Showing papers in "Quaestiones Mathematicae in 2021"
TL;DR: The only Fibonacci numbers that are concatenations of two repdigits are 13, 21, 34, 55, 89, 144, 233, 377 as discussed by the authors, and 14.
Abstract: We show that the only Fibonacci numbers that are concatenations of two repdigits are 13, 21, 34, 55, 89, 144, 233, 377.
24 citations
TL;DR: In this paper, a contact metric manifold whose metric is a Riemann soliton was studied and it was shown that the manifold is either of constant curvature + 1 (and V is Killing) or D-homothetically invariant.
Abstract: In this paper, we study contact metric manifold whose metric is a Riemann soliton. First, we consider Riemann soliton (g; V ) with V as contact vector eld on a Sasakian manifold (M; g) and in this case we prove that M is either of constant curvature +1 (and V is Killing) or D-homothetically xed -Einstein manifold (and V leaves the structure tensor φ invariant). Next, we prove that if a compact K-contact manifold whose metric g is a gradient almost Riemann soliton, then it is Sasakian and isometric to a unit sphere S2n+1. Further, we study H-contact manifold admitting a Riemann soliton (g; V ) where V is pointwise collinear with .Key words: Contact metric manifold, Riemann soliton, gradient almost Riemann soliton.
17 citations
TL;DR: In this article, the concomitants of generalized order statistics from iterated Farlie-Gumbel-Morgenstern (FGM) bivariate distribution are studied.
Abstract: In this paper, we study the concomitants of generalized order statistics from iterated Farlie-Gumbel-Morgenstern (FGM) bivariate distribution. Three information measures, the Shannon entropy, the Kullback-Leibler distance and the Fisher information number, are derived and studied for this model. For each of these information measures, a computational study is conducted, in which we compare themodel of order statistics and model of sequential order statistics.
Key words: Concomitants, generalized order statistics, iterated FGM family, Shannon's entropy, Kullback-Leibler distance, Fisher information number.
13 citations
TL;DR: In this paper, the Drazin inverse, the group inverse, and the core-EP inverse with the Moore-Penrose inverse are investigated, solving some type of matrix equations.
Abstract: Various compositions of the Drazin inverse, the group inverse or the core-EP inverse with the Moore-Penrose inverse have investigated last years. Solving some type of matrix equations, we introduce...
12 citations
TL;DR: In this article, the authors established some important results for the impulsive wave equation and studied the impulse approximate controllability where the impulse wave equation is controllable by a solution.
Abstract: In this paper, we establish some important results for the impulsive wave equation. We begin by proving the existence of a solution. Then, we study the impulse approximate controllability where the...
11 citations
TL;DR: In this paper, the spectra of a discrete Sturm-Liouville problem with two eigenparameter-dependent boundary conditions were considered and the operator corresponding to the boundary condition was defined.
Abstract: In this paper, we consider the spectra of a discrete Sturm-Liouville problem with two eigenparameter-dependent boundary conditions. Different from the previous results, the operator corresponding to...
9 citations
TL;DR: In this article, the authors extend the definition of the relative group homology the- ories of the pair (G, H) defined by Adamso... to the case of groups, where G is a group, H a subgroup of G and Or(G) is the orbit category.
Abstract: Let G be a group, let H be a subgroup of G and let Or(G) be the orbit category. In this paper we extend the definition of the relative group homology the- ories of the pair (G, H) defined by Adamso...
8 citations
TL;DR: In this article, the transfer of relative CS-Rickart properties via functors between abelian categories is studied, where fully faithful functors as well as adjoint pairs of functors are considered.
Abstract: We study the transfer of (dual) relative CS-Rickart properties via functors between abelian categories. We consider fully faithful functors as well as adjoint pairs of functors. We give several app...
7 citations
TL;DR: In this article, it was shown that if LmLn is a repd-order Lucas number, then it is possible to construct a Lucas number with L n−1+L n−2 for n ≥ 2.
Abstract: Let (Ln ) be the sequence of Lucas numbers defined by L 0 = 2, L 1 = 1, and Ln = L n−1 + L n−2 for n ≥ 2. Let 0 ≤ m ≤ n and b = 2, 3, 4, 5, 6, 7, 8, 9. In this study, we show that if LmLn is a repd...
