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  • On the product of primal spaces
    Quaest. Math. (IF 1.049) Pub Date : 2020-10-19
    Othman Echi

    Abstract Let X be a set and f : X → X be a map. We denote by 𝒫(f) the topology defined on X whose closed sets are the subsets A of X with f (A) ⊆ A. A topology on X is said to be a primal topology, if it is a 𝒫(f) for some map f. Our aim here is to characterize when the product of an arbitrary family of topological spaces is a primal space.

    更新日期:2020-10-19
  • Double outer-independent domination number of graphs
    Quaest. Math. (IF 1.049) Pub Date : 2020-10-19
    Abel Cabrera Martínez

    Abstract Let G be a graph with no isolated vertex. A set D ⊆ V(G) is a double outer-independent dominating set of G if V (G) \ D is an independent set and | N[υ] ∩ D| ≥ 2 for every v ϵ V(G), where N[υ] denotes the closed neighbourhood of v. The minimum cardinality among all double outer-independent dominating sets of G is the double outer-independent domination number of G. In this paper, we continue

    更新日期:2020-10-19
  • Weighted inner inverse for rectangular matrices
    Quaest. Math. (IF 1.049) Pub Date : 2020-10-19
    Ratikanta Behera; Dijana Mosić; Jajati Kesahri Sahoo; Predrag S. Stanimirović

    Abstract. To extend the notation of inner inverses, we define weighted inner inverses of a rectangular matrix. In particular, we introduce a W -weighted (B, C)-inner inverse of A, for given matrices A, W, B, C, and present some characterizations and conditions for its existence. Since this new inverse is not unique, we describe the set of all W -weighted (B, C)-inner inverses of a given matrix. Several

    更新日期:2020-10-19
  • Durrmeyer variant of apostol-genocchi-baskakov operators
    Quaest. Math. (IF 1.049) Pub Date : 2020-10-19
    Naokant Deo; Sandeep Kumar

    Abstract We study the approximation behavior of the Durrmeyer form of Apostol- Genocchi polynomials with Baskakov type operators including K-functional and second-order modulus of smoothness, Lipschitz space and find the rate of conver­gence for continuous functions whose derivative satisfies the condition of bounded variation. In the last section, we estimate weighted approximation behavior for these

    更新日期:2020-10-19
  • Matrix characterization of asymptotically deferred equivalent sequences
    Quaest. Math. (IF 1.049) Pub Date : 2020-10-19
    Rabia Savaş

    Abstract In 1932 Agnew [1] introduced the concept of deferred Ceśaro means. Taking inspiration from this new approach, in this paper we introduce deferred asymptotically equivalent sequences using statistical convergence and prove some important results. This will be accomplished through a series of regularity type theorems.

    更新日期:2020-10-19
  • A Zariski topology on integrally closed maximal subrings of a commutative ring
    Quaest. Math. (IF 1.049) Pub Date : 2020-09-22
    Alborz Azarang

    Abstract Let R be a commutative ring and Xi.c (R) denotes the set of all integrally closed maximal subrings of R. It is shown that if R is a non-field G-domain, then there exists S ∈ Xi.c (R) with (S : R) = 0. If K is an algebraically closed field which is not absolutely algebraic, then we prove that the polynomial ring K[X] has an integrally closed maximal subring with zero conductor too; a characterization

    更新日期:2020-10-19
  • The powers of two as sums over partitions
    Quaest. Math. (IF 1.049) Pub Date : 2020-10-16
    Mircea Merca

    Abstract In this paper, we investigate two methods to express the natural powers of 2 as sums over integer partitions. First we consider a formula by N. J. Fine that allows us to express a binomial coefficient in terms of multinomial coefficients as a sum over partitions. The second method invokes the central binomial coefficients and the logarithmic differentiation of their generating function. Some experimental

