Abstract A group G is said to be capable if it occurs as the central factor group H/Z(H) for some group H. Motivated by the results of Isaacs [11], in Proc. Amer. Math. Soc. 129(10) (2001), pp. 2853-2859, we show that if G is a capable group with cyclic derived subgroup G′ of odd order, then |G/Z(G)| divides |(G/L)′|2ϕ(|L|)|L|, in which ϕ is Euler’s function and L is the smallest term of the lower

Abstract In a recent paper [I. Altun and A. Tasdemir, On best proximity points of interpolative proximal contractions, Quaestiones Math. (2020), DOI: 10.2989/16073606.2020.1785576] the authors proved two best proximity point theorems for a new class of non-self mappings, called interpolative Reich-Rus-Ćirić type proximal contractions of the first and second kinds. Our purpose is to show that their

Abstract In this paper, we use two different approaches to introduce q-analogs of Riemann’s zeta function and prove that their values at even integers are related to the q-Bernoulli and q-Euler’s numbers introduced by Ismail and Mansour [Analysis and Applications, 17(6) (2019), 853–895].

Abstract We introduce a new class of operators “DPu(E, Y)” which lives between the class of Dunford-Pettis, the class of AM-compact operators and that of order weakly compact “Lowc(E, Y)”, more precisely we have “DP (E, Y) ⊂ DPu(E, Y) ⊂ Lowc(E, Y)” and “AMcp(E, Y) ⊂ DPu(E, Y) ⊂ Lowc(E, Y)”, where DP (E, Y), AMcp(E, Y) denote the class of Dunford-Pettis operators, AM-compact operators, respectively

Abstract We utilise the invariant method for scalar linear (1+1) parabolic partial differential equations so as to effect reductions via invertible transformations to Lie canonical forms of the first and third types. This is performed for the one-factor commodity models that have parameters which are constants or dependent on the price of stock or the time. The unknown parameters of the equations are

Abstract In this paper the system of ordinary impulse differential equations with nonlocal conditions is investigated. First, the boundary value problem is reduced to the equivalent integral equation. Further, using the fixed point theorem, conditions for the existence and uniqueness of the solution of the boundary value problem are obtained. The continuous dependence of the solutions on the right-hand

Abstract We explicitly compute the exponents of quadratic approximation of two algebraic elements over fields of power series with coefficients in a finite field. We prove that they have well quadratic approximation although their rational approximation is bad.

Abstract The purpose of this article is to investigate almost Ricci solitons on para- contact manifolds. We demonstrate that a gradient almost Ricci soliton whose metric is para-sasakian turns into Einstein with a constant scalar curvature −2n(2n + 1). Next, we get a few relationships between almost Ricci solitons and Ricci solitons on a K-paracontact manifold and its generalizations. Finally, some

Abstract The purpose of this paper is to establish the solvability results to direct and inverse problems for time-fractional pseudo-parabolic equations with the self-adjoint operators. We are especially interested in proving existence and uniqueness of the solutions in the abstract setting of Hilbert spaces.

Abstract In this paper, biholomorphically projective and equitorsion biholomorphically projective mappings are defined. Some relations between corresponding curvature tensors of the generalized Riemannian spaces GRN and are obtained. At the end, invariant geometric object of equitorsion biholomorphically projective mapping are found.

Abstract In this article, we study some first-order differential subordinations. We determine the conditions on β such that and implies . Similarly, some results are also obtained for the expressions and . We also give applications of these results to obtain some sufficient conditions for a function to be starlike related to exponential functions.

Abstract The paper is devoted to the analysis of queueing systems in the context of the network and communication theory (called a multi-server multi-core open queueing network). The ob ject of this research on the queueing theory is theorems about the Functional Strong Laws of Large Numbers (FSLLN) in multi-server multi-core open queueing networks, working under overload heavy traffic conditions. FSLLN

Abstract The article is devoted to integral operators for nonlocally compact group modules. Operator valued functions for nonlocally compact groups and their normed spaces of different types are investigated. For this purpose quasi-invariant measures on nonlocally compact groups are used. Estimates of norms of integral operators are given. Moreover, convolutions of functions having operator values and

Abstract This paper presents several sufficient conditions for the existence of at least three weak solutions for the following Kirchhoff-type second-order impulsive differential equation where λ and µ are referred to as two control parameters and is an L2 -Carathéodory function. Our technical approach is based on variational methods. The main results are also demonstrated with examples.

