Abstract In this paper, we consider extensions of Spivey’s Bell number formula wherein the argument of the polynomial factor is translated by an arbitrary amount. This idea is applied more generally to the r-Whitney numbers of the second kind, denoted by W (n, k), where some new identities are found by means of algebraic and combinatorial arguments. The former makes use of infinite series manipulations

Abstract Let α be a Salem number with conjugates , where α 1 := α. We prove some properties of the products of the form α 1 α 2 · · · αn, called, by A. Dubickas and C.J. Smyth, Salem half-norms. This allows us to complete, partially, two related results due to C. Christopoulos and J. McKee about the Galois group of the splitting field of the minimal polynomial of α, and to A. Dubickas on a question

Abstract We define the star partial order for matrices in spaces with an indefinite inner product. We also give a characterization of that order in terms of matrices and their Moore-Penrose inverses. Finally, some interesting properties are shown.

Abstract If X is Hausdorff topological space and Cc (X) is the topological algebra obtained by endowing the algebra C(X) of all continuous functions on X with the topology τc of uniform convergence on the compact subsets of X, then the set Δ(ϕ) := {g ∈ C(X) : |g(x)| ≤ ϕ(x), x ∈ X} is bounded in Cc (X), for every non-negative ϕ ∈ C(X). In this note we deal with the question whether the collection C

Abstract In this paper we study dimensions of the type dim for the class of ideal topological spaces. We shall start from the classical definition of the dimension functions dim and dim*, continue with the dimension -dim and finally, give two different kinds of functions of covering dimensional type.

Abstract Let N be a p-solvable normal subgroup of a finite group G, and Np′ be a p′ -Hall subgroup of N . If x is an element of G, then the conjugacy class size |xG| = |G : CG(x)|. Obviously, when CG(x) is a maximal subgroup of G, |xG| is minimal. In this paper, we investigate the structure of Np′ by assuming that |xG | is 1 or minimal for every p-regular element x of N

Abstract We investigate under what conditions n-Jordan homomorphisms between rings are n-homomorphism, or homomorphism; and under what conditions, n-Jordan homomorphisms are continuous. One of the main goals in this work is to show that every n-Jordan homomorphism f : A → B, from a unital ring A into a ring B with characteristic greater than n, is a multiple of a Jordan homomorphism and hence, it is

Abstract By using the cycle-circuit representation theory of Markov processes we investigate the continuous parameter analogue of the existence and construction of a class of irreducible, denumerable Markov chains generated by a collection of overlapping directed weighted circuits regarding a generalized sample path case.

Abstract In this study we introduce a second type of higher order generalized geometric polynomials. This we achieve by examining the generalized stirling numbers S(n, k, α, β, γ) [Hsu and Shiue, 1998] for some negative arguments. We study their number theoretic properties, asymptotic properties, and their combinatorial properties using the notion of barred preferential arrangements. We also proposed

Abstract This work studies the blow up result of the solution of a coupled nonlocal singular viscoelastic equation with general source terms under some suitable conditions. This work is a natural continuation to the previous recent article in ([4]).

Abstract We provide properties of almost η-Ricci and almost η-Yamabe solitons on submanifolds isometrically immersed into a Riemannian manifold whose potential vector field is the tangential component of a torse-forming vector field on , treating also the case of a minimal or pseudo quasi-umbilical hypersurface. Moreover, we give necessary and sufficient conditions for an orientable hypersurface of the

Abstract In this note, we propose an elementary method to study the existence and uniqueness of solutions to a type of variational problems which arise naturally in the theory of large deviations. This type of problems involves a movable boundary and may not have the coercivity condition in general. Our method is elementarily based on direct analysis over the space of absolutely continuous functions

Abstract It is known that the connectednesses of topological spaces in the sense of Preuß is the topological analogue of the Kurosh-Amistsur radicals of algebraic structures in a categorical sense. Here this connection is further explored. As in universal algebra, a congruence on a topological space has been defined. It is shown that a connectedness can be characterized in terms of conditions on congruences

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.

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

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

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

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.

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.

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

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

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

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

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

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].

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

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

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

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

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

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

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

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.

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

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

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

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.

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

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

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

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.

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

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

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

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.

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.

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.

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

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.

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

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

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

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.

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

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.

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.

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.

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].

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

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.