    更新日期:2020-10-17
  • Multivalued generalized graphic θ-contraction on directed graphs and application to mixed volterra-fredholm integral inclusion equations
    Quaest. Math. (IF 1.049) Pub Date : 2020-10-16
    Lakshmi Kanta Dey; Hiranmoy Garai; Hemant Kumar Nashine; Can Huu Nguyen

    Abstract The purpose of the present work is to introduce a generalized graphic θ-contraction conditions on a family of mappings defined on subsets of a metric space endowed with a set-transitive directed graph, and discuss common fixed point results without considering any kind of commutativity and continuity of the family of mappings. Useful examples illustrate the applicability and effectiveness of

    更新日期:2020-10-17
  • Quadratic model updating for damped gyroscopic systems
    Quaest. Math. (IF 1.049) Pub Date : 2020-10-14
    Yongxin Yuan

    Abstract This paper is concerned with the problem of the optimal approximation for a given matrix pencil (Ma, Da, Ga, Ka, Na ) under the spectral constraint and the symmetric constraint. Such a problem arises in finite element model updating for damped gyroscopic systems. By using constrained optimization theory and matrix derivatives, an explicit formulation for the solution of the problem is established

    更新日期:2020-10-15
  • Notes on star covering properties
    Quaest. Math. (IF 1.049) Pub Date : 2020-10-14
    Yan-Kui Song; Wei-Feng Xuan

    Abstract In this paper, we show the following statements: (1) There exists a pseudocompact star Lindelöf Tychonoff space which is not star σ-compact. (2) There exists a Tychonoff pseudocompact star countable (hence, star Lindelöf) space having a pseudocompact, Gδ regular closed subspace which is not star Lindelöf. (3) Assuming , there exists a normal star countable (hence, star Lindelöf) space having

    更新日期:2020-10-15
  • Frame congruences via subkernels
    Quaest. Math. (IF 1.049) Pub Date : 2020-10-14
    Halimeh Moghbeli

    Abstract To study the quotient of algebras, like frames, whose algebraic structures are determined by a partial order, it is often more common to think about sub-kernels of homomorphisms between such algebras. So, in this paper, we first introduce the concept of a pre-congruence on a frame and then characterize them as the sub-kernels of the frame homomorphisms. Second, we characterize the frame congruences

    更新日期:2020-10-15
  • Joint discrete universality for periodic zeta-functions. III
    Quaest. Math. (IF 1.049) Pub Date : 2020-10-14
    Antanas Laurinčikas

    Abstract In the paper, a joint theorem on the approximation of collections of analytic functions by generalized discrete shifts of zeta-functions with periodic coefficients is obtained. The latter result extend theorems of [9].

    更新日期:2020-10-15
  • A two-variable dirichlet series and its applications
    Quaest. Math. (IF 1.049) Pub Date : 2020-10-14
    Mehmet Cenkci; Abdurrahman Ünal

    Abstract We define a two-variable Dirichlet series associated with two arithmetic functions, which is related to the Riemann zeta function, the Dirichlet L-function, the Dirichlet series associated to the harmonic numbers, and truncated multiple zeta functions. Using the periodic Euler-Maclaurin summation formula, we obtain a representation in terms of an ordinary Dirichlet series, which leads to the

    更新日期:2020-10-15
  • On Rall's 1/2-conjecture on the domination game
    Quaest. Math. (IF 1.049) Pub Date : 2020-10-14
    Csilla Bujtás; Vesna Iršič; Sandi Klavžar; Kexiang Xu

    Abstract The 1/2-conjecture on the domination game asserts that if G is a traceable graph, then the game domination number γg (G) of G is at most A traceable graph is a 1/2-graph if holds. It is proved that the so-called hatted cycles are 1/2-graphs and that unicyclic graphs fulfill the 1/2-conjecture. Several additional families of graphs that support the conjecture are determined and computer experiments

    更新日期:2020-10-15
  • k−Fibonacci numbers close to a power of 2
    Quaest. Math. (IF 1.049) Pub Date : 2020-10-14
    Jhon J. Bravo; Carlos A. Gómez; Jose L. Herrera

