Mathematica Slovaca
type: channel
description: Note: Due to change of plans for Mathematica Slovaca, this website will not be used. Please use the original website https://maslo.mat.savba.sk/ojs instead. The aim of this journal is to publish original research papers in all areas of mathematics containing new substantial and significant results or methods, with complete proofs. Contributions presented to the journal can also be short notes, surveys and possibly research problems. Occasionally the journal publishes book reviews, notices and news about topical events interesting to the mathematical community. In addition to regular issues, supplementary issues are published focusing on a theme of current interest, honoring an individual, or containing proceedings of a conference. Editor in Chief: Silvia Pulmannová Managing Editor: Anatolij Dvurečenskij The journal is covered by Current Mathematical Publications, Mathematical Reviews, Zentralblatt MATH, and Referativnyi Zhurnal Matematika. ISSN: 1337-2211 (online) ISSN: 0139-9918 (print)
publisher: De Gruyter
language: en
publication name: Mathematica Slovaca
issn: 0139-9918
items: Oscillation of nonlinear third-order differential equations with several sublinear neutral terms
items: Composition of binary quadratic forms over number fields
items: Univariate and bivariate extensions of the generalized exponential distributions
items: On log-bimodal alpha-power distributions with application to nickel contents and erosion data
items: A certain η-parallelism on real hypersurfaces in a nonflat complex space form
items: Conformal vector fields on almost co-Kähler manifolds
items: The form of locally defined operators in Waterman spaces
items: New fixed point theorems for countably condensing maps with an application to functional integral inclusions
items: Semidistributivity and Whitman property in implication zroupoids
items: Common fixed point results under w-distance with applications to nonlinear integral equations and nonlinear fractional differential equations
items: On the continuity of lattice isomorphisms on C(X, I)
items: On absolute double summability methods with high indices
items: Existence of traveling wave solutions in nonlocal delayed higher-dimensional lattice systems with quasi-monotone nonlinearities
items: Multiplicity of solutions for a class of fourth-order elliptic equations of p(x)-Kirchhoff type
items: On rapidly oscillating solutions of a nonlinear elliptic equation
items: Coefficient estimates for Libera type bi-close-to-convex functions
items: On the factorable spaces of absolutely p-summable, null, convergent and bounded sequences
items: Pellian equations of a special type
items: On Z-symmetric rings
items: The U family of distributions: Properties and applications
items: Some characterizations of mixed renewal processes
items: Set star-Menger and set strongly star-Menger spaces
items: Hyperbolic geometry for non-differential topologists
items: Existence and asymptotic periodicity of solutions for neutral integro-differential evolution equations with infinite delay
items: Existence and multiplicity of radially symmetric k-admissible solutions for Dirichlet problem of k-Hessian equations
items: Oscillation of second order delay differential equations with nonlinear nonpositive neutral term
items: Joint approximation by Dirichlet $L$-functions
items: Quartic polynomials with a given discriminant
items: Expanding lattice ordered abelian groups to Riesz spaces
items: Ordinary generating functions of binary products of third-order recurrence relations and 2-orthogonal polynomials

Oscillation of nonlinear third-order differential equations with several sublinear neutral terms
type: item
description: A class of third order differential equations with several sublinear neutral terms of the type (a(t) (b(t) (x(t) + ∑ j = 1 n pj(t) xαj ( τj(t) ) )' )' )' + ∑ j = 1 m fi(t, x(σi(t))) = 0, t ≥ t0 > 0 is considered. Some oscillation criteria are presented to improve and complement those in the literature. Two examples are established to illustrate the main results.
subject: Articles - Other topics
  topic: section
subject: oscillation
  topic: keywords
subject: third order differential equation
  topic: keywords
subject: sublinear neutral term
  topic: keywords
subject: nonoscillation
  topic: keywords
creator: Mohamed M. A. El-Sheikh
creator: Ragaa Sallam
creator: Shaimaa Salem
rights: Copyright (c) 2021 Mathematica Slovaca
date: 2021-12-10
publication date: 2021-12-10
starting page: 1411
ending page: 1426
doi: 10.1515/ms-2021-0061

