φ}) is chaotic in the sense of Devaney - the dynamical system (
*X*^{Г},*σ*_{φ}) is topologically transitive - the map
*φ*: Г → Г is one to one without any periodic point.

*X*with at least two elements (

*X*

^{Г},

*σ*

_{φ}) is exact Devaney chaotic, if and only if

*φ*: Г → Г is one to one and

*φ*: Г → Г has niether periodic points nor

*φ*-backwarding infinite sequences.

Let *C* be a class of some finitely presented left *R*-modules. A left *R*-module *M* is called *C*-injective, if Ext_{R}
^{1}(*C*, *M*) = 0 for each *C* ∈ *C*. A right *R*-module *M* is called C-flat, if Tor_{1}
^{R}(*M*, *C*) = 0 for each *C* ∈ *C*. A ring *R* is called *C*-coherent, if every *C* ∈ *C* is 2-presented. A ring *R* is called *C*-semihereditary, if whenever 0 → *K* → *P* → *C* → 0 is exact, where *C* ∈ *C* and *P* is finitely generated projective and *K* is finitely generated, then *K* is also projective. A ring *R* is called *C*-regular, if whenever *P*/*K* ∈ *C*, where *P* is finitely generated projective and *K* is finitely generated, then *K* is a direct summand of *P.* Using the concepts of *C*-injectivity and *C*-flatness of modules, we present some characterizations of *C*-coherent rings, *C*-semihereditary rings, and *C*-regular rings.

A general class of linear and positive operators dened by nite sum is constructed. Some of their approximation properties, including a convergence theorem and a Voronovskaja-type theorem are established. Next, the operators of the considered class which preserve exactly two test functions from the set {*e*
_{0}, *e*
_{1}, *e*
_{2}} are determined. It is proved that the test functions *e*
_{0} and *e*
_{1} are preserved only by the Bernstein operators, the test functions *e*
_{0} and *e*
_{2} only by the King operators while the test functions *e*
_{1} and *e*
_{2} only by the operators recently introduced by P. I. Braica, O. T. Pop and A. D. Indrea in [4].

The beta generalized half-normal distribution is commonly used to model lifetimes. We propose a new wider distribution called the beta generalized half-normal geometric distribution, whose failure rate function can be decreasing, increasing or upside-down bathtub. Its density function can be expressed as a linear combination of beta generalzed half-normal density functions. We derive quantile function, moments and generating unction. We characterize the proposed distribution using a simple relationship between wo truncated moments. The method of maximum likelihood is adapted to estimate the model parameters and its potentiality is illustrated with an application to a real fatigue data set. Further, we propose a new extended regression model based on the logarithm of the new distribution. This regression model can be very useful for the analysis of real data and provide more realistic fits than other special regression models.

The purpose of this paper is to revise von Neumann’s characterizations of selfadjoint operators among symmetric ones. In fact, we do not assume that the underlying Hilbert space is complex, nor that the corresponding operator is densely defined, moreover, that it is closed. Following Arens, we employ algebraic arguments instead of the geometric approach of von Neumann using the Cayley transform.

In the paper we give some remarks on the article of Janet Mills. In particular, the proof of Lemma 1.2 (in her work) is incorrect, and so the proof of Theorem 3.5 is not valid, too. Using different methods we show the mentioned theorem. Moreover, we find a new equivalent condition to the statements in Theorem 3.5. In particular, an explicit definition of a new class of orthodox semigroups is introduced.