    Abstract A generalization of the well-known Fibonacci sequence is the k-generalized Fibonacci sequence whose first k terms are 0, . . . , 0, 1 and each term afterwards is the sum of the preceding k terms. In this paper, by using a lower bound to linear forms in logarithms of algebraic numbers due to Matveev and some argument of the theory of continued fractions, we find all the members of F (k) which

    更新日期:2020-10-15
  • On a power-type coupled system of k-hessian equations
    Quaest. Math. (IF 1.049) Pub Date : 2020-10-08
    Chenghua Gao; Xingyue He; Maojun Ran

    Abstract We deal with a coupled system of k-Hessian equations: where k = 1, 2, · · · , N , B is a unit ball in ℝ N , N ≥ 2, α and β are positive constants. By using the fixed-point index theory in cone, we obtain the existence, uniqueness and nonexistence of radial convex solutions for some suitable constants α and β. Furthermore, by using a generalized Krein-Rutman theorem, we also obtain a necessary

    更新日期:2020-10-08
  • Partially ordered objects in a topos
    Quaest. Math. (IF 1.049) Pub Date : 2020-09-29
    A. Homayoun Nejah; Mojgan Mahmoudi; M. Mehdi Ebrahimi

    Abstract In this paper we study the category of partially ordered objects in a topos E . The definition of a partially ordered object or internal poset is taken from [10], ϵ. Mac Lane and I. Moerdijk, Sheaves in geometry and logic, 1992. We will define the concept of monotone morphism between internal posets and then study the resulting category. We will show that the category of partially ordered

    更新日期:2020-09-29
  • Symmetry analysis for a fourth-order noise-reduction partial differential equation
    Quaest. Math. (IF 1.049) Pub Date : 2020-09-29
    P.G.L. Leach; Andronikos Paliathanasis

    Abstract We apply the theory of Lie symmetries in order to study a fourth-order 1+2 evolutionary partial differential equation which has been proposed for the image processing noise reduction. In particular we determine the Lie point symmetries for the specific 1+2 partial differential equations and we apply the invariant functions to determine similarity solutions. For the static solutions we observe

    更新日期:2020-09-29
  • Biderivations and linear commuting maps on the restricted contact lie algebras K(n; )
    Quaest. Math. (IF 1.049) Pub Date : 2020-09-23
    Yuan Chang; Liangyun Chen; Xin Zhou

    Let K be the restricted contact Lie algebras K(n, ) over an algebraically closed field F of characteristic p > 3. We prove that each skew-symmetric biderivation of K is inner and show that commuting maps on K are scalar multiplication maps. Moreover, it is showed that the commuting automorphisms and dertivations of K are proved to be the identity mappings and zero mappings, respectively. Meanwhile

    更新日期:2020-09-23
  • Spacetimes admitting the Z-symmetric tensor
    Quaest. Math. (IF 1.049) Pub Date : 2020-09-22
    Füsun Özen Zengin; Ayşe Yavuz Taşci

    This paper aims to introduce the spacetimes admitting the Z-symmetric tensor. We investigate the properties of these spacetimes for a perfect fluid and a pressureless perfect fluid (a dust). Some theorems about the properties are proved.

    更新日期:2020-09-22
  • A representation of continuous lattices based on closure spaces
    Quaest. Math. (IF 1.049) Pub Date : 2020-09-22
    Qingguo Li; Longchun Wang; Lingjuan Yao

    In this paper, we establish the link between continuous lattices and closure spaces. By generalizing the notion of algebraic closure space to continuous closure space, we show that continuous lattices can be represented by continuous closure spaces, just as algebraic lattices can be represented by algebraic closure spaces. We also introduce the notion of approximable mappings between continuous closure

    更新日期:2020-09-22
  • On poly-Bell numbers and polynomials
    Quaest. Math. (IF 1.049) Pub Date : 2020-09-22
    Ghania Guettai; Diffalah Laissaoui; Mourad Rahmani; Madjid Sebaoui