Composition of binary quadratic forms over number fields
type: item
description: In this article, the standard correspondence between the ideal class group of a quadratic number field and the equivalence classes of binary quadratic forms of given discriminant is generalized to any base number field of narrow class number one. The article contains an explicit description of the correspondence. In the case of totally negative discriminants, equivalent conditions are given for a binary quadratic form to be totally positive definite.
subject: Articles - Other topics
  topic: section
subject: binary quadratic forms
  topic: keywords
subject: Gauss composition
  topic: keywords
subject: class group
  topic: keywords
creator: Kristýna Zemková
rights: Copyright (c) 2021 Mathematica Slovaca
date: 2021-12-10
publication date: 2021-12-10
starting page: 1339
ending page: 1360
doi: 10.1515/ms-2021-0057

Univariate and bivariate extensions of the generalized exponential distributions
type: item
description: The main aim of this paper is to introduce a new class of continuous generalized exponential distributions, both for the univariate and bivariate cases. This new class of distributions contains some newly developed distributions as special cases, such as the univariate and also bivariate geometric generalized exponential distribution and the exponential-discrete generalized exponential distribution. Several properties of the proposed univariate and bivariate distributions, and their physical interpretations, are investigated. The univariate distribution has four parameters, whereas the bivariate distribution has five parameters. We propose to use an EM algorithm to estimate the unknown parameters. According to extensive simulation studies, we see that the effectiveness of the proposed algorithm, and the performance is quite satisfactory. A bivariate data set is analyzed and it is observed that the proposed models and the EM algorithm work quite well in practice.
subject: Articles - Other topics
  topic: section
subject: Bivariate geometric generalized exponential distribution
  topic: keywords
subject: discrete generalized exponential distribution
  topic: keywords
subject: EM algorithm
  topic: keywords
subject: generalized exponential distribution
  topic: keywords
subject: maximum likelihood estimators
  topic: keywords
subject: univariate geometric generalized exponential distribution
  topic: keywords
creator: Vahid Nekoukhou
creator: Ashkan Khalifeh
creator: Hamid Bidram
rights: Copyright (c) 2021 Mathematica Slovaca
date: 2021-12-10
publication date: 2021-12-10
starting page: 1581
ending page: 1598
doi: 10.1515/ms-2021-0073

On log-bimodal alpha-power distributions with application to nickel contents and erosion data
type: item
description: In this paper, we present a new parametric class of distributions based on the log-alpha-power distribution, which contains the well-known log-normal distribution as a special case. This new family is useful to deal with unimodal as well as bimodal data with asymmetry and kurtosis coefficients ranging far from that expected based on the log-normal distribution. The usual approach is considered to perform inferences, and the traditional maximum likelihood method is employed to estimate the unknown parameters. Monte Carlo simulation results indicate that the maximum likelihood approach is quite effective to estimate the model parameters. We also derive the observed and expected Fisher information matrices. As a byproduct of such study, it is shown that the Fisher information matrix is nonsingular throughout the sample space. Empirical applications of the proposed family of distributions to real data are provided for illustrative purposes.
subject: Articles - Other topics
  topic: section
subject: bimodality
  topic: keywords
subject: maximum likelihood estimation
  topic: keywords
subject: parametric inference
  topic: keywords
creator: Hugo S. Salinas
creator: Guillermo Martínez-Flórez
creator: Artur J. Lemonte
creator: Heleno Bolfarine
rights: Copyright (c) 2021 Mathematica Slovaca
date: 2021-12-10
publication date: 2021-12-10
starting page: 1565
ending page: 1580
doi: 10.1515/ms-2021-0072

A certain η-parallelism on real hypersurfaces in a nonflat complex space form
type: item
description: In this paper, we give the complete classification of real hypersurfaces in a nonflat complex space form from the viewpoint of the η-parallelism of the tensor field h(= (1/2)Lξφ). In addition we investigate real hypersurfaces whose tensor h is either Killing type or transversally Killing tensor. In particular, we shall determine Hopf hypersurfaces whose tensor h is transversally Killing tensor by using an application of the classification of real hypersurfaces admitting η-parallelism with respect to the tensor h.
subject: Articles - Other topics
  topic: section
subject: nonflat complex space forms
  topic: keywords
subject: real hypersurfaces
  topic: keywords
subject: Hopf hypersurfaces
  topic: keywords
subject: the tensor field h
  topic: keywords
creator: Kazuhiro Okumura
rights: Copyright (c) 2021 Mathematica Slovaca
date: 2021-12-10
publication date: 2021-12-10
starting page: 1553
ending page: 1564
doi: 10.1515/ms-2021-0071