7 citations
TL;DR: In this article, the authors studied the Borsuk-Ulam theorem for triple (M, τ, ℝ n ), where M is a compact, connected, 3-manifold equipped with a fixed-point-free involution τ.
Abstract: We study the Borsuk-Ulam theorem for triple (M, τ, ℝ n ), where M is a compact, connected, 3-manifold equipped with a fixed-point-free involution τ. The largest value of n for which the Borsuk-Ulam...
6 citations
TL;DR: In this article, the authors established cyclic inequality, monotonous inequality and product inequality for the (p, q)-mixed affine surface areas, and established some inequalities including cyclic inequalities, notonous inequalities and product inequalities.
Abstract: The notion of (p; q)-mixed volume was rst introduced by Lutwak, Yang and Zhang in 2018. According to this concept, Li, Wang and Zhou de ned the (p; q)- mixed affine surface areas in 2019. In this paper, we establish some inequalities including cyclic inequality, monotonous inequality and product inequality for the (p; q)-mixed affine surface areas.
Key words: (p; q)-mixed volume, (p; q)-mixed affine surface area, cyclic inequality, mo- notonous inequality, product inequality.
TL;DR: In this article, the authors consider a 3D almost co-Kahler manifold where the Reeb vector field ξ is an eigenvector field of the Ricci operator Q, where ρ is a smooth function on M.
Abstract: Let (M3, g) be a three dimensional almost coKahler manifold such that the Reeb vector field ξ is an eigenvector field of the Ricci operator Q, i.e. Qξ = ρξ, where ρ is a smooth function on M. In th...
TL;DR: In this article, the authors define the perfect neighbourhood of a set S ⊆V(G) as the set Np (S) of all vertices in V(G ) having exactly one neighbour in S.
Abstract: Let G be a graph of order n(G) and vertex set V(G). Given a set S ⊆ V(G), we define the perfect neighbourhood of S as the set Np (S) of all vertices in V(G)\S having exactly one neighbour in S. The...
TL;DR: In this paper, it was shown that the category L-Fil of L-filter spaces is monoidal closed and that the L-fil of a complete residuated lattice is a complete lattice.
Abstract: Considering L as a complete residuated lattice, some further investigations on L-filter spaces are made. Firstly, it is shown that the category L-Fil of L-filter spaces is monoidal closed. Secondly...
TL;DR: In this article, the authors explore the space of all differentially recursive sequences over a given field with a non-zero differential and show that these sequences form a two-sided vector space that admits, in a canonical way, a structure of Hopf algebroid over the subfield of constant elements.
Abstract: A differentially recursive sequence over a differential field is a sequence of elements satisfying a homogeneous differential equation with non-constant coefficients (namely, Taylor expansions of elements of the field) in the differential algebra of Hurwitz series. The main aim of this paper is to explore the space of all differentially recursive sequences over a given field with a non-zero differential. We show that these sequences form a two-sided vector space that admits, in a canonical way, a structure of Hopf algebroid over the subfield of constant elements. We prove that it is the direct limit, as a left comodule, of all spaces of formal solutions of linear differential equations and that it satisfies, as Hopf algebroid, an additional universal property. When the differential on the base field is zero, we recover the Hopf algebra structure of linearly recursive sequences.
TL;DR: In this paper, it was shown that if E is an uniquely remotal subset of a real normed linear space such that E has a Chebyshev center c ∈ and the farthest point map F : → E restricted to [c, F (c)] is p...
Abstract: In this paper, we prove that if E is an uniquely remotal subset of a real normed linear space such that E has a Chebyshev center c ∈ and the farthest point map F : → E restricted to [c, F (c)] is p...
TL;DR: In this paper, a novel feedback control of the Leslie-Gower system on time scales is proposed by using the time scale calculus theory, and the permanence of the model is studied.
Abstract: A novel feedback control of Leslie-Gower system on time scales is proposed in this paper. By using the time scale calculus theory, the permanence of the model is studied. Further, the influences of...
TL;DR: In this article, a new proof of the extension of the Stone duality theorem to the category BooleSp of zero-dimensional locally compact Hausdor spaces and Boolean spaces was presented.
Abstract: Using our results from [4], we present a new proof of the extension of the Stone duality theorem to the category BooleSp of zero-dimensional locally compact Hausdorff spaces (= Boolean spaces) and c...
TL;DR: In this paper, the authors considered a fractional-order, incompressible power-law fluid on a horizontal plane, where the time component is defined by Riemann-Liouville derivatives.