    This paper aims to construct a new family of numbers and polynomials which are related to the Bell numbers and polynomials by means of the confluent hypergeometric function. We give various properties of these numbers and polynomials (generating functions, explicit formulas, integral representations, recurrence relations, probabilistic representation, …). We also derive some combinatorial sums including

    更新日期:2020-09-22
  • Paths in primal spaces and the Collatz conjecture
    Quaest. Math. (IF 1.049) Pub Date : 2020-09-22
    Angel Guale; Fernando Mejias; Jorge Vielma

    The Collatz conjecture establishes that for every natural number n ∈ ℕ, there exists an r ∈ ℕ such that κr (n) = 1, where κ : ℕ → ℕ is the function defined as n/2 if n es even and as 3n + 1 if n is odd. The map κ induces a topology τκ on ℕ. We prove that the Collatz conjecture and connectedness of the space (ℕ, τκ ) imply that the space is simply connected. Furthermore, we prove that the Collatz conjecture

    更新日期:2020-09-22
  • A new transcendental number from the digits of NN
    Quaest. Math. (IF 1.049) Pub Date : 2020-09-22
    Hùng Việt Chu

    We first give a summary of the history of transcendental numbers, and then we use a nice technique by G. Dresden to find a new transcendental number. In particular, while previous work looked at the last non-zero digit of nn , we consider the digit immediately before its last non-zero digit and show that the infinite decimal built from these digits is transcendental.

    更新日期:2020-09-22
  • The riesz tensor product of d-algebras
    Quaest. Math. (IF 1.049) Pub Date : 2020-09-22
    Mohamed Amine Ben Amor

    In this work we prove that the Riesz tensor product of two archimedean d-algebras is again a d-algebra.

    更新日期:2020-09-22
  • Permanence for Leslie-Gower predator-prey system with feedback controls on time scales
    Quaest. Math. (IF 1.049) Pub Date : 2020-08-25
    Zhouhong Li; Tianwei Zhang

    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 the feedback controls on the upper and lower bounds of prey and predator populations are also discussed. The work of this paper improves some research findings in recent years. Some illustrative examples

    更新日期:2020-08-25
  • Almost quasi-Yamabe solitons and gradient almost quasi-yamabe solitons in paracontact geometry
    Quaest. Math. (IF 1.049) Pub Date : 2020-08-25
    Krishnendu De; Uday Chand De

    The purpose of the present paper is to investigate the almost quasi- Yamabe soliton and gradient almost quasi-Yamabe solitons under the framework of three-dimensional normal almost paracontact metric manifolds.

    更新日期:2020-08-25
  • Reducibility sets for sequences of matrices
    Quaest. Math. (IF 1.049) Pub Date : 2020-08-25
    Luis Barreira; Claudia Valls

    Our main aim is to give a complete characterization of the reducibility sets of continuous 1-parameter families of sequences of matrices, which turn out to be the Fσ -sets. We also show that for any Fσ -set containing zero, one can find a family with this reducibility set. In addition, we obtain corresponding results for the reducibility-stability set and we give an optimal condition for the reducibility

    更新日期:2020-08-25
  • On the continuity of the adjoint of evolution operators
    Quaest. Math. (IF 1.049) Pub Date : 2020-08-25
    Diómedes Bárcenas; Bladismir Leal; Hugo Leiva; Ambrosio Tineo Moya

    By associating a quasi semigroup to a commutative evolution operator and using techniques from vector measures like the Gel’fand integral and the Radon- Nikodym theorem for Bochner integral, we prove the continuity on [0, +∞) of the adjoint of a certain class of evolution operators. Furthermore, we provide examples of evolution operators satisfying our conclusion. We also provide an application to

    更新日期:2020-08-25
  • Uniformly graded-coherent rings
    Quaest. Math. (IF 1.049) Pub Date : 2020-08-25
    Chahrazade Bakkari; Najib Mahdou; Abdelkbir Riffi

