Volume 72, Issue 1

First we give a necessary and sufficient condition for an abelian lattice ordered group to admit an expansion to a Riesz space (or vector lattice). Then we construct a totally ordered abelian group with two non-isomorphic Riesz space structures, thus improving a previous paper where the example was a non-totally ordered lattice ordered abelian group. This answers a question raised by Conrad in 1975. We give also a partial solution to another problem considered in the same paper. Finally, we apply our results to MV-algebras and Riesz MV-algebras.

In this paper, we introduce the new generating functions for the product of some numbers and 2-orthogonal polynomials by making use of the symmetrizing endomorphism operators π e 2 e 3 π e 1 e 2 to the series ∑n=0+∞Sn(A3)e1nzn.

Let 0 ≠ D ∈ ℤ and let Q D be the set of all monic quartic polynomials x 4 + ax 3 + bx 2 + cx + d ∈ ℤ[ x ] with the discriminant equal to D . In this paper we will devise a method for determining the set Q D . Our method is strongly related to the theory of integral points on elliptic curves. The well-known Mordell’s equation plays an important role as well in our considerations. Finally, some new conjectures will be included inspired by extensive calculations on a computer.

In the paper, collections of analytic functions are simultaneously approximated by collections of shifts of Dirichlet L -functions ( L ( s + i γ 1 ( τ ), χ 1 ),…, L ( s + i γ r ( τ ), χ r )), with arbitrary Dirichlet characters χ 1 ,…, χ r . The differentiable functions γ 1 ( τ ), …, γ r ( τ ) and their derivatives satisfy certain growth conditions. The obtained results extend those of [PAŃKOWSKI, Ł.: Joint universality for dependent L-functions , Ramanujan J. 45 (2018), 181–195].

In this paper, we use Taylor’s formula to prove new Hardy-type inequalities involving convex functions. We give new results that involve the Hardy–Hilbert inequality, Pólya–Knopp inequality and bounds for the identity related to the Hardy-type functional. At the end, mean value theorems of Cauchy type are given.

Let ϕ be a normalized convex function defined on open unit disk D. For a unified class of normalized analytic functions which satisfy the second order differential subordination f′ ( z ) + αzf″ ( z ) ≺ ϕ ( z ) for all z∈D, we investigate the distortion theorem and growth theorem. Further, the bounds on initial logarithmic coefficients, inverse coefficient and the second Hankel determinant involving the inverse coefficients are examined.

This paper deals with oscillation of a second order delay differential equations with a nonlinear nonpositive neutral term. Some new oscillation criteria and three examples are presented which improve and generalize the results reported in the literature.

In this paper, we study the existence and multiplicity of radially symmetric k -admissible solutions for the k -Hessian equation with 0-Dirichlet boundary condition {Sk(D2u)=f(−u)in B,u=0on ∂B, and the corresponding one-parameter problem, where B is a unit ball in ℝ n with n ≥ 1, k ∈ {1,…, n }, f : [0, +∞) → [0, +∞) is continuous. We show that the k -admissible solutions are not convex, so we construct a new cone and obtain the existence of triple and arbitrarily many k -admissible solutions via the Leggett-Williams’ fixed point theorem.

In this work, making use of the theory of resolvent operators and Banach fixed point theorem, we first discuss the existence and regularity of mild solutions for neutral partial functional integro-differential equations with infinite delay. We assume that the linear part of the considered equation generates a resolvent operator and the nonlinear function satisfies Lipschitz conditions. Then we investigate the asymptotic periodicity of mild solutions under asymptotic periodic assumption on the nonlinear function. The obtained results extend somewhat the related conclusions in literature. In the end, an example is presented to illustrate the obtained results.

The goal of this paper is to construct a new type of Bernstein operators depending on the shape parameter λ ∈ [–1,1]. For these new type operators a uniform convergence result is presented. Furthermore, order of approximation in the sense of local approximation is investigated and Voronovskaja type theorem is proved. Lastly, some graphical results are given to show the rate of convergence of constructed operators to a given function f .

