Article Prof. RNDr. Michal Fečkan, DrSc. – Sexagenarian? was published on April 1, 2021 in the journal Mathematica Slovaca (volume 71, issue 2).

The Tribonacci sequence is a generalization of the Fibonacci sequence which starts with 0,0,1 and each term afterwards is the sum of the three preceding terms. Here, we show that the only Tribonacci numbers that are concatenations of two repdigits are 13,24,44,81. This paper continues a previous work that searched for Fibonacci numbers which are concatenations of two repdigits.

Let ( P n ) n ≥0 be the sequence of Padovan numbers defined by P 0 = 0, P 1 = 1 = P 2 , and P n +3 = P n +1 + P n for all n ≥ 0. In this paper, we find all Padovan numbers that are concatenations of two distinct repdigits.

Let K = ℚ(pd24)$\begin{array}{} \displaystyle (\sqrt[4]{pd^{2}}) \end{array}$ be a real pure quartic number field and k = ℚ(p$\begin{array}{} \displaystyle \sqrt{p} \end{array}$) its real quadratic subfield, where p ≡ 5 (mod 8) is a prime integer and d an odd square-free integer coprime to p . In this work, we calculate r 2 ( K ), the 2-rank of the class group of K , in terms of the number of prime

We propose a matrix analogue of a general inverse series relation with an objective to introduce the generalized Humbert matrix polynomial, Wilson matrix polynomial, and the Rach matrix polynomial together with their inverse series representations. The matrix polynomials of Kiney, Pincherle, Gegenbauer, Hahn, Meixner-Pollaczek etc. occur as the special cases. It is also shown that the general inverse

We establish several versions of the subcritical and critical Hardy type inequalities with Bessel pairs on the Euclidean space endowed with a Finsler norm.

In this paper we introduce some new subclasses of the p -valent analytic functions with higher-order derivatives that generalize some related subclasses of starlike and convex functions of a positive order. We found the order of ( p , q )-valent starlikeness and convexity for the products of functions that belong to these classes. The order of ( p , q )-valent starlikeness and convexity of certain

In this contribution, we study properties of block Hessenberg matrices associated with matrix orthonormal polynomials on the unit circle. We also consider the Uvarov and Christoffel spectral matrix transformations of the orthogonality measure, and obtain some relations between the associated Hessenberg matrices.

For the period T ( α ) of a simple pendulum with the length L and the amplitude (the initial elongation) α ∈ (0, π ), a strictly increasing sequence T n ( α ) is constructed such that the relations T1(α )=2Lgπ − 2+1ϵ ln1+ϵ 1− ϵ +π 4− 23ϵ 2,Tn+1(α )=Tn(α )+2Lgπ wn+12− 22n+3ϵ 2n+2,$$\begin{array}{c} \displaystyle T_1(\alpha)=2\sqrt{\frac{L}{g}}\left[\pi-2+\frac{1}{\epsilon} \ln\left(\frac{1+\epsilon

In this paper, we study convolution operators on an Orlicz space L Φ ( G ) commuting with left translations, where Φ is an N-function and G is a locally compact group. We also present some basic properties of the Fourier transform of a Φ-convolution operator in the context of locally compact abelian groups.

In this paper, we obtain some characterizations on the Reeb vector field for a trans-Sasakian manifold to be proper.

The p -adic completion ℚ p of the rational numbers induces a different absolute value |⋅| p than the typical | ⋅| we have on the real numbers. In this paper we compare and contrast functions f : ℝ + → ℝ + , for which the composition with the p-adic metric d p generated by |⋅| p is still a metric on ℚ p , with the usual metric preserving functions and the functions that preserve the Euclidean metric

In this paper, we do further investigations on the statistical inner and outer limits of sequences of closed sets in metric spaces, which were introduced by Nuray, Rhoades, and Talo, Sever, Başar, and generalize the conventional Painleve-Kuratowski inner and outer limits. Also, we provide criteria for checking statistical Wijsman and Hausdorff set convergences and we examine the relationship between

We characterize the uniform convergence points set of a pointwisely convergent sequence of real-valued functions defined on a perfectly normal space. We prove that if X is a perfectly normal space which can be covered by a disjoint sequence of dense subsets and A ⊆ X , then A is the set of points of the uniform convergence for some convergent sequence ( f n ) n ∈ ω of functions f n : X → ℝ if and only

In this paper, we investigate the problem of the local linear estimation of the conditional ageing intensity function, when the variable of interest is subject to random right-censored. We establish under appropriate conditions the asymptotic normality of this estimator.