    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-module homomorphism of degree 0, where λ 1 , … ,λn are degrees in Γ, ker f can be generated by ϕ(n) homogeneous elements. In this paper, we provide the elementary properties of uniformly graded-coherent rings

    更新日期:2020-08-25
  • Approximate properties of the p-Bieberbach polynomials in regions with simultaneously exterior and interior zero angles
    Quaest. Math. (IF 1.049) Pub Date : 2020-08-25
    F.G. Abdullayev; M. Imashkyzy; P. Özkartepe

    In this paper, we study the uniform convergence of p-Bieberbach polynomials in regions with a finite number of both interior and exterior zero angles at the boundary.

    更新日期:2020-08-25
  • Inequalities about normalized Lp projection body
    Quaest. Math. (IF 1.049) Pub Date : 2020-08-25
    Zhongwen Tang; Lin Si

    In this paper, we establish a Loomis-Whitney type inequality about volume normalized Lp projection body for p ≥ 1 with complete equality conditions for p ̸= 2. Meanwhile, an estimate for the weighted Lp zonoid is given.

    更新日期:2020-08-25
  • On the lower Lie nilpotency index of a group algebra
    Quaest. Math. (IF 1.049) Pub Date : 2020-08-25
    Meena Sahai; Bhagwat Sharan

    In this article, we show that if KG is a Lie nilpotent group algebra of a group G over a field K of characteristic p > 0, then tL (KG) = k if and only if tL (KG) = k, for k ∈ {5p − 3, 6p − 4}, where tL (KG) and tL (KG) are the lower and the upper Lie nilpotency indices of KG, respectively.

    更新日期:2020-08-25
  • Corrigendum
    Quaest. Math. (IF 1.049) Pub Date : 2020-08-25

    (2020). Corrigendum. Quaestiones Mathematicae. Ahead of Print.

    更新日期:2020-08-25
  • On global values of virtual waiting time of a customer in open queueing networks
    Quaest. Math. (IF 1.049) Pub Date : 2020-08-25
    Saulius Minkevičius; Leonidas L. Sakalauskas

    The object of this research on queueing theory is to analyze the behaviour of open queueing network, working under overload heavy traffic conditions. We have proved probability limit theorem for the global values of virtual waiting time of a customer in open queueing networks. Finally, we present application of the recurrent method in the further analysis of open queuing networks.

    更新日期:2020-08-25
  • Moving front solutions of a time-fractional power-law fluid under gravity
    Quaest. Math. (IF 1.049) Pub Date : 2020-08-25
    Sameerah Jamal; Nkosingiphile Mnguni

    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 nonlinear second-order partial differential equation comprising of a power-law parameter β. We transform the model into nonlinear fractional ordinary differential equations and subsequently, solutions of

    更新日期:2020-08-25
  • Pseudo core inverses of a sum of morphisms
    Quaest. Math. (IF 1.049) Pub Date : 2020-08-25
    Jianlong Chen; Wende Li; Mengmeng Zhou

    Let be an additive category with an involution ∗. Suppose that both ϕ : X → X is a morphism of with pseudo core inverse ϕ and η : X → X is a morphism of such that 1 + ϕ η is invertible. Let α = (1 + ϕ η) − 1 , β = (1+ηϕ ) − 1 , ε = (1−ϕϕ )ηα(1−ϕ ϕ), γ = α(1−ϕ ϕ)ηϕ β, σ = αϕ ϕα− 1(1− ϕϕ )β, δ = β∗ (ϕ ) ∗η∗ (1−ϕϕ )β. Then we present a sufficient condition such that f = ϕ + η − ε has pseudo core inverse

    更新日期:2020-08-25
  • Two types of Galois correspondences over quantaloid-typed sets
    Quaest. Math. (IF 1.049) Pub Date : 2020-07-15
    Jinming Fang; Zhou Fang

