Let G = (V (G), E(G)) be a graph. A set M ⊆ E(G) is a matching if no two edges in M share a common vertex. A matching of G is perfect if it covers every vertex in G. A matching of a graph G with odd order is called a near perfect matching if it has edges. In this paper, we completely characterize the forbidden subgraph and pairs of forbidden subgraphs that force a 2-connected graph with a (near) perfect

In 1974, P. Hartung proved the existence of infinitely many imaginary quadratic fields with class numbers not divisible by 3. We generalize this result to show the existence of infinitely many imaginary quadratic fields with class numbers not divisible by any integer n > 2. We conclude by providing some interesting applications.

Invariants for geodesic and F-planar mappings defined on a generalized Riemannian space are obtained in this paper. These invariants are generalizations of the Thomas projective parameter and the Weyl projective tensor.

The paper proposes to introduce incomplete Srivastava’s triple hypergeometric matrix functions through application of the incomplete Pochhammer matrix symbols. We also derive certain properties such as matrix differential equation, integral formula, reduction formula, recursion formula, recurrence relation and differentiation formula of the incomplete Srivastava’s triple hypergeometric matrix functions

If N1 is a nearring, V is a faithful tame N1-module and N2 is a nearring containing N1 such that V is a faithful tame N2-module and the N1- and N2-ideals of V coincide, we study when N1-isomorphic minimal factors of V are N2-isomorphic. We also study a stronger form of such preservation called type preservation. Particular attention is paid to the case where N2 is the nearring of 0-preserving and congruence

We give a new bound for the dimension of the Schur multiplier of an n-dimensional nilpotent Lie algebra of class c with the derived subalgebra of dimension n − 2. This new bound sharpens the earlier upper bounds on the dimension of Schur multiplier of such Lie algebras, especially for Lie algebras of maximal class.

Let G and H be graphs, and G H the strong product of G and H. We prove that for any connected graphs G and H there is a strongly connected orientation D of G H such that diam (D) ≤ 2r + 15, where r is the radius of G H. This improves the general bound diam(D) ≤ 2r2 +2r for arbitrary graphs, proved by Chvátal and Thomassen.

For a commutative ring with identity, it is consistently L∗ if and only if it is consistently O∗. This result is generalized to noncommutative rings with identity in the section 2. In the section 3, it is shown that for any abelian group G and integral domain D, the group ring D[G] is L∗ if and only if it is O∗.

For a topological zero-dimensional Hausdorff space (X, ) it is well known that the Banaschewski compactification ζ(X, ) is of Wallman-Shanin-type, meaning that there exists a closed basis (the collection of all clopen sets), such that the Wallman-Shanin compactification with respect to this closed basis is isomorphic to ζ(X, ). For an approach space (X, ) the Wallman-Shanin compactification W (X, )

We investigate, at the level of functors, the effect of definitions mimicking those of Mal’tsev and naturally Mal’tsev categories, and show that they give rise to the same kind of characterizations. We give, among others, an application concerning the characterization of the Smith=Huq condition.

Let be a ring containing a nontrivial idempotent with the center Z() and ℕ be the set of all non-negative integers. Let Δ = {Gn}n∈ℕ be a family of mappings Gn : (not necessarily additive) such that , the identity mapping of . Then Δ is said to be a generalized Lie triple higher derivable mapping of holds for all a; b; c ∈ and for each n ∈ ℕ, where is a family of mappings (not necessarily additive)

Intermediate rings of the functionally countable subalgebra of C(X) (i.e., the rings Ac(X) lying between Cc∗(X) and Cc(X)), where X is a Hausdorff zero-dimensional space, are studied in this article. It is shown that the structure space of each Ac(X) is homeomorphic to β0X, the Banaschewski compactification of X. From this a main result of [A. Veisi, ec-filters and ec-ideals in the function-ally countable

The notion of (p, q)-mixed volume was first introduced by Lutwak, Yang and Zhang in 2018. According to this concept, Li, Wang and Zhou defined the (p, q)- mixed affine surface areas in 2019. In this paper, we establish some inequalities including cyclic inequality, monotonous inequality and product inequality for the (p, q)-mixed affine surface areas.

We investigate the different forms of Aupetit's perturbation theorem and its variants, and provide some generalisations.

In the paper, we consider a bipolynomial fractional Dirichlet-Laplace problem with a functional parameter u. The main goal is to prove theorems on the existence and continuous dependence of solution on functional parameter u for the above problem. Since the solution to the above fractional problem is not unique in general, we use some set-valued approach. We consider two cases (depending on a real

Suppose that (X, d, µ) is a metric measure space of homogeneous type in the sense of Coifman and Weiss with a reverse doubling condition. By establishing the Littlewood-Paley characterization of Lipschitz spaces, a density argument in the weak sense and almost orthogonality estimate we prove that a Caldeŕon-Zygmund operator T is bounded on Lipschitz space if and only if T 1 = 0.

In this paper, we study contact metric manifold whose metric is a Riemann soliton. First, we consider Riemann soliton (g, V ) with V as contact vector field on a Sasakian manifold (M, g) and in this case we prove that M is either of constant curvature +1 (and V is Killing) or D-homothetically fixed η-Einstein manifold (and V leaves the structure tensor ϕ invariant). Next, we prove that if a compact

In this paper, we apply a group theory method to derive the generators of the Lie algebra for a class of (k+1)th order difference equations. We then find solutions to the difference equations and study periodicity by giving sufficient conditions for existence of certain periodicities. We further look at the asymptotic behaviour of solutions satisfying certain properties. Our results generalise some

In this paper, we consider the stability and nonstability results for the following system of functional equations where a, b ∈ ℤ\{0}, on r-divisible abelian groups.

Let A be an integral domain with quotient field K. A. Badawi and E. Houston called a strongly primary ideal I of A if whenever x, y ∈ K and xy ∈ I, we have x ∈ I or y ∈ I for some n ≥ 1. In this note, we study the generalization of strongly primary ideal to the context of arbitrary commutative rings. We define a primary ideal P of A to be strongly primary if for each a, b ∈ A, we have aP ⊆ bA or bnA

In this paper, we present the notions of α-ideal and α-congruence on a distributive nearlattice. We prove that the α-ideals and α-congruences of a normal distributive lattice A are in a one-to-one correspondence with the ideals and congruences of the distributive nearlattice R(A) of the annihilators of A, respectively.

In this paper, we study the concomitants of generalized order statistics from iterated Farlie-Gumbel-Morgenstern (FGM) bivariate distribution. Three information measures, the Shannon entropy, the Kullback-Leibler distance and the Fisher information number, are derived and studied for this model. For each of these information measures, a computational study is conducted, in which we compare the model

Let F be a finite field of characteristic p. There are five non-isomorphic groups of order 20. The structure of U (FD20) is given in [2, 6, 10] and that of U (FQ20) is given in [3, 6], for p = 2, 5. In this article, the unit groups of the group algebras FG are established for all the remaining groups of order 20, namely, U (FC20), U (F (C10 × C2)), U (FQ20) (the semisimple case) and U (FGA(1, 5)) where

In this paper we introduce and investigate new classes of bi-Bazilevič functions of Ma-Minda type involving the Sălăgean integro-differential operator. Bounds of the first three coefficients |a2|, |a3| and |a4| are given.

We introduce the notion of hyperbolic congruent numbers which is a hyperbolic analogue of congruent numbers, and investigate the relations between congruent numbers and hyperbolic congruent numbers.

We study properties of the Golomb topology on polynomial rings over fields, in particular trying to determine conditions under which two such spaces are not homeomorphic. We show that if K is an algebraic extension of a finite field and K′ is a field of the same characteristic, then the Golomb spaces of K[X] and K′[X] are homeomorphic if and only if K and K′ are isomorphic.

In this paper, we consider several statistics on t-compositions. We exhibit a bijection between the set of t-compositions and a set of bargraphs, introduced in this paper, named t-bargraphs. As our main statistic is per – the perimeter of a given t-bargraph, we obtain the corresponding generating function. We find both an explicit and an asymptotic formula for the total length of the perimeter over

In this article we will give a characterization for the profinite Cappitt groups.

In this paper, we show that the Cauchy extensions of C*-algebras and Hilbert C*-modules preserve Morita equivalence of C*-algebras and Hilbert C*- modules, respectively. In particular, we show that the Cauchy extensions of Hilbert C*-modules preserve adjointable, unitary operators and partial isometries as well as full Hilbert C*-modules and linking algebras associated to Hilbert C*-modules.

In this paper we give new characterizations for almost Menger and weakly Menger spaces by neighborhood assignments and define a natural weakening of almost D-spaces and weakly D-spaces. We discuss the relationships among the properties “D-type”, “Menger”, “Alster”, and the weak versions of these properties in Lindelöf spaces.

This work is a continuation of our recent investigation in [15] where we characterized various topological and dynamical properties of the composition operator Cψ acting between Fock-type spaces and when both exponents p and q are finite. Now we investigate the structures when at least one of the spaces is growth type and determine the spectrum of the operator Cψ on all the Banach spaces . The results

Given an infinite set X and a function f : X → X, the primal topology on X induced by f is the topology τf = {U ⊆ X : f−1(U ) ⊆ U}. In this paper, we prove that there are 2ω pairwise non-homemomorphic primal topologies on ℕ. We also prove that an infinite set cannot have more than 2ω pairwise non-homeomorphic primal topologies. We give a necessary and sufficient condition to guarantee that an Alexandroff

This paper is concerned with closure systems defined on groups such that the product of any two closed sets is again closed. The main objective of this paper is to show that if enough “small” subsets are closed, then all subsets are closed. It is shown that this is true for groups without any elements of order 2 provided all 2-element subsets are closed. The same holds for all Abelian groups with one

Let D be a finite and simple digraph with vertex set V (D). A Roman dominating function (RDF) on a digraph D is a function f : V (D) → {0, 1, 2} satisfying the condition that every vertex v with f (v) = 0 has an in-neighbor u with f (u) = 2. The weight of an RDF f is the value . An RDF f on D with no isolated vertex is called a total Roman dominating function if the subdigraph of D induced by the set

Given a graph G = (V, E), a function f: V → {0, 1, 2} is a total Roman {2}-dominating function if every vertex ʋ ∈ V for which f (ʋ) = 0 satisfies that ∑u∈N (ʋ) f (ʋ) ≥ 2, where N (ʋ) represents the open neighborhood of ʋ, and every vertex x ∈ V for which f (x) ≥ 1 is adjacent to at least one vertex y ∈ V such that f (y) ≥ 1. The weight of the function f is defined as ω(f ) = ∑ʋ∈V f (ʋ). The total

We recently answered the three questions of Bertram in the finite abelian case in https://link.springer.com/article/10.1007/s00200-018-0364-0, Applicable Algebra in Engineering, Communication and Computing 30(2) (2019), 127–134. In this paper, we answer the nonabelian analogues of the three questions of Bertram on locally maximal sum-free sets.

In this paper, we investigate the t-quasi continuous property for modules. It is proved that M is t-quasi continuous, if and only if M is a direct sum of a Z2-torsion module and a quasi-continuos module. Moreover we characterize the rings R for which certain R-modules are t-quasi continuous. We show that every R-module is t-quasi continuous, if and only if R(ℕ) is t-quasi continuous, if and only if

In this paper, we introduce two series expansions whose basis functions are two sequences of hypergeometric polynomials. We then present a systematic and detailed study of the general properties of each of these series expansions. We consider several illustrative examples to show the computational efficiency of our expansions in comparison to the usual Taylor series expansion. We also discuss some

In this paper, for a topological space X and any positive integer n, we define the cardinal functions sLθ(n) (X), θ(n)-quasi-Menger number qMθ(n) (X) and s(n)-quasi-Menger number qMs(n) (X). We prove the following statements: For every S(2n)-space X, |X| ≤ 2sL θ (n) (X) κθ (n) (X). For every S(2n)-space X, |X| ≤ 2qM θ (n) (X) κθ (n) (X). For every S(2n)-space X, |X| ≤ 2qM s (n) (X) κθ (n) (X). Similar

Various compositions of the Drazin inverse, the group inverse or the core-EP inverse with the Moore-Penrose inverse have investigated last years. Solving some type of matrix equations, we introduce three new generalized inverses of a rectangular matrix, which are called the OMP, MPO and MPOMP inverses, because the outer inverse and the Moore-Penrose inverse are incorporated in their definition. As

In this paper we study probabilistic aspects, such as the subgroup commutativity degree and the cyclic subgroup commutativity degree, of (generