Volume 69, Issue 5

Given any punctured surface F 2 , we present a method for generating all of F 2 triangulations with inner vertices of degree ≥ 4 and boundary vertices of degree ≥ 3. The method is based on a set of expansive operations which includes the well-known vertex splitting and octahedron addition. By reversing this method we get a procedure to obtain minimal triangulations by a sequence of intermediate triangulations, all of them within the given family.

Two problems concerning EF -frames and EZ -frames are investigated. In [ Some new classes of topological spaces and annihilator ideals , Topology Appl. 165 (2014), 84–97], Tahirefar defines a Tychonoff space X to be an EF (resp., EZ )-space if disjoint unions of clopen sets are completely separated (resp., every regular closed subset is the closure of a union of clopen subsets). By extending these notions to locales, we give several characterizations of EF and EZ -frames, mostly in terms of certain ring-theoretic properties of 𝓡 L , the ring of real-valued continuous functions on L . We end by defining a qsz -frame which is a pointfree context of qsz -space and, give a characterization of these frames in terms of rings of real-valued continuous functions on L .

In the paper weak isometries in directed groups are investigated. It is proved that for every weak isometry f in a directed group G the relation f ( UL ( x , y ) ∩ LU ( x , y )) = UL ( f ( x ), f ( y )) ∩ LU ( f ( x ), f ( y )) is valid for each x , y ∈ G . The notions of an orthogonality of two elements and of a subgroup symmetry in directed groups are introduced and it is shown that each weak isometry in a 2-isolated directed group or in an abelian directed group is a composition of a subgroup symmetry and a right translation. It is also proved that stable weak isometries in a 2-isolated abelian directed group G are directly related to subdirect decompositions of the subgroup G 2 = {2 x ; x ∈ G } of G .

Let 𝓕 𝓟 L := Frm(𝓟(ℝ), L ). We show that if L is a P -frame then 𝓕 𝓟 L is an ℵ 0 -self-injective ring. We prove that a zero-dimensional frame L is extremally disconnected if and only if 𝓕 𝓟 L is a self-injective ring. Finally, it is shown that 𝓕 𝓟 L is a Baer ring if and only if 𝓕 𝓟 L is a continuous ring if and only if 𝓕 𝓟 L is a complete ring if and only if 𝓕 𝓟 L is a CS -ring.

Let K be a number field defined by a monic irreducible polynomial F ( X ) ∈ ℤ [ X ], p a fixed rational prime, and ν p the discrete valuation associated to p . Assume that F ( X ) factors modulo p into the product of powers of r distinct monic irreducible polynomials. We present in this paper a condition, weaker than the known ones, which guarantees the existence of exactly r valuations of K extending ν p . We further specify the ramification indices and residue degrees of these extended valuations in such a way that generalizes the known estimates. Some useful remarks and computational examples are also given to highlight some improvements due to our result.

Our purpose in this paper is to investigate some particular classes of generalized derivations and their relationship with commutativity of prime rings with involution. Some well-known results characterizing commutativity of prime rings have been generalized. Furthermore, we provide examples to show that the assumed restrictions cannot be relaxed.

We show without the Kuratowski-Zorn lemma that the set of all nilpotent elements of a medial semigroup (with zero) is the set-theoretic intersection of all its prime ideals. Moreover, some applications of the above theorem are given.

In this paper we consider the situation when a power of a transcendental meromorphic function shares non-zero polynomials with derivative of it’s combination with it’s shift. Also we exhibit some examples to fortify the conditions of our results.

Let SB∗ $\begin{array}{} \mathcal{S}^*_B \end{array}$ be the class of normalized starlike functions associated with a function related to the Bell numbers. By establishing bounds on some coefficient functionals for the family of functions with positive real part, we derive for functions in the class SB∗ $\begin{array}{} \mathcal{S}^*_B \end{array}$ several sharp coefficient bounds on the first six coefficients and also further sharp bounds on the corresponding Hankel determinants. Bounds on the first three consecutive higher-order Schwarzian derivatives for functions in the class SB∗ $\begin{array}{} \mathcal{S}^*_B \end{array}$ are investigated.

In this paper, the authors derive several sufficient conditions for a function to be the Carathéodory function in the unit disk 𝔻: = { z ∈ ℂ: | z | < 1}. More precisely, for given β ∈ (– π /2, π /2), γ ∈ [0, cos β ) and δ ∈ (0, π /2], we find some sufficient conditions for an analytic function p such that p (0) = 1 to satisfy Re{e −i β p ( z )} > γ or | arg { p ( z )– γ } | < δ for all z ∈ 𝔻 by using the first-order differential subordination. We then apply the results obtained here in order to find some conditions for univalent functions with geometric properties such as spirallikeness and strongly starlikeness.

In the present article, we deal with the overconvergence of the Szász-Durrmeyer-Chlodowsky operators. Here we study the approximation properties e.g. upper estimates, Voronovskaja type result for these operators attached to analytic functions in compact disks. Also, we discuss the exact order in simultaneous approximation by these operators and its derivatives and the asymptotic result with quantitative upper estimate. In such a way, we put in evidence the overconvergence phenomenon for the Szász-Durrmeyer-Chlodowsky operators, namely the extensions of approximation properties with exact quantitative estimates and orders of these convergencies to sets in the complex plane that contain the interval [0, ∞).