    For a small, integral and meet-continuous quantaloid , we establish two types of Galois correspondences by considering a limit structure on a set as a -multiple limit structure on a -typed set. One Galois correspondence shows that the stratified -topologies and the -multiple limit structures based on -typed sets can be converted to each other categorically. Moreover, the other one shows that a new

    更新日期:2020-07-15
  • General multiplicative Zagreb indices of trees with given independence number
    Quaest. Math. (IF 1.049) Pub Date : 2020-07-15
    Selvaraj Balachandran; Tomáš Vetrík

    We obtain lower and upper bounds on general multiplicative Zagreb indices for trees with given independence number and order. Bounds on basic multiplicative Zagreb indices follow from our results. We also show that the bounds are best possible.

    更新日期:2020-07-15
  • Lower topological algebraic domain models of topological spaces
    Quaest. Math. (IF 1.049) Pub Date : 2020-07-13
    Hui Li; Qingguo Li

    The maximal point space of a domain (resp. algebraic domain) with the Scott topology is Choquet complete. Thus, not every T 1 topological space can be represented as the maximal point space of some algebraic domain equipped with the Scott topology. However, in this paper, we prove that: (1) Every T 1 topological space is homeomorphic to the set of all maximal points of some algebraic domain equipped

    更新日期:2020-07-13
  • Multiply warped products with compact Einstein manifolds
    Quaest. Math. (IF 1.049) Pub Date : 2020-07-13
    Fatma Karaca

    We study multiply warped products with compact Einstein manifolds. We obtain that there does not exist connected, compact Einstein multiply warped products if the scalar curvature is non-positive. It is also found that there does not exist non-trivial connected Einstein multiply warped product manifolds with compact base or compact fibres.

    更新日期:2020-07-13
  • A new factor theorem on generalized absolute Cesàro summability
    Quaest. Math. (IF 1.049) Pub Date : 2020-07-13
    Hüseyin Bor

    In this paper, we have proved a general theorem dealing with the ϕ −| C, α, β |k summability factors of infinite series. Also, some new and known results are deduced.

    更新日期:2020-07-13
  • On some new Gaussian hypergeometric summation formulae with applications
    Quaest. Math. (IF 1.049) Pub Date : 2020-07-13
    Insuk Kim; T.K. Pogány; Arjun K. Rathie

    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 obtained results by Bailey, Choi and Rathie and Qureshi et al. follow special cases of our main findings.

    更新日期:2020-07-13
  • On equivalence of absolute double weighted mean methods
    Quaest. Math. (IF 1.049) Pub Date : 2020-07-13
    Mehmet Ali Sarigöl

    Bor [1], Bor and Thorpe [2] and the author [8] established the set of necessary and sufficient condition for the equivalence of absolute weighted mean summability methods of infinite series. In the present paper we extend their result to doubly infinite series by two dimensional weighted mean, which also includes the result of Rhoades [7].

    更新日期:2020-07-13
  • Einstein type tensors in the generalized Riemannian space
    Quaest. Math. (IF 1.049) Pub Date : 2020-07-13
    Vladislava M. Stanković

    In [22], V.M. Stankovíc introduced generalized Einstein type tensors of the kind θ (θ = 1, 2) in the generalized Riemannian space, and some relations which they satisfy are obtained using the first and the second kind of covariant derivative. In the present paper, generalized Einstein type tensors of the kind θ (θ = 3, 4) are introduced. Also, some relations which Einstein type tensors of the kind

    更新日期:2020-07-13
  • Positioned numerical semigroups
    Quaest. Math. (IF 1.049) Pub Date : 2020-07-13
    M.B. Branco; M.C. Faria; J.C. Rosales

    A numerical semigroup S is positioned if for all s ∈ ℕ\S we have that F(S) + m(S) − s ∈ S. In this paper, we give algorithms to compute the set of positioned semigroups and a criterium to check whether S is or not is positioned. Furthermore, we prove the Wilf’s conjecture for this type of numerical semigroups.