Abstract Let M be a trans-Sasakian 3-manifold such that the Ricci curvature of the structure vector field vanishes. In this paper, it is proved that if M is compact, then it is homothetic to a cosymplectic manifold. Without the compactness assumption, we prove that M is locally isometric to the product of ℝ and a Kahler surface of constant curvature if the Ricci operator of M is of Codazzi type or

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 identities of Kusraeva involving the root mean power and the geometric mean. Furthermore, it is shown that a polynomial on a vector lattice is orthogonally additive whenever it is orthogonally additive on

Abstract In a metric space M = (X, d), a line induced by two distinct points x, x′ ∈ X, denoted by , is the set of points given by A line is universal whenever . Chen and Chvátal [Disc. Appl. Math. 156 (2008), 2101-2108.] conjectured that in any finite metric space M = (X, d) either there is a universal line, or there are at least |X| different (nonuniversal) lines. A particular problem derived from

Abstract We consider a class of a convection-dispersion equation describing the transport model of oil spilled in sea water with concentration-dependent dispersion and spatial velocity. A potential variable is introduced to the governing equation such that the governing equation is written in conserved form (or auxiliary system). The conserved form admits a number of classical symmetries which induce

Abstract In this paper, we investigate the existence of an elementary abelian closure in characteristic not 2 for biquadratic extensions. We discover that it exists for any non-cyclic extension. We make use of it to obtain a classification for this class of extensions up to isomorphism via descent. This permits us to describe the geometry of this moduli space in group theoretic terms. We also provide

Abstract In this paper we consider the set of Mahler measures of generalized Pisot and Salem numbers and give a characterization of such numbers in terms of their minimal polynomials. We show that every real quadratic algebraic integer β can be expressed by the difference of the Mahler measure of a generalized Pisot number and a Pisot number in ℚ(β).

Abstract We propose a new coloring game on a graph, called the independence coloring game, which is played by two players with opposite goals. The result of the game is a proper coloring of vertices of a graph G, and Alice’s goal is that as few colors as possible are used during the game, while Bob wants to maximize the number of colors. The game consists of rounds, and in round i, where i = 1, 2,

Abstract In this paper, we study essential norm and Schatten class membership of the generalized weighted composition operators acting on Fock-type spaces. An asymptotic estimate for the essential norm and norm of the operators have been also provided. Moreover, we characterize the path-connected components of space of all bounded generalized weighted composition operators acting between Fock-type

Abstract Let X be a completely regular Hausdorff space and E be a Banach space. Let Cb(X, E) (resp. ) be the space of all bounded continuous (resp. bounded strongly Borel-measurable) functions f : X → E, equipped with the natural mixed topologies. Then whenever X or E is separable. We study the problem of extension of different classes of continuous linear operators acting from Cb(X, E) to a Banach space

Abstract Let f (n) be the number of distinct exponents in the prime factorization of the natural number n. For every r-tuple of positive integers k = (k1, . . . , kr) and for all x > 1, let be the set of natural numbers n ≤ x such that f (n+i−1) = ki for i = 1, . . . , r. We prove that where Ak ≥ 0 depends only on k and αr ∈ (0, 1) depends only on r. Moreover, we provide a characterization of the k’s

Abstract In this paper we continue our research about links and link topologies on ℓ-groups and Riesz spaces. We show that in a Riesz space E, a link topology τ is a vector topology, if and only if the link consists of all order units in E. We also compare the link topologies with the positive filter topologies on an ℓ-group. In addition, we provide some examples of these constructions.