In this paper, we obtain a Korovkin type approximation theorem for power series statistical convergence of functions belonging to the class produced by multivariable modulus of continuity function. As an application of this theorem, we construct a non-tensor product Balázs type BBH operator which does not converge in ordinary sense. Moreover, we study promised approximation properties of this operator and compute the rate of convergence. Finally, we prove that our new approximation result works but its classical case fails.

A soft presentation of hyperbolic spaces (as metric spaces), free of differential apparatus, is offered. Fifth Euclid’s postulate in such spaces is overthrown and, among other things, it is proved that spheres (equipped with great-circle distances) and hyperbolic and Euclidean spaces are the only locally compact geodesic (i.e., convex) metric spaces that are three-point homogeneous.

Motivated by the Arhangel’skii “s-Lindelöf cardinal function” definition, Kočinac and Konca defined and studied set covering properties and set star covering properties. In this paper, we present results on the star covering properties called set star-Menger and set strongly star-Menger. We investigate the relationship among set star-Menger, set strongly star-Menger and other related properties and study the topological properties of set star-Menger and set strongly star-Menger properties.

Some characterizations of mixed renewal processes in terms of exchangeability and of different types of regular conditional probabilities are given. As a consequence, an existence result for mixed renewal processes, providing also a new construction for them, is obtained. As an application, some concrete examples of constructing such processes are presented and the corresponding regular conditional probabilities are explicitly computed.

In this article, we develop a new general family of distributions aimed at unifying some well-established lifetime distributions and offering new work perspectives. A special family member based on the so-called modified Weibull distribution is highlighted and studied. It differs from the competition with a very flexible hazard rate function exhibiting increasing, decreasing, constant, upside-down bathtub and bathtub shapes. This panel of shapes remains rare and particularly desirable for modeling purposes. We provide the main mathematical properties of the special distribution, such as a tractable infinite series expansion of the probability density function, moments of several kinds (raw, incomplete, probability weighted…) with discussions on the skewness and kurtosis. The stochastic ordering structure and stress-strength parameter are also considered, as well as the basics of the order statistics. Then, an emphasis is put on the inferential features of the related model. In particular, the estimation of the model parameters is employed by the maximum likelihood method, with a simulation study to confirm the suitability of the approach. Three practical data sets are then analyzed. It is observed that the proposed model gives better fits than other well-known lifetime models derived from the Weibull model.

A new method has been proposed to generalize Burr-XII distribution, also called Burr distribution, by adding an extra parameter to an existing Burr distribution for more flexibility. In this method, the exponent of the Burr distribution is modeled using a nonlinear function of the data and one additional parameter. The models of this newly introduced generalized Burr family can significantly increase the flexibility of the former Burr distribution with respect to the density and hazard rate shapes. Families expanded using the method proposed here is heavy-tailed and belongs to the maximum domain of attractions of the Frechet distribution. The method is further applied to yield three-parameter classical Pareto and generalized exponentiated distributions which shows the broader application of the proposed idea of generalization. A relevant model of the new generalized Burr family has been considered in detail, with particular emphasis on the hazard functions, stochastic orders, estimation procedures, and testing methods are derived. Finally, as empirical evidence, the new distribution is applied to the analysis of large-scale heavy-tailed network data and compared with other commonly used distributions available for fitting degree distributions of networks. Experimental results suggest that the proposed Burr distribution with nonlinear exponent better fits the large-scale heavy-tailed networks better than the popularly used Marhsall-Olkin generalization of Burr and exponentiated Burr distributions.

Let K be a finite field, K ( x ) be the field of rational functions in x over K and K be the field of formal power series over K . We show that under certain conditions integral combinations with algebraic formal power series coefficients of a U 1 -number in K are U m -numbers in K, where m is the degree of the algebraic extension of K ( x ), determined by these algebraic formal power series coefficients.