Conformal vector fields on almost co-Kähler manifolds
type: item
description: In this paper, we characterize almost co-Kähler manifolds with a conformal vector field. It is proven that if an almost co-Kähler manifold has a conformal vector field that is collinear with the Reeb vector field, then the manifold is a K-almost co-Kähler manifold. It is also shown that if a (κ, μ)-almost co-Kähler manifold admits a Killing vector field V, then either the manifold is K-almost co-Kähler or the vector field V is an infinitesimal strict contact transformation, provided that the (1,1) tensor h remains invariant under the Killing vector field.
subject: Articles - Other topics
  topic: section
subject: co-Kähler manifolds
  topic: keywords
subject: (κ, μ)-almost co-Kähler manifolds
  topic: keywords
subject: K-almost co-Kähler manifolds
  topic: keywords
subject: conformal vector field
  topic: keywords
creator: Uday Chand De
creator: Young Jin Suh
creator: Sudhakar K. Chaubey
rights: Copyright (c) 2021 Mathematica Slovaca
date: 2021-12-10
publication date: 2021-12-10
starting page: 1545
ending page: 1552
doi: 10.1515/ms-2021-0070

The form of locally defined operators in Waterman spaces
type: item
description: A representation formula for locally defined operators acting between Banach spaces of continuous functions of bounded variation in the Waterman sense is presented. Moreover, the Nemytskij composition operators will be investigated and some consequences for locally bounded as well as uniformly bounded local operators will be given.
subject: Articles - Other topics
  topic: section
subject: locally defined operator
  topic: keywords
subject: Nemytskij composition operator
  topic: keywords
subject: Waterman type variation
  topic: keywords
subject: continuous function
  topic: keywords
subject: locally bounded operator
  topic: keywords
subject: uniformly bounded operator
  topic: keywords
creator: Małgorzata Wróbel
rights: Copyright (c) 2021 Mathematica Slovaca
date: 2021-12-10
publication date: 2021-12-10
starting page: 1529
ending page: 1544
doi: 10.1515/ms-2021-0069

New fixed point theorems for countably condensing maps with an application to functional integral inclusions
type: item
description: This paper presents new fixed point theorems for 2 × 2 block operator matrix with countably condensing or countably D-set-contraction multi-valued inputs. Our theory will then be used to establish some new existence theorems for coupled system of functional differential inclusions in general Banach spaces under weak topology. Our results generalize, improve and complement a number of earlier works.
subject: Articles - Other topics
  topic: section
subject: countably condensing multimap
  topic: keywords
subject: functional-integral inclusions
  topic: keywords
subject: Banach spaces
  topic: keywords
subject: measure of weak non-compactness
  topic: keywords
subject: fixed point theorems
  topic: keywords
creator: Khaled Ben Amara
creator: Aref Jeribi
creator: Najib Kaddachi
rights: Copyright (c) 2021 Mathematica Slovaca
date: 2021-12-10
publication date: 2021-12-10
starting page: 1487
ending page: 1510
doi: 10.1515/ms-2021-0067

Semidistributivity and Whitman property in implication zroupoids
type: item
description: In 2012, the second author introduced and initiated the investigations into the variety I of implication zroupoids that generalize De Morgan algebras and ∨-semilattices with 0. An algebra A = (A, →, 0), where → is binary and 0 is a constant, is called an implication zroupoid (I-zroupoid, for short) if A satisfies: (x → y) → z ≈ [(z' → x) → (y → z)']', where x' := x → 0, and 0'' ≈ 0. Let I denote the variety of implication zroupoids and A ∈ I. For x, y ∈ A, let x ∧ y := (x → y')' and x ∨ y := (x' ∧ y')'. In an earlier paper, we had proved that if A ∈ I, then the algebra Amj = ⟨ A, ∨, ∧ ⟩ is a bisemigroup. The purpose of this paper is two-fold: First, we generalize the notion of semidistributivity from lattices to bisemigroups and prove that, for every A ∈ I, the bisemigroup Amj is semidistributive. Secondly, we generalize the Whitman Property from lattices to bisemigroups and prove that the subvariety MEJ of I, defined by the identity: x ∧ y ≈ x ∨ y, satisfies the Whitman Property. We conclude the paper with two open problems.
subject: Articles - Other topics
  topic: section
subject: Implication zroupoid
  topic: keywords
subject: De Morgan algebra
  topic: keywords
subject: semilattice, Birkhoff identity
  topic: keywords
subject: Birkhoff bisemigroup
  topic: keywords
subject: semidistributivity
  topic: keywords
subject: Whitman Property
  topic: keywords
creator: Juan M. Cornejo
creator: Hanamantagouda P. Sankappanavar
rights: Copyright (c) 2021 Mathematica Slovaca
date: 2021-12-10
publication date: 2021-12-10
starting page: 1329
ending page: 1338
doi: 10.1515/ms-2021-0056

