Abstract Let ℂQ denote a rational quantum torus with d variables, and be the centre of ℂQ. In this paper we give a explicit description of the structure of the cuspidal modules for the derivation Lie algebra over ℂQ, with an extra associative -action.

Abstract In this paper, we introduce the T-function, T(s), which is a polynomial defined by means of a univariate resultant constructed from a given parametrization of an algebraic space curve . It is shown that , where are polynomials (the fibre functions) whose roots are the fibre of the ordinary singularities of multiplicity . Therefore, a complete classification of the singularities of , via the

Abstract In this paper we define the class GMSF(α, β, γ) of General Monotone Sequence of Functions with majorants . For a sequence of admissible functions belonging to this class we find necessary and sufficient conditions under which the sine integral-series converges in the regular sense uniformly in .

Abstract In this paper, we obtain a generalized Wintgen-type inequality for submanifolds in generalized (κ,µ)-space forms. Further, we discuss the inequality for bi-slant submanifolds, semi-slant submanifolds, hemi-slant submanifolds, CR-submanifolds and slant submanifolds in various ambient spaces. In particular, we generalize some recent results of Mihai, Tohoku Math. J. 69 (2017), and Aquib et al

Abstract Assume that A, B are uniform algebras on compact Hausdorff spaces X and Y, respectively, and ∂A, ∂B are the Šilov boundaries of A, B. Let T : A−1 → B−1 be a map with T1 = 1. We show that, if there exist constants α, β ≥ 1 such that β−1‖f·g−1‖ ≤ ‖Tf·(Tg)−1∥ ≤ α∥f·g−1∥ for all f, g ∈ A−1, then there is a non-empty closed subset Y0 of ∂B and a surjective continuous map τ : Y0 → ∂A such that for

Abstract For a metrizable topological space X it is well known that in general the Čech-Stone compactification β(X) or the Wallman compactification W(X) are not metrizable. To remedy this fact one can alternatively associate a point-set distance to the metric, a so called approach distance. It is known that in this setting both a Čech-Stone compactification β*(X) and a Wallman compactification W*(X)

Abstract We characterize the three-dimensional Riemannian manifolds endowed with a semi-symmetric metric ρ-connection if its Riemannian metrics are Ricci and gradient Ricci solitons, respectively. It is proved that if a three-dimensional Riemannian manifold equipped with a semi-symmetric metric ρ-connection admits a Ricci soliton, then the manifold possesses the constant sectional curvature −1 and

Abstract In this paper, we consider a half inverse problem for a diffusion operator on a time scale which is the union of an interval and another arbitrary time scale such as . We give a Hochstadt-Lieberman type theorem for this problem and some appropriate examples.

Abstract In the paper, we introduce the concept of a preorder on a category and study its relation to categorical closure operators. In particular, employing a Galois connection, we show that there is a one-to-one correspondence between the idempotent closure operators and certain preorders on a category.

Abstract In the present paper, we introduce left-invariant (almost) Kenmotsu structures on Hom-Lie groups (or, almost Kenmotsu Hom-Lie algebras). Also, we present examples of such structures. It is proved that if the Ricci tensor of Kenmotsu Hom-Lie algebras is η-parallel, then the scalar curvature is constant. We describe η-Einstein Kenmotsu Hom-Lie algebras. Then we show that an involutive Kenmotsu

Abstract In this paper we are going to prove that the Hardy-Litllewood maximal operators on variable Lebesgue spaces L p(·)(µ) with respect to a probability Borel measure µ, are weak type and strong type for two conditions of regularity on the exponent function p(·); following [2] and [3]. Also following [2] we extend some important properties of this operator to a probability Borel measure µ, the

Abstract Following the theory of symmetrically connected T 0-quasi-metric spaces constructed lately, in the present investigation the authors introduce and study the localized version of symmetric connectedness under the name local symmetric connectedness, as a new approach to determining the degree of the asymmetry and symmetry of T 0-quasi-metric spaces. In this context, some properties and topological

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

Abstract In this paper, we aim to understand the characteristics of dynamical behaviour for a higher order Kirchhoff type systems with logarithmic nonlinearities. Based on the potential well method, the main ingredient of this study is to construct several conditions for initial data leading to the solution global existence in case of E (0) < d. On the other hand, we proved that if the solution lies

Abstract Existence and uniqueness of strong solutions for the three dimensional system of globally modified magnetohydrodynamics equations with locally Lipschitz delays terms are established in this article. Galerkin’s method and Aubin Lions compactness theorem are the main mathematical tools we use to prove the existence result. Moreover, we prove that, from a sequence of weak solutions of globally

Abstract This article is a continuation of the study of bornological open covers and related selection principles in metric spaces done in (Chandra et al. 2020 [6]) using the idea of strong uniform convergence (Beer and Levi, 2009 [3]) on a bornology. Here we explore further ramifications, presenting characterizations of various selection principles related to certain classes of bornological covers

Abstract In the present paper, we first investigate a Sasakian 3-metric as a quasi-Yamabe gradient soliton. In the sequel, extending the notions of quasi-Yamabe soliton and Ricci-Yamabe soliton, the notion of generalized Ricci-Yamabe soliton is introduced. It is shown that if (g, V, λ, α, β, γ) is a generalized gradient Ricci-Yamabe soliton on a complete Sasakian 3-manifold M with potential function

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 theorem holds is called the ℤ2-index and in our case it takes value 1, 2 or 3. We fully discuss this index according to cohomological operations applied on the characteristic class x ∈ H 1 (N, ℤ2)

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 partially statistically continuous at c, then E is a singleton. We obtain a necessary and sufficient condition on uniquely remotal subsets of uniformly rotund Banach spaces to be a singleton. Moreover

Abstract Given a finite group G, two elements are ≡ m -related if they lie in exactly the same maximal subgroups of G. This equivalence relation was introduced by P. J. Cameron, A. Lucchini and C. M. Roney-Dougal to understand better the generated set for finite groups. We study the relation ≡ m in a conjugacy class of G and determine sufficient conditions to ensure that such conjugacy class is contained

Abstract We study relativizations and potential isomorphisms of quantale-valued approach spaces. We show how the category of generalized approach spaces and injective maps can be encoded using higher order structures, but under such an encoding generalized approach spaces need not have a relativization. We then provide an alternate encoding of generalized approach spaces using higher order structures

Abstract In this paper, we study a nonlinear elliptic system involving a fractional Laplacion: where 0 < α < 2, p, q > 0 and max{p, q} ≥ 1, τ ≥ 0, n ≥ 2. There are two cases to be considered. The first one is where the domain is bounded, and the second one is where the domain is the whole space. First of all, we consider the above system in the star-shaped and bounded domain Ω, by using the Pohozaev

Abstract In this paper, we are concerned with the positive solutions of the Wolfftype integral system where n ≥ 1, γ > 1, β > 0, βγ ̸= n and Ci (x) (i = 1, · · ·, m) are double bounded functions. Discussed in three situations of the integral system, a special iteration scheme in integral form as well as in differential form are applied. By some critical asymptotic analysis with Wolff potential integral

Abstract Let R be a non commutative prime ring of characteristic different from 2, U be the Utumi quotient ring of R with the extended centroid C, f(x1, … , xn ) a multilinear polynomial over C which is not central valued on R, f(R) the set of all evaluations of the polynomial f (x 1, … , xn ). Suppose F and G are two nonzero generalized derivations on R and let p, q, ∈ R be such that f(R) satisfies

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 perfect differential of S is defined to be ∂p (S) = |Np (S)| − |S|. In this paper, we introduce the study of the perfect differential of a graph, which we define as ∂p (G) = max{∂p (S) : S ⊆ V(G)}

Abstract We study the construction of extrapolation spaces of operator-valued multiplication operators on Bochner L p -spaces by means of L p -fiber spaces.

Abstract This paper is a natural continuation of our previous joint paper [Albu, Kara, Tercan, Fully invariant-extending modular lattices, and applications (I), J. Algebra 517 (2019), 207–222], where we introduced and investigated the notion of a fully invariant-extending lattice, the latticial counterpart of a fully invariant-extending module. In this paper we introduce and investigate the latticial

Abstract The objective is to study the existence and uniqueness questions for a nonlinear Volterra-Fredholm integro-differential equation, then, develop a numerical approach using the Nyström method coupled with successive approximations algorithm. A numerical example is presented to examine the efficiency of the proposed method according to the existence and uniqueness conditions.

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