Abstract: This paper considers a fractional-order, incompressible power-law fluid on a horizontal plane, where the time component is defined by Riemann-Liouville derivatives. The model is characterized by a ...
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TL;DR: In this paper, a uniformly graded-coherent ring is defined as a ring in which there is a map ϕ : ℕ → τ such that for every n ∈ τ, and any nonzero graded R-modul...
Abstract: Let be a ring graded by an arbitrary grading abelian group Γ. We say that R is a uniformly graded-coherent ring if there is a map ϕ : ℕ → ℕ such that for every n ∈ ℕ, and any nonzero graded R-modul...
TL;DR: In this article, two new characterizations of bounded orthogonally additive polynomials from a uniformly complete vector lattice into a convex bornological space using separately two polynomial identitie...
Abstract: We provide two new characterizations of bounded orthogonally additive polynomials from a uniformly complete vector lattice into a convex bornological space using separately two polynomial identitie...
TL;DR: In this article, the authors studied probabilistic aspects of the subgroup commutativity degree of generalized dicyclic groups, such as the cyclic subgroup subgroup degree.
Abstract: In this paper we study probabilistic aspects, such as the subgroup commutativity degree and the cyclic subgroup commutativity degree, of (generalized) dicyclic groups. We find explicit formulas for...
TL;DR: In this paper, the authors studied multiplicity of multiplicative matrix algebras in commutative rings with unity and showed that multiplicity can be achieved by a generalized matrix algebra defined by the Morita context.
Abstract: Let be a commutative ring with unity, be -algebras, be ()-bimodule and be ()-bimodule. The -algebra is a generalized matrix algebra defined by the Morita context . In this article, we study multipl...
TL;DR: In this article, it was shown that if a compact trans-Sasakian 3-manifold has a η-parallel Ricci operator, then it is proper.
Abstract: In this paper, we present a new characterization for a trans-Sasakian 3-manifold to be proper. More precisely, we prove that if a compact trans-Sasakian 3-manifold has η-parallel Ricci operator, th...
TL;DR: In this article, the authors consider an additive category with an involution ∗ and assume that both ϕ : X → X is a morphism of with pseudo core inverse ϕ and Ϸ : X→ X is an additive morphism such that 1 + ϕη is invertible.
Abstract: Let be an additive category with an involution ∗. Suppose that both ϕ : X → X is a morphism of with pseudo core inverse ϕand η : X → X is a morphism of such that 1 + ϕη is invertible. Let α = (1 + ...
TL;DR: In this article, it was shown that the relation between the number of parts in the odd partitions and the number in the distinct partitions of n satisfies Euler's recurrence relation.
Abstract: In this paper, we show that the difference between the number of parts in the odd partitions of n and the number of parts in the distinct partitions of n satisfies Euler’s recurrence relation for th...
TL;DR: In this paper, two series expansions whose basis functions are two sequences of hypergeometric polynomials are introduced, and a detailed study of the general properties of these expansions is presented.
Abstract: In this paper, we introduce two series expansions whose basis functions are two sequences of hypergeometric polynomials. We then present a systematic and detailed study of the general properties of...
TL;DR: In this article, the titular Diophantine equation for a fixed positive integer y ≥ 3 in nonnegative integers m, n, and a was studied, and it was shown that the nonnegative integer solutions (n, m, a) are ǫnite in number and provided a bound for them.
Abstract: In this paper, we study the titular Diophantine equation for a fixed positive integer y≥3 in nonnegative integers m, n, and a. We show that the nonnegative integer solutions (n; m; a) are nite in number, and we provide a bound for them.
TL;DR: In this paper, the authors provide new Gaussian hypergeometric summation formulae for the product of hypergeometrical series, which are further used to obtain certain new expressions for the products of these summation forms.
Abstract: The aim of this note is to provide some new Gaussian hypergeometric summation formulae. These are further used to obtain certain new expressions for the product of hypergeometric series. Already ob...
TL;DR: In this article, the authors describe the recurrence relation associated to the sums of diagonal elements lying along a finite ray of square binomial triangle, and also give the generating function, which is the same as in this paper.
Abstract: Our purpose is to describe the recurrence relation associated to the sums of diagonal elements lying along a finite ray of square binomial triangle. We also give the generating function. As consequ...