We prove an analogue of the Donsker theorem under the Lindeberg condition in a fuzzy setting. Specifically, we consider a certain triangular system of d -dimensional fuzzy random variables {Xn,i∗ },$\begin{array}{} \{X_{n,i}^*\}, \end{array}$ n ∈ ℕ and i = 1, 2, …, k n , which take as their values fuzzy vectors of compact and convex α -cuts. We show that an appropriately normalized and interpolated

Having only two parameters, the Gamma-Lindley distribution does not provide enough flexibility for analyzing different types of lifetime data. From this perspective, in order to further enhance its flexibility, we set forward in this paper a new class of distributions named Generalized Gamma-Lindley distribution with four parameters. Its construction is based on certain mixtures of Gamma and Lindley

Matrix variate generalizations of Pareto distributions are proposed. Several properties of these distributions including cumulative distribution functions, characteristic functions and relationship to matrix variate beta type I and matrix variate type II distributions are studied.

In this paper, the global exponential stability and periodicity are investigated for delayed neural network models with continuous coefficients and piecewise constant delay of generalized type. The sufficient condition for the existence and uniqueness of periodic solutions of the model is established by applying Banach’s fixed point theorem and the successive approximations method. By constructing

In [ An optimal inequality for CR - warped products in complex space forms involving CR δ - invariant , Internat. J. Math. 23 (3) (2012)], B.-Y. Chen introduced the CR δ -invariant for CR-submanifolds. Then, in [ Two optimal inequalities for anti - holomorphic submanifolds and their applications , Taiwan. J. Math. 18 (2014), 199–217], F. R. Al-Solamy, B.-Y. Chen and S. Deshmukh proved two optimal inequalities

Article Prof. RNDr. Ing. Lubomír Kubáček, DrSc., Dr.h.c. –Nonagenarian was published on February 1, 2021 in the journal Mathematica Slovaca (volume 71, issue 1).

Article Doc. RNDr. Roman Frič, DrSc. passed away was published on February 1, 2021 in the journal Mathematica Slovaca (volume 71, issue 1).

The present paper introduces and studies the concepts of K -outer approximation and K -inner approximation for a monotone function μ defined on a D -poset P , by a subfamily K of P . Some desirable properties of K -approximable functions are established and it is shown that the family of all elements of P that possess K -approximation, forms a lattice and is closed under orthosupplementation. We have

In this paper, it is shown that there is no positive integer n such that the set of x∈A$ x\in \mathfrak{A} $ for which [(xδ)n,(x∗δ)n(xδ)n]∈Z(A)$ [(x^{\delta})^n, (x^{*{\delta}})^n(x^{\delta})^n]\in \mathcal{Z}(\mathfrak{A}) $, where δ is a linear derivation on A$ \mathfrak{A} $ or there exists a central idempotent e∈Q$ e\in \mathcal{Q} $ such that δ =0 on eQ$ e\mathcal{Q} $ and (1−e)Q$ (1-e)\mathcal{Q}

The aim of this study is to establish new discrete Grüss type inequality using fractional order h-sum and h-difference operators that generalize the fractional sum and difference operators.

In this manuscript, we introduce and study the concept of exponential trigonometric convex functions and their some algebraic properties. We obtain Hermite-Hadamard type inequalities for the newly introduced class of functions. We also obtain some refinements of the Hermite-Hadamard inequality for functions whose first derivative in absolute value, raised to a certain power which is greater than one

In this paper some properties of the pseudo-integral are summarized and a characterization theorem for this integral is proposed. Using the characterization theorem, we obtain that the pseudo-integral with respect to the pseudo-product of two σ -⊕-measures can be reduced to repeated pseudo-integrals. As a consequence of that claim and the Hölder type inequality for the pseudo-integral, we get the generalized

This paper aims to introduce the q -analogue of subclasses of the spiral-like functions of complex order and derive some inclusion properties by applying certain linear operators. The invariance of these classes under q -Bernardi integral operator has been discussed. Our results yield some known results as special case.

This paper studies analytic functions f defined on the open unit disk of the complex plane for which f / g and (1 + z ) g / z are both functions with positive real part for some analytic function g . We determine radius constants of these functions to belong to classes of strong starlike functions, starlike functions of order α , parabolic starlike functions, as well as to the classes of starlike functions

We give some sufficient conditions for the convergence of the sequence of successive approximations to the unique solution of first order Cauchy problem in a Banach space. Our approach is based on a generalized Nagumo condition due to A. Constantin and the properties of the Kuratowski measure of noncompactness.

In this article, by using a new form of multi-quadratic mapping, we define multi- m -Jensen-quadratic mappings and then unify the system of functional equations defining a multi- m -Jensen-quadratic mapping to a single equation. Using a fixed point theorem, we study the generalized Hyers-Ulam stability of multi-quadratic and multi- m -Jensen-quadratic functional equations. As a consequence, we show

In this article we obtain sufficient conditions for the oscillation of all solutions of the higher-order delay difference equation Δ m(yn− ∑ j=1kpnjyn− mj)+vnG(yσ (n))− unH(yα (n))=fn,$$\begin{array}{} \displaystyle \Delta^{m}\big(y_n-\sum_{j=1}^k p_n^j y_{n-m_j}\big) + v_nG(y_{\sigma(n)})-u_nH(y_{\alpha(n)})=f_n\,, \end{array}$$ where m is a positive integer and Δ x n = x n +1 − x n . Also we obtain

Recently Bukovský, Das and Šupina [ Ideal quasi - normal convergence and related notions , Colloq. Math. 146 (2017), 265–281] started the study of sequence selection properties (𝓘, 𝓙- α 1 ) and (𝓘, 𝓙- α 4 ) of C p ( X ) using the double ideals, where 𝓘 and 𝓙 are the proper admissible ideals of ω , which are motivated by Arkhangeľskii local α i -properties [ The frequency spectrum of a topological

In this article we introduce paranormed Nörlund difference sequence space of fractional order α , N t ( p , Δ ( α ) ) defined by the composition of fractional difference operator Δ ( α ) , defined by (Δ (α )x)k=∑ i=0∞ (− 1)iΓ (α +1)i!Γ (α − i+1)xk− i,$\begin{array}{} \displaystyle (\Delta^{(\alpha)}x)_k=\sum_{i=0}^{\infty}(-1)^i\frac{\Gamma(\alpha+1)}{i!\Gamma(\alpha-i+1)}x_{k-i}, \end{array}$ and

Using the theory of elliptic curve, we show that all right triangles, such that the sum of the area and the square of the sum of legs is a square, are given by an infinite set. Similarly, we get all right triangles such that the sum of the area and the square of the semi-perimeter is a square. Using the theory of Pell’s equation, we prove that there are infinitely many non-primitive right triangles

In this paper, we introduce the weighted projective Ricci curvature as an extension of projective Ricci curvature introduced by Z. Shen. We characterize the class of Randers metrics of weighted projective Ricci flat curvature. We find the necessary and sufficient condition under which a Kropina metric has weighted projective Ricci flat curvature. Finally, we show that every projectively flat metric

Let 𝓔 k denote the set of diffeomorphism classes of closed connected smooth k -manifolds X with the property that for any oriented vector bundle α over X , the Euler class e ( α ) = 0. We show that if X ∈ 𝓔 2 n +1 is orientable, then X is a rational homology sphere and π 1 ( X ) is perfect. We also show that 𝓔 8 = ∅ and derive additional cohomlogical restrictions on orientable manifolds in 𝓔 k

We propose a new generalized class of distributions called Lindley-Weibull Power Series (LWPS) distributions and their special case called Lindley-Weibull logarithmic (LWL) distributions. Structural properties of the LWPS class of distributions and its sub-model LWL distribution including moments, order statistics, Rényi entropy, mean and median deviations, Bonferroni and Lorenz curves, and maximum

In this paper, a stochastic prey-predator model is investigated and analyzed, which possesses foraging arena scheme in polluted environments. Sufficient conditions are established for the extinction and persistence in the mean. These conditions provide a threshold that determines the persistence in the mean and extinction of species. Furthermore, it is also shown that the stochastic system has a periodic

Let L be a number field. For a given prime p , we define integers αpL$ \alpha_{p}^{L} $ and βpL$ \beta_{p}^{L} $ with some interesting arithmetic properties. For instance, βpL$ \beta_{p}^{L} $ is equal to 1 whenever p does not ramify in L and αpL$ \alpha_{p}^{L} $ is divisible by p whenever p is wildly ramified in L . The aforementioned properties, although interesting, follow easily from definitions;

We outline the transition from classical probability space (Ω, A, p) to its "divisible" extension, where (as proposed by L. A. Zadeh) the σ-field A of Boolean random events is extended to the class 𝓜(A) of all measurable functions into [0,1] and the σ-additive probability measure p on A is extended to the probability integral ∫(·) dp on 𝓜(A). The resulting extension of (Ω, A,p) can be described as

In the paper, we introduce 𝔏-fuzzy state filters in state residuated lattices and investigate their related properties, where 𝔏 is a complete Heyting algebra. Moreover, we study the 𝔏-fuzzy state co-annihilator of an 𝔏-fuzzy set with respect to an 𝔏-fuzzy state filter. Finally, using the 𝔏-fuzzy state co-annihilator, we investigate lattice structures of the set of some types of 𝔏-fuzzy state

The theory of fuzzy deductive systems in RM algebras is developed. Various characterizations of fuzzy deductive systems are given. It is proved that the set of all fuzzy deductive systems of a RM algebra 𝒜 is a complete lattice (it is distributive if 𝒜 is a pre-BBBCC algebra). Some characterizations of Noetherian RM algebras by fuzzy deductive systems are obtained. In pre-BBBZ algebras, the fuzzy

In the paper, employing methods and techniques in analysis and linear algebra, the authors find a simple formula for computing an interesting Hessenberg determinant whose elements are products of binomial coefficients and falling factorials, derive explicit formulas for computing some special Hessenberg and tridiagonal determinants, and alternatively and simply recover some known results.

