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)
Oscillation of nonlinear third-order differential equations with several sublinear neutral terms
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.
Composition of binary quadratic forms over number fields
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.
Univariate and bivariate extensions of the generalized exponential distributions
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.
Bivariate geometric generalized exponential distribution
discrete generalized exponential distribution
univariate geometric generalized exponential distribution
On log-bimodal alpha-power distributions with application to nickel contents and erosion data
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.
A certain η-parallelism on real hypersurfaces in a nonflat complex space form
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.
Conformal vector fields on almost co-Kähler manifolds
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.
The form of locally defined operators in Waterman spaces
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.
New fixed point theorems for countably condensing maps with an application to functional integral inclusions
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.
Semidistributivity and Whitman property in implication zroupoids
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.
Common fixed point results under w-distance with applications to nonlinear integral equations and nonlinear fractional differential equations
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.
On the continuity of lattice isomorphisms on C(X, I)
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.
On absolute double summability methods with high indices
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.
Existence of traveling wave solutions in nonlocal delayed higher-dimensional lattice systems with quasi-monotone nonlinearities
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.
Multiplicity of solutions for a class of fourth-order elliptic equations of p(x)-Kirchhoff type
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.
On rapidly oscillating solutions of a nonlinear elliptic equation
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.
Coefficient estimates for Libera type bi-close-to-convex functions
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.
On the factorable spaces of absolutely p-summable, null, convergent and bounded sequences
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.
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.
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.
The U family of distributions: Properties and applications
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.
Some characterizations of mixed renewal processes
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.
subfield regular conditional probability
Set star-Menger and set strongly star-Menger spaces
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.
Hyperbolic geometry for non-differential topologists
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.
Existence and asymptotic periodicity of solutions for neutral integro-differential evolution equations with infinite delay
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.
Neutral integro-differential evolution equation
Existence and multiplicity of radially symmetric k-admissible solutions for Dirichlet problem of k-Hessian equations
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.
Oscillation of second order delay differential equations with nonlinear nonpositive neutral term
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.
Joint approximation by Dirichlet $L$-functions
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].
Quartic polynomials with a given discriminant
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.
Expanding lattice ordered abelian groups to Riesz spaces
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.
Ordinary generating functions of binary products of third-order recurrence relations and 2-orthogonal polynomials
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.