Common fixed point results under w-distance with applications to nonlinear integral equations and nonlinear fractional differential equations
type: item
description: In this article, we prove some new common fixed point results under the generalized contraction condition using w-distance and weak altering distance functions. Also, the validity of the results is demonstrated by an example along with numerical experiment for approximating the common fixed point. Later, as applications, the unique common solutions for the system of nonlinear Fredholm integral equations, nonlinear Volterra integral equations and nonlinear fractional differential equations of Caputo type are derived.
subject: Articles - Other topics
  topic: section
subject: common fixed point
  topic: keywords
subject: w-distance
  topic: keywords
subject: altering distance function
  topic: keywords
subject: integral equation
  topic: keywords
subject: fractional differential equation
  topic: keywords
creator: D. Ramesh Kumar
rights: Copyright (c) 2021 Mathematica Slovaca
date: 2021-12-10
publication date: 2021-12-10
starting page: 1511
ending page: 1528
doi: 10.1515/ms-2021-0068

On the continuity of lattice isomorphisms on C(X, I)
type: item
description: We investigate topological conditions on a compact Hausdorff space Y, such that any lattice isomorphism φ: C(X, I) -> C(Y, I), where X is a compact Hausdorff space and I is the unit interval [0, 1], is continuous. It is shown that in either of cases that the set of Gδ points of Y has a dense pseudocompact subset or Y does not contain the Stone-Čech compactification of N, such a lattice isomorphism is a homeomorphism.
subject: Articles - Other topics
  topic: section
subject: lattice isomorphisms
  topic: keywords
subject: continuous functions
  topic: keywords
subject: Stone-Čech compactification
  topic: keywords
subject: order preserving bijections
  topic: keywords
creator: Vahid Ehsani
creator: Fereshteh Sady
rights: Copyright (c) 2021 Mathematica Slovaca
date: 2021-12-10
publication date: 2021-12-10
starting page: 1477
ending page: 1486
doi: 10.1515/ms-2021-0066

On absolute double summability methods with high indices
type: item
description: In a recent paper, [SARIGÖL, M. A.: Characterization of summability methods with high indices, Math. Slovaca 63 (2013), 1053–1058], the equivalence | C , 0 | k ⟺ | R , p n | k , k ≥ 1 was characterized for infinite single series. In the present paper, this result is extended to doubly summability a different approach.
subject: Articles - Other topics
  topic: section
subject: double series
  topic: keywords
subject: absolute Riesz summability
  topic: keywords
subject: Hölder's inequality
  topic: keywords
creator: Mehmet Ali Sarigöl
rights: Copyright (c) 2021 Mathematica Slovaca
date: 2021-12-10
publication date: 2021-12-10
starting page: 1471
ending page: 1476
doi: 10.1515/ms-2021-0065

Existence of traveling wave solutions in nonlocal delayed higher-dimensional lattice systems with quasi-monotone nonlinearities
type: item
description: In this paper, we are concerned with the existence of traveling wave solutions in nonlocal delayed higher-dimensional lattice systems with quasi-monotone nonlinearities. By using the upper and lower solution method and Schauder’s fixed point theorem, we establish the existence of traveling wave solutions. To illustrate our results, the existence of traveling wave solutions for a nonlocal delayed higher-dimensional lattice cooperative system with two species are considered.
subject: Articles - Other topics
  topic: section
subject: higher-dimensional lattice
  topic: keywords
subject: traveling wave solution
  topic: keywords
subject: nonlocal delay
  topic: keywords
subject: upper and lower solutions
  topic: keywords
creator: Kun Li
creator: Yanli He
rights: Copyright (c) 2021 Mathematica Slovaca
date: 2021-12-10
publication date: 2021-12-10
starting page: 1459
ending page: 1470
doi: 10.1515/ms-2021-0064

Multiplicity of solutions for a class of fourth-order elliptic equations of p(x)-Kirchhoff type
type: item
description: This paper deals with a class of fourth order elliptic equations of Kirchhoff type with variable exponent Δ2p(x) u − M( ∫Ω 1/ p(x) |∇u|p(x)dx) Δp(x) u + |u|p(x)−2u = λ f(x,u) + μ g(x,u) in Ω, <span data-mathml=" <mfenced open="{" close=""> &#x394; p ( x ) 2 u &#x2212; M ( &#x222B; &#x3A9; 1 p ( x ) | &#x2207; u | p ( x ) d x ) &#x394; p ( x ) u + | u | p ( x ) &#x2212; 2 u = &#x3BB; f ( x , u ) + &#x3BC; g ( x , u ) &#x2009;in&#x2009; &#x3A9; , u = &#x394; u = 0 &#x2009;on&#x2009; &#x2202; &#x3A9; , </mfenced> ">u = Δu =0 on ∂Ω, where p− := inf x∈\bar{Ω} p(x) > max{1, N/2}, λ>0 and μ ≥ 0 are real numbers, Ω ⊂ ℝN (N ≥ 1) is a smooth bounded domain, Δ2p(x)u=Δ(|Δu|p(x)−2Δu) is the operator of fourth order called the p(x)-biharmonic operator, Δp(x)u = div(|∇u|p(x)–2∇u) is the p(x)-Laplacian, p : Ω -> ℝ is a log-Hölder continuous function, M : [0, +∞) -> ℝ is a continuous function and f, g : Ω × ℝ -> ℝ are two L1-Carathéodory functions satisfying some certain conditions. Using two kinds of three critical point theorems, we establish the existence of at least three weak solutions for the problem in an appropriate space of functions.
subject: Articles - Other topics
  topic: section
subject: Fourth order elliptic equations
  topic: keywords
subject: Kirchhoff type problems
  topic: keywords
subject: variable exponents
  topic: keywords
subject: three critical point theorem
  topic: keywords
subject: variational methods
  topic: keywords
creator: Nguyen Thanh Chung
creator: Zohreh Naghizadeh
rights: Copyright (c) 2021 Mathematica Slovaca
date: 2021-12-10
publication date: 2021-12-10
starting page: 1441
ending page: 1458
doi: 10.1515/ms-2021-0063

On rapidly oscillating solutions of a nonlinear elliptic equation
type: item
description: The aim of this article is to examine the solutions of the boundary value problem of the nonlinear elliptic equation ε2△u = f(u). We describe the asymptotic behavior as ε tends to zero of the solutions on a spherical crown C of RN, (N ≥ 2) in a direct non-classical formulation which suggests easy proofs. We propose to look for interesting solutions in the case where the condition at the edge of the crown is a constant function. Our results are formulated in classical mathematics.Their proofs use the stroboscopic method which is a tool of the nonstandard asymptotic theory of differential equations.
subject: Articles - Other topics
  topic: section
subject: non standard analysis(NSA)
  topic: keywords
subject: boundary value problem
  topic: keywords
subject: elliptic PDE
  topic: keywords
subject: reduced problem
  topic: keywords
subject: vector field
  topic: keywords
subject: stroboscopy
  topic: keywords
creator: Houssem Eddine Kadem
creator: Saida Bendaas
rights: Copyright (c) 2021 Mathematica Slovaca
date: 2021-12-10
publication date: 2021-12-10
starting page: 1427
ending page: 1440
doi: 10.1515/ms-2021-0062