In this paper, we suggest a novel public key scheme by incorporating the twisted Edwards model of elliptic curves. The security of the proposed encryption scheme depends on the hardness of solving elliptic curve version of discrete logarithm problem and Diffie-Hellman problem. It then ensures secure message transmission by having the property of one-wayness, indistinguishability under chosen-plaintext

The Kumaraswamy generalized family of distributions proposed by Cordeiro and de-Castro (2011), has received increased attention in modern distribution theory with 624 google citations, and more than 50 special models have been studied so far. We define another generator, and then propose a new Kumaraswamy generalized family of distributions by inducting this new generator. Some useful properties of

In this paper, we investigate the asymptotic properties of a nonparametric estimator of the relative error regression given a functional explanatory variable, in the case of a scalar censored response, we use the mean squared relative error as a loss function to construct a nonparametric estimator of the regression operator of these functional censored data. We establish the strong almost complete

In this paper, we investigate the asymptotic behavior of the multivariate record values by using the Reduced Ordering Principle (R-ordering). Necessary and sufficient conditions for weak convergence of the multivariate record values based on sup-norm are determined. Some illustrative examples are given.

To a coarse structure we associate a Grothendieck topology which is determined by coarse covers. A coarse map between coarse spaces gives rise to a morphism of Grothendieck topologies. This way we define sheaves and sheaf cohomology on coarse spaces. We obtain that sheaf cohomology is a functor on the coarse category: if two coarse maps are close they induce the same map in cohomology. There is a coarse

Fundamental concepts for variational integrals evaluated on the solutions of a system of ordinary differential equations are revised. The variations, stationarity, extremals and especially the Poincaré-Cartan differential forms are relieved of all additional structures and subject to the equivalences and symmetries in the widest possible sense. Theory of the classical Lagrange variational problem eventually

In this paper we prove existence and uniqueness of a common fixed point for non-self coincidentally commuting mappings with nonlinear, generalized contractive condition defined on strictly convex Menger PM-spaces proved.

The disjoint properties of finitely many composition operators acting on the weighted Banach spaces of holomorphic functions in the unit disk were investigated in this paper.

We consider properties of defined earlier families of sets which are microscopic (small) in some sense. An equivalent definition of considered families is given, which is helpful in simplifying a proof of the fact that each Lebesgue null set belongs to one of these families. It is shown that families of sets microscopic in more general sense have properties analogous to the properties of the σ-ideal

In this paper, we find all the solutions of the title Diophantine equation in positive integers (m, n, k, x), where Pi is the ith term of the Pell sequence.

In this paper, we apply the module theory to EQ-algebras and we introduce EQ-modules, multiplication EQ-modules and investigate some properties about them. Then we construct the fraction of EQ-algebras, the fraction of EQ-modules, and prove some related results.

We introduce and investigate central lifting property (CLP) for orthomodular lattices as a property whereby all central elements can be lifted modulo every p-ideal. It is shown that prime ideals, maximal ideals and finite p-ideals have CLP. Also Boolean algebras, simple chain finite orthomodular lattices, subalgebras of an orthomodular lattices generated by two elements and finite orthomodular lattices

The notion of a congruence pair for principal MS-algebras, simpler than the one given by Beazer for K2-algebras [], is introduced. It is proved that the congruences of the principal MS-algebras L correspond to the MS-congruence pairs on simpler substructures L°° and D(L) of L that were associated to L in [].

In this paper, we mainly consider the existence and Hyers-Ulam stability of solutions for a class of fractional differential equations involving time-varying delays and non-instantaneous impulses. By the Krasnoselskii’s fixed point theorem, we present the new constructive existence results for the addressed equation. In addition, we deduce that the equations have Hyers-Ulam stable solutions by utilizing

In this paper, a bivariate extension of exponentiated Fréchet distribution is introduced, namely a bivariate exponentiated Fréchet (BvEF) distribution whose marginals are univariate exponentiated Fréchet distribution. Several properties of the proposed distribution are discussed, such as the joint survival function, joint probability density function, marginal probability density function, conditional

We prove that the topological complexity of a quaternionic flag manifold is half of its real dimension. For the real oriented Grassmann manifolds G͠n,k, 3 ≤ k ≤ [n/2], the zero-divisor cup-length of the rational cohomology of G͠n,k is computed in terms of n and k which gives a lower bound for the topological complexity of G͠n,k, TC(G͠n,k). When k = 3, it is observed in certain cases that better lower