    更新日期:2020-07-13
  • Similarity solutions and conservation laws for the Bogoyavlensky-Konopelchenko equation by Lie point symmetries
    Quaest. Math. (IF 1.049) Pub Date : 2020-07-13
    Amlan K. Halder; P.G.L. Leach; Andronikos Paliathanasis

    The 1 + 2 dimensional Bogoyavlensky-Konopelchenko equation is investigated for its solution and conservation laws using the Lie point symmetry analysis. In the recent past, certain work has been done describing the Lie point symmetries for the equation and this work seems to be incomplete (S.S. Ray, Computers & Mathematics with Applications 74(6) (2017), 1158–1165). We obtained certain new symmetries

    更新日期:2020-07-13
  • Perturbations of determinants of nuclear operators in a Hilbert space
    Quaest. Math. (IF 1.049) Pub Date : 2020-07-13
    Michael Gil’

    Let be a complex separable Hilbert space with the unit operator I and {dk } be an orthonormal basis in . Let A, Ã be linear operators in , satisfying the conditions . It is proved that the determinants satisfy the inequalities . These inequalities refine the well-known ones and enable us to establish upper and lower bounds for the determinants of infinite matrices which are “close” to triangular matrices

    更新日期:2020-07-13
  • Global existence and blow-up for a space and time nonlocal reaction-diffusion equation
    Quaest. Math. (IF 1.049) Pub Date : 2020-07-13
    Ahmed Alsaedi; Mokhtar Kirane; Berikbol T. Torebek

    A time-space fractional reaction-diffusion equation in a bounded domain is considered. Under some conditions on the initial data, we show that solutions may experience blow-up in a finite time. However, for realistic initial conditions, solutions are global in time. Moreover, the asymptotic behavior of bounded solutions is analysed.

    更新日期:2020-07-13
  • Generating integer polynomials from X 2 and X 3 using function composition: a study of subnearrings of (ℤ[X], +, ◦)
    Quaest. Math. (IF 1.049) Pub Date : 2020-07-13
    Erhard Aichinger; Sebastian Kreinecker

    Which integer polynomials can we write down if the only exponent to be used is 3? Such problems can be considered as instances of the subnearring generation problem. We show that the nearring (ℤ[x], +, ◦) of integer polynomials, where the nearring multiplication is the composition of polynomials, has uncountably many subnearrings, and we give an explicit description of those nearrings that are generated

    更新日期:2020-07-13
  • A note on Tingley’s problem and Wigner’s theorem in the unit sphere of ∞(Γ)-type spaces
    Quaest. Math. (IF 1.049) Pub Date : 2020-07-07
    Dongni Tan; Xiaolei Xiong

    Suppose that f : SX → SY is a surjective map between the unit spheres of two real ∞ (Γ)-type spaces X and Y satisfying the following equation We show that such a mapping f is phase equivalent to an isometry, i.e., there exists a function ε : SX → {−1, 1} such that εf is an isometry. We further show that this isometry is the restriction of a linear isometry between the whole spaces. These results can

    更新日期:2020-07-07
  • Infinitely many solutions for a class of sublinear fractional schrödinger-poisson systems
    Quaest. Math. (IF 1.049) Pub Date : 2020-07-07
    Wen Guan; Lu-Ping Ma; Da-Bin Wang; Jin-Long Zhang

    In this paper, we consider the following nonlinear fractional Schrödinger-Poisson system where s, t ∈ (0, 1) and 4s + 2t ≥ 3, 0 < q < 1, and a, K, V ∈ L∞ (ℝ3). When a, V both change sign in ℝ3, by applying the symmetric mountain pass theorem, we prove that the problem has infinitely many solutions under appropriate assumptions on a, K, V .

    更新日期:2020-07-07
  • Computations and global properties for traces of Bessel’s Dirichlet form
    Quaest. Math. (IF 1.049) Pub Date : 2020-07-07
    Ali BenAmor; Rafed Moussa

    By an approximation method we compute explicitly traces of the Dirichlet form related to the Bessel process with respect to discrete measures as well as measures of mixed type. Then some global properties of the obtained Dirichlet forms, such as conservativeness, irreducibility and compact embedding for their domains are discussed.