Coefficient estimates for Libera type bi-close-to-convex functions
type: item
description: In a very recent paper, Wang and Bulut [A note on the coefficient estimates of bi-close-to-convex functions, C. R. Acad. Sci. Paris, Ser. I 355 (2017), 876–880] determined the estimates for the general Taylor-Maclaurin coefficients of functions belonging to the bi-close-to-convex function class. In this study, we introduce the class of Libera type bi-close-to-convex functions and obtain the upper bounds for the coefficients of functions belonging to this class. Our results generalize the results in the above mentioned paper.
subject: Articles - Other topics
  topic: section
subject: analytic functions
  topic: keywords
subject: univalent functions
  topic: keywords
subject: bi-close-to-convex functions
  topic: keywords
subject: bi-starlike functions
  topic: keywords
subject: Faber polynomials
  topic: keywords
creator: Serap Bulut
rights: Copyright (c) 2021 Mathematica Slovaca
date: 2021-12-10
publication date: 2021-12-10
starting page: 1401
ending page: 1410
doi: 10.1515/ms-2021-0060

On the factorable spaces of absolutely p-summable, null, convergent and bounded sequences
type: item
description: Let F denote the factorable matrix and X ∈ {lp, c0, c, l∞}. In this study, we introduce the domains X(F ) of the factorable matrix in the spaces X. Also, we give the bases and determine the alpha-, beta- and gamma-duals of the spaces X(F ). We obtain the necessary and sufficient conditions on an infinite matrix belonging to the classes (lp(F ), l∞), (lp(F ), f ) and (X, Y(F)) of matrix transformations, where Y denotes any given sequence space. Furthermore, we give the necessary and sufficient conditions for factorizing an operator based on the matrix F and derive two factorizations for the Cesàro and Hilbert matrices based on the Gamma matrix. Additionally, we investigate the norm of operators on the domain of the matrix F. Finally, we find the norm of Hilbert operators on some sequence spaces and deal with the lower bound of operators on the domain of the factorable matrix.
subject: Articles - Other topics
  topic: section
subject: domain of factorable matrix
  topic: keywords
subject: almost convergence
  topic: keywords
subject: weighted mean matrix
  topic: keywords
subject: Hilbert matrix
  topic: keywords
subject: gamma matrix
  topic: keywords
subject: Cesàro matrix
  topic: keywords
creator: Feyzi Başar
creator: Hadi Roopaei
rights: Copyright (c) 2021 Mathematica Slovaca
date: 2021-12-10
publication date: 2021-12-10
starting page: 1375
ending page: 1400
doi: 10.1515/ms-2021-0059

Pellian equations of a special type
type: item
description: In this paper, we consider the solvability of the Pellian equation x2 - (d2 + 1)y2 = -m; in cases d = nk, m = n2l-1, where k; l are positive integers, n is a composite positive integer and d = pq, m = pq2, p, q are primes. We use the obtained results to prove results on the extendibility of some D(-1)-pairs to quadruples in the ring Z[√-t], with t > 0.
subject: Articles - Other topics
  topic: section
subject: Pellian equation
  topic: keywords
subject: Diophantine m-tuple
  topic: keywords
subject: quadratic field
  topic: keywords
creator: Mirela Jukić Bokun
creator: Ivan Soldo
rights: Copyright (c) 2021 Mathematica Slovaca
date: 2021-12-10
publication date: 2021-12-10
starting page: 1599
ending page: 1607
doi: 10.1515/ms-2021-0074

On Z-symmetric rings
type: item
description: We introduce the concept of Z-symmetric rings. In fact, the classes of all semicommutative rings, nil rings, reduced rings, Artinian rings and eversible rings are Z-symmetric rings. In order to sustain our assertion, we provide a number of examples of Z-symmetric and non Z-symmetric rings. We observe that the class of Z-symmetric rings lies strictly between the classes of eversible rings and the Dedekind finite rings. In particular, we consider the extensions of Z-symmetric rings. Finally, some new results between the Z-symmetric rings and Armendariz rings will be explored and investigated.
subject: Articles - Other topics
  topic: section
subject: Z-symmetric rings
  topic: keywords
subject: eversible rings
  topic: keywords
subject: Dedekind finite rings
  topic: keywords
subject: matrix rings
  topic: keywords
subject: Dorroh extensions
  topic: keywords
creator: Avanish Kumar Chaturvedi
creator: Nirbhay Kumar
creator: K. P. Shum
rights: Copyright (c) 2021 Mathematica Slovaca
date: 2021-12-10
publication date: 2021-12-10
starting page: 1361
ending page: 1374
doi: 10.1515/ms-2021-0058