We study sufficient conditions of boundedness of L -index in a direction b ∈ ℂ n ∖ {0} for analytic solutions in the unit ball of a linear higher order non-homogeneous differential equation with directional derivatives. These conditions are restrictions by the analytic coefficients in the unit ball of the equation. Also we investigate asymptotic behavior of analytic functions of bounded L -index in the direction and estimate its growth. The results are generalizations of known propositions for entire functions of several variables.

In this paper, oscillation of all solutions of fourth order functional differential equations of neutral type of the form (r(t)(y(t)+p(t)y(t−τ))″)″+q(t)G(y(t−σ))=0$$\begin{array}{} \displaystyle (r(t)(y(t)+p(t)y(t-\tau))'')''+q(t)G(y(t-\sigma))=0 \end{array}$$ are studied under the assumption ∫0∞tr(t)dt<∞$$\begin{array}{} \displaystyle \int\limits^{\infty}_{0}\frac{t}{r(t)}\text{d}t \lt \infty \end{array}$$ for various ranges of p ( t )

This article concerns the oscillatory behavior of solutions to second-order half-linear delay differential equations with mixed neutral terms. The authors present new oscillation criteria that improve, extend, and simplify existing ones in the literature. The results are illustrated with examples.

The paper discusses uniqueness of Laplace transform considered on nabla time scales. As the main result, a nabla time scales analogue of Lerch’s theorem ensuring uniqueness of Laplace image is proved for so-called simply periodic time scales. Moreover, several presented counterexamples demonstrate that the uniqueness of Laplace image does not occur on general time scales when the nabla approach is employed. Other special properties of Laplace transform on nabla time scales, such as potential disconnectedness of domain of convergence, are addressed as well.

We continue to investigate the notion of IK${\mathcal I}^{\mathcal K}$-convergence (which concerns with the convergence with respect to one ideal along a set which is “big” with respect to another ideal) introduced by M. Mačaj and M. Sleziak [10] with primary focus on sequences of real functions. Our investigation is based on results by R. Filipów and M. Staniszewski [5, 6] or M. Staniszewski [11].

This paper considers two finite integral transforms of Fourier-type, in view to propose a set of eight new convolutions, and to analyze the solvability of a class of the integral equations of Wiener-Hopf plus Hankel type, defined on finite intervals, which is involved in engineering problems. The solvability and solution of the considered equations are investigated by means of Fourier-type series, and a Shannon-type sampling formula is obtained. Some concluding remarks with respect to theoretical issues and engineering applications are emphasized in the last section, along with the analysis of some illustrative cases, which exemplify that the present method solves cases which are not under the conditions of previously known techniques.

There are almost no results on the exponential stability of differential equations with unbounded memory in mathematical literature. This article aimes to partially fill this gap. We propose a new approach to the study of stability of integro-differential equations with unbounded memory of the following forms x‴(t)+∑ i=1m∫ t− τ i(t)tbi(t)e− α i(t− s)x(s)ds=0,x‴(t)+∑ i=1m∫ 0t− τ i(t)bi(t)e− α i(t− s)x(s)ds=0,$$\begin{array}{} \begin{split} \displaystyle x'''(t)+\sum_{i=1}^{m}\int\limits_{t-\tau_{i}(t)}^{t}b_{i}(t)\text{e}^{-\alpha _{i}(t-s) }x(s)\text{d} s &=0, \\ x'''(t)+\sum_{i=1}^{m}\int\limits_{0}^{t-\tau _{i}(t)}b_{i}(t)\text{e}^{-\alpha _{i}(t-s) }x(s)\text{d} s &= 0, \end{split} \end{array}$$ with measurable essentially bounded b i ( t ) and τ i ( t ), i = 1, …, m . We demonstrate that, under certain conditions on the coefficients, integro-differential equations of these forms are exponentially stable if the delays τ i ( t ), i = 1, …, m , are small enough. This opens new possibilities for stabilization by distributed input control. According to common belief this sort of stabilization requires first and second derivatives of x . Results obtained in this paper prove that this is not the case.

Let 𝓛 be a Lau algebra and X be a topologically invariant subspace of 𝓛 * containing UC (𝓛). We prove that if 𝓛 has a bounded approximate identity, then strict inner amenability of 𝓛 is equivalent to the existence of a strictly inner invariant mean on X . We also show that when 𝓛 is inner amenable the cardinality of the set of topologically left invariant means on 𝓛 * is equal to the cardinality of the set of topologically left invariant means on RUC (𝓛). Applying this result, we prove that if 𝓛 is inner amenable and 〈𝓛 2 〉 = 𝓛, then the essential left amenability of 𝓛 is equivalent to the left amenability of 𝓛. Finally, for a locally compact group G , we consider the measure algebra M ( G ) to study strict inner amenability of M ( G ) and its relation with inner amenability of G .

In this paper, we introduce a new bivariate Kumaraswamy exponential distribution, whose marginals are univariate Kumaraswamy exponential. Some probabilistic properties of this bivariate distribution are derived, such as joint density function, marginal density functions, conditional density functions, moments and stress-strength reliability. Also, we provide the expected information matrix with its elements in a closed form. Estimation of the parameters is investigated by the maximum likelihood, Bayesian and least squares estimation methods. A simulation study is carried out to compare the performance of the estimators by estimation methods. Further, one data set have been analyzed to show how the proposed distribution works in practice.

In this paper, we discuss wavelet estimation of time-varying coefficient models based on censored data where the survival and the censoring times are from a stationary α -mixing sequence. Under the appropriate conditions, the Berry-Esseen bouds of wavelet estimators are established. For the purpose of statistical inference, a random weighted wavelet estimator of the time-varying coefficient is also constructed, and some approximation rates are given.