    更新日期:2020-07-07
  • Repdigits base b as products of two Lucas numbers
    Quaest. Math. (IF 1.049) Pub Date : 2020-07-07
    Fatih Erduvan; Refik Keskin; Zafer Şiar

    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 repdigit in the base b and has at least two digits, then LmLn ∈ {3, 4, 6, 7, 8, 9, 12, 14, 16, 18, 21, 28, 36, 54, 121, 228}. Furthermore, it is shown that if Ln is a repdigit in the base b and has at least two

    更新日期:2020-07-07
  • On property of the amalgamated duplication of a ring along an ideal
    Quaest. Math. (IF 1.049) Pub Date : 2020-07-07
    Youssef Arssi; Samir Bouchiba

    The main purpose of this paper is to totally characterize when the amalgamated duplication R ⋈ I of a ring R along an ideal I is an -ring as well as an -ring. In this regard, we prove that R ⋈ I is an -ring if and only if R is an -ring and I is contained in the set of zero divisors Z(R) of R. As to the Property () of R ⋈ I, it turns out that its characterization involves a new concept that we introduce

    更新日期:2020-07-07
  • Global behavior and oscillation of a third order difference equation
    Quaest. Math. (IF 1.049) Pub Date : 2020-07-07
    R. Abo-Zeid

    In this paper, we solve and study the global behavior of the admissible solutions of the difference equation where a, b > 0 and the initial values x −2, x −1, x 0 are real numbers. We study also the oscillation of the admissible solutions of the aforementioned difference equation and give some illustrative examples.

    更新日期:2020-07-07
  • Weak compactness of almost L-weakly and almost M-weakly compact operators
    Quaest. Math. (IF 1.049) Pub Date : 2020-07-07
    Farid Afkir; Khalid Bouras; Aziz Elbour; Safae El Filali

    In this paper, we investigate conditions on a pair of Banach lattices E and F that tells us when every positive almost L-weakly compact (resp. almost M- weakly compact) operator T : E → F is weakly compact. Also, we present some necessary conditions that tells us when every weakly compact operator T : E → F is almost M-weakly compact (resp. almost L-weakly compact). In particular, we will prove that

    更新日期:2020-07-07
  • Weak exceptional sequences
    Quaest. Math. (IF 1.049) Pub Date : 2020-07-07
    Emre Sen

    We introduce weak exceptional sequence of modules which can be viewed as another modification of the standard case, different from the works of Igusa-Todorov [IT17] and Buan-Marsh [BM18]. For hereditary algebras it is equivalent to standard exceptional sequences. One important new feature is: if the global dimension of an algebra is greater than one, then the size of a full sequence can exceed the

    更新日期:2020-07-07
  • Shephard type problem for Lp-mixed blaschke-minkowski homomorphisms
    Quaest. Math. (IF 1.049) Pub Date : 2020-07-07
    Bin Chen; Weidong Wang; Peibiao Zhao

    In 2006, Schuster introduced the concept of Blaschke-Minkowski homo-morphism of convex bodies. In this paper, we introduce the Lp -mixed Blaschke-Minkowski homomorphism in Lp -Brunn-Minkowski theory. We then further study the Shephard type problem involving an affirmative answer and two negative answers for Lp -mixed Blaschke-Minkowski homomorphism.

    更新日期:2020-07-07
  • On best proximity points of interpolative proximal contractions
    Quaest. Math. (IF 1.049) Pub Date : 2020-07-07
    Ishak Altun; Ayşenur Taşdemir

    In this paper, we introduce some kinds of interpolative proximal contractions named as Reich-Rus-Ćirić and Kannan types. Then taking into account the aforementioned mappings, we give a few best proximity point results. As special cases we obtain some fixed point results for interpolative contractions. To support the theory, some examples are provided.

    更新日期:2020-07-07
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