The U family of distributions: Properties and applications
type: item
description: 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.
subject: Articles - Other topics
  topic: section
subject: Weibull distribution
  topic: keywords
subject: general family of distributions
  topic: keywords
subject: moments; simulation
  topic: keywords
subject: data analysis
  topic: keywords
creator: Farrukh Jamal
creator: Christophe Chesneau
creator: Abdus Saboor
creator: Muhammad Aslam
creator: Muhammad H. Tahir
creator: Wali Khan Mashwani
rights: Copyright (c) 2022 Mathematica Slovaca
date: 2022-02-16
publication date: 2022-02-16
starting page: 217
ending page: 240
doi: 10.1515/ms-2022-0015

Some characterizations of mixed renewal processes
type: item
description: 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.
subject: Articles - Other topics
  topic: section
subject: mixed renewal process
  topic: keywords
subject: regular conditional probability
  topic: keywords
subject: product regular conditional probability
  topic: keywords
subject: subfield regular conditional probability
  topic: keywords
subject: exchangeability
  topic: keywords
creator: Demetrios P. Lyberopoulos
creator: Nikolaos D. Macheras
rights: Copyright (c) 2022 Mathematica Slovaca
date: 2022-02-16
publication date: 2022-02-16
starting page: 197
ending page: 216
doi: 10.1515/ms-2022-0014

Set star-Menger and set strongly star-Menger spaces
type: item
description: Motivated by the Arhangeľskii "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.
subject: Articles - Other topics
  topic: section
subject: Menger
  topic: keywords
subject: star-Menger
  topic: keywords
subject: strongly star-Menger
  topic: keywords
subject: set star-Menger
  topic: keywords
subject: set strongly star-Menger
  topic: keywords
creator: Ljubiˇsa D. R. Koˇcinac
creator: Şukran Konca
creator: Sumit Singh
rights: Copyright (c) 2022 Mathematica Slovaca
date: 2022-02-16
publication date: 2022-02-16
starting page: 185
ending page: 196
doi: 10.1515/ms-2022-0013

Hyperbolic geometry for non-differential topologists
type: item
description: A soft presentation of hyperbolic spaces (as metric spaces), free of di erential apparatus, is off ered. 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.
subject: Articles - Other topics
  topic: section
subject: Hyperbolic geometry
  topic: keywords
subject: non-Euclidean geometry
  topic: keywords
subject: fifth Euclid's postulate
  topic: keywords
subject: parallel postulate
  topic: keywords
subject: free mobility
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subject: three-point homogeneous space
  topic: keywords
subject: metric homogeneity
  topic: keywords
creator: Piotr Niemiec
creator: Piotr Pikul
rights: Copyright (c) 2022 Mathematica Slovaca
date: 2022-02-16
publication date: 2022-02-16
starting page: 165
ending page: 184
doi: 10.1515/ms-2022-0012

Existence and asymptotic periodicity of solutions for neutral integro-differential evolution equations with infinite delay
type: item
description: 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.
subject: Articles - Other topics
  topic: section
subject: Neutral integro-differential evolution equation
  topic: keywords
subject: asymptotic periodicity
  topic: keywords
subject: infinite delay
  topic: keywords
subject: resolvent operator
  topic: keywords
creator: Jianbo Zhu
creator: Xianlong Fu
rights: Copyright (c) 2022 Mathematica Slovaca
date: 2022-02-16
publication date: 2022-02-16
starting page: 121
ending page: 140
doi: 10.1515/ms-2022-0009

Existence and multiplicity of radially symmetric k-admissible solutions for Dirichlet problem of k-Hessian equations
type: item
description: 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(D2 u)= f(-u) in B u=0 on ∂B and the corresponding one-parameter problem, where B is a unit ball in Rn 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.
subject: Articles - Other topics
  topic: section
subject: k-Hessian equation
  topic: keywords
subject: admissible solution
  topic: keywords
subject: multiplicity
  topic: keywords
subject: Leggett-Williams' fixed point theorem
  topic: keywords
creator: Zhiqian He
creator: Liangying Miao
rights: Copyright (c) 2022 Mathematica Slovaca
date: 2022-02-16
publication date: 2022-02-16
starting page: 111
ending page: 120
doi: 10.1515/ms-2022-0008

Oscillation of second order delay differential equations with nonlinear nonpositive neutral term
type: item
description: This paper deals with oscillation of a second order delay di erential 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.
subject: Articles - Other topics
  topic: section
subject: Oscillation
  topic: keywords
subject: neutral differential equation
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subject: nonpositive sublinear neutral term
  topic: keywords
creator: Blanka Baculíková
creator: B. Sudha
creator: K. Thangavelu
creator: E. Thandapani
rights: Copyright (c) 2022 Mathematica Slovaca
date: 2022-02-16
publication date: 2022-02-16
starting page: 103
ending page: 110
doi: 10.1515/ms-2022-0007

Joint approximation by Dirichlet $L$-functions
type: item
description: In the paper, collections of analytic functions are simultaneously approximated by collections of shifts of Dirichlet $L$-functions $\left(L(s+i\gamma_1(\tau), \chi_1),\right.$ $\left. \dots, L(s+i\gamma_r(\tau), \chi_r)\right)$, with arbitrary Dirichlet characters $\chi_1,\dots, \chi_r$. The differentiable functions $\gamma_1(\tau), \dots, \gamma_r(\tau)$ and their derivatives satisfy certain growth conditions. The obtained results extend those of [17].
subject: Articles - Other topics
  topic: section
subject: Dirichlet L-functions
  topic: keywords
subject: joint universality
  topic: keywords
subject: functional independence
  topic: keywords
subject: weak convergence
  topic: keywords
creator: Antanas Laurinčikas
creator: Darius Šiaučiūnas
rights: Copyright (c) 2022 Mathematica Slovaca
date: 2022-02-16
publication date: 2022-02-16
starting page: 51
ending page: 66
doi: 10.1515/ms-2022-0004

Quartic polynomials with a given discriminant
type: item
description: Let $0\ne D\in Z$ and let $Q_D$ be the set of all monic quartic polynomials $x^4 + ax^3 + bx^2 + cx + d \in Z[x]$ 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.
subject: Articles - Other topics
  topic: section
subject: quartic polynomial
  topic: keywords
subject: discriminant
  topic: keywords
subject: Mordell's equation
  topic: keywords
subject: elliptic curve
  topic: keywords
creator: Jiří Klaška
rights: Copyright (c) 2022 Mathematica Slovaca
date: 2022-02-16
publication date: 2022-02-16
starting page: 35
ending page: 50
doi: 10.1515/ms-2022-0003

Expanding lattice ordered abelian groups to Riesz spaces
type: item
description: First we give a necessary and sufficient condition for an Abelian lattice ordered group to allow expansion into a Riesz space (or vector lattice). So we build a totally ordered Abelian group with two non-isomorphic Riesz spatial structures, thus improving a previous document in which the example was an Abelian trellis group not totally ordered. This answers a question raised by Conrad in 1975. We also give a partial solution to another problem considered in the same document. Finally, we apply our results to MV-algebras and Riesz MV-algebras.
subject: Articles - Other topics
  topic: section
subject: Abelian lattice ordered group
  topic: keywords
subject: Riesz space
  topic: keywords
subject: MV-algebra
  topic: keywords
subject: Riesz MV-algebra
  topic: keywords
creator: Antonio Di Nola
creator: Giacomo Lenzi
creator: Gaetano Vitale
rights: Copyright (c) 2022 Mathematica Slovaca
date: 2022-02-16
publication date: 2022-02-16
starting page: 1
ending page: 10
doi: 10.1515/ms-2022-0001

Ordinary generating functions of binary products of third-order recurrence relations and 2-orthogonal polynomials
type: item
description: 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 endomrphism operators π_{e₂e₃}π_{e₁e₂} to the series ∑_{n=0}^\infty S_{n}(A₃)e₁ⁿzⁿ.
subject: Articles - Other topics
  topic: section
subject: Symmetric functions
  topic: keywords
subject: generating functions
  topic: keywords
subject: Tribonacci polynomials
  topic: keywords
subject: Narayana numbers
  topic: keywords
creator: Hind Merzouk
creator: Ali Boussayoud
creator: Abdelhamid Abderrezzak
rights: Copyright (c) 2022 Mathematica Slovaca
date: 2022-02-16
publication date: 2022-02-16
starting page: 11
ending page: 34
doi: 10.1515/ms-2022-0002