Abstract Let A be a Banach algebra. For f ∈ A*, we inspect the weak sequential properties of the well-known map Tf : A → A*, Tf (a) = fa, where fa ∈ A* is defined by fa(x) = f (ax) for all x ∈ A. We provide equivalent conditions for when Tf is completely continuous for every f ∈ A*, and for when Tf maps weakly precompact sets onto L-sets for every f ∈ A*. Our results have applications to the algebra

Abstract Let G be a finite group and p be a prime. A vanishing conjugacy class of G is a conjugacy class of G which consists of vanishing elements of G. A p-singular vanishing conjugacy class is a vanishing conjugacy class with elements of order divisible by p. Dolfi, Pacifici, Sanus and Spiga proved that if a group has no p-singular vanishing elements, then it has a normal Sylow p-subgroup. In this

Abstract It is well-known that the family of coneat-injective modules has many properties that resemble the classes of injective modules, pure-injective modules and RD-injective modules. Moreover, injective modules are coneat-injective which, in turn, are RD-injective and, finally, RD-injective modules are pure-injective. For injective (respectively, pure-injective, RD-injective) modules, two such

Abstract In this paper, we characterize various division closed lattice-ordered rings with the identity.

Abstract The same-order type τe(G) of a finite group G is a set formed of the sizes of the equivalence classes containing the same order elements of G. In this paper, we study an arithmetical property of this set. More exactly, we outline some results on the classification and existence of finite groups whose same-order types are arithmetic progressions formed of 3 or 4 elements, the latter being the

Abstract Let C(1)([0, 1]) be the Banach space of continuously differentiable functions on the closed unit interval [0, 1] equipped with the norm ||f||σ= | f (0)| +|| f ′||∞, where ||g||∞= sup{|g(t)| : t ∈ [0, 1]} for g. If T : C(1) ([0, 1]) → C(1) ([0, 1]) is a 2-local real-linear isometry, then T is a surjective real-linear isometry.

Abstract We are interested in the behavior of relative multifractal box-dimensions, density results and multifractal dimensions under projections onto a lower-dimensional linear subspace. The results in this paper establish the connections with various multifractal and fractal dimensions and their projections, and generalize many known results about Hausdorff and packing measures and dimensions of

Abstract In this work we investigate the general relation between the density of a subset of the ring of integers D of a general global field and the Haar measure of its closure in the profinite completion . We then study a specific family of sets, the preimages of k-free elements (for any given k ∈ ℕ\{0, 1}) via one variable polynomial maps, showing that under some hypotheses their asymptotic density

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 control function acts on a subdomain ω and at one instant of time τ ∈ (0, T). Afterward, we study impulse observability.

Abstract. Inspired by circular complex interval arithmetic, an arithmetic for closed balls in ℝn is pursued. In this sense, the properties of certain operations on closed balls in ℝn, some of which related either to the Hadamard product of vectors or to the 2-fold vector cross product when n ∈ {3,7}, are studied. In particular, known results for operations on closed balls in ℂ, which can be identified

Abstract A subgroup H of a group G is called a power subgroup of G if there exists a non-negative integer m such that H = ⟨gm : g ∈ G⟩. Any subgroup of G which is not a power subgroup is called a nonpower subgroup of G. Zhou, Shi and Duan, in a 2006 paper, asked whether for every integer k (k ≥ 3), there exist groups possessing exactly k nonpower subgroups. We answer this question in the affirmative

Abstract We use the theory of semigroups to obtain the existence and uniqueness of solutions for multilayer diffusion models with possibly non linear reactions terms as well as local non-homogeneous boundary conditions on the first and the last layers. We also allow the possibility of having Dirichlet, Newman or mixed type conditions in the first and the last layers. We express the solutions in terms

Abstract Let η(G) be the number of connected induced subgraphs in a graph G, and Ḡ the complement of G. We prove that η(G) + η(Ḡ) is minimum, among all n-vertex graphs, if and only if G has no induced path on four vertices. Since the n-vertex star Sn with maximum degree n − 1 is the unique tree of diameter 2, is minimum among all n-vertex trees, while the maximum is shown to be achieved only by the

Abstract We apply the theory of infinitesimal transformations for the study of a family of 1+1 fifth-order partial differential equations which have been proposed before for the description of multiple kink solutions. In this analysis we perform a complete classification of the Lie symmetries and of the one-dimensional optimal system. The results are applied for the derivation of similarity solutions

Abstract Let M be a smooth manifold of dimension 2n, and let OM be the dense open subbundle in ∧2 T*M of 2-covectors of maximal rank. The algebra of Diff M -invariant smooth functions of first order on OM is proved to be isomorphic to the algebra of smooth Sp(Ωx)-invariant functions on , x being a fixed point in M , and Ωx a fixed element in (OM )x. The maximum number of functionally independent invariants

Abstract We determine the complete membership to Kaplan classes of a family of functions that can be presented in the form of integral operators I1(f, g; α, β) introduced by Kim and Merkes as well as I2(f, g; α) introduced by Ularu and Breaz. In this way we obtain close-to-convexity criteria for these functions.

Abstract In this paper we show that the limit of a sequence of porous sets under Hausdorff convergence is also porous. This purely topological result is then applied to Kleinian group theory in order to construct a Kleinian group with exponent of convergence arbitrarily small and Hausdorff dimension of the limit set strictly less than two.

Abstract In this paper we present the case of an eigenvalue-type problem involving the p-Laplace operator, studied on an exterior domain, which possesses, on the one hand, a continuous family of eigenvalues and, on the other hand, at least one more eigenvalue which is isolated in the set of eigenvalues of that problem.

Abstract In this paper, we investigated the Dirichlet initial boundary value prob- lem of a weakly coupled nonlocal reaction-diffusion system with time-dependent co- efficients. With several suitable weighted measures in whole-dimensional space, we obtained the lower bounds for the blow-up time of the solution to the problem by using the technique of modified differential inequality.

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 continuous maps that was provided by Dimov [3], and obtain two new duality theorems for the category BooleSp.

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 applications to Grothendieck categories and, in particular, to (graded) module and comodule categories.

Abstract Let P be a prime ideal of the ring of continuous real-valued functions on a completely regular frame L, i.e., L. We study many new results about the residue class domains L/P with an emphasis on determining when the ordered L/P is a valuation domain (i.e., when given any two non-zero elements of L/P , one divides the other). A prime ideal P of L is called a valuation prime ideal if L/P is

Abstract Asinowski, Bacher, Banderier and Gittenberger [1] recently developed the vectorial kernel method – a powerful extension of the classical kernel method useable for paths that obey constraints that can be described by finite automata, e.g. avoid a fixed pattern, avoid several patterns at once, stay in a horizontal strip and many others more. However, they only considered walks with steps of

Abstract Recently, Masjed-Jamei and Koepf established the extension of several classical summation theorems (including Gauss’s second summation theorem). Our aim in this paper is to establish a further extension of Gauss’s second summation formulas due to Masjed-Jamei and Koepf in the most general form. The result is then applied to obtain extensions of (i) Knuth’s old sum (or the Reed Dawson identity)

Abstract Iannucci considered the positive divisors of a natural number n that do not exceed and found all forms of numbers whose such divisors are in arithmetic progression. In this paper, we generalize Iannucci’s result by excluding the trivial divisors 1 and (when n is a square). Surprisingly, the length of our arithmetic progression cannot exceed 5.

Abstract We previously have developed two methods for constructing codes and designs from finite simple groups. In a recent paper we introduced a new method (Method 3) for constructing codes and designs from fixed points of elements of finite transitive groups. This new method together with background material and results required from finite groups, permutation groups and representation theory were

Abstract In this paper we introduce and study a class of ideals between z-ideals and z°-ideals (=d-ideals) namely zr-ideals. A zr-ideal is a z-ideal which is at the same time an r-ideal (an ideal I in a ring R is called an r-ideal if for each non-zerodivisor r ∈ R and each a ∈ R, ra ∈ I implies a ∈ I). In contrast to the sum of z-ideals in C(X) which is a z-ideal, the sum of zr-ideals need not be a

Abstract Intermediate rings A(X, K) of K-valued continuous functions lying between B(X, K) and C(X, K), defined over a zero dimensional space X, are investigated and studied in this article, here K stands for a countable subfield of ℝ. It is realized that the structure space of A(X, K) is β0X, the Banaschewski compactification of X. The Hewitt realcompactification analogue υK (X) of υX is defined.

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 consequences of the main theorem we prove some recurrence relations conjectured in Sloane’s OEIS, furthermore we also give some combinatorial identities.

Abstract We classify the filled groups of order pqr for primes p, q and r. Our result confirms a conjecture of Anabanti, Erskine and Hart for these examples of soluble groups.

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 finite in number, and we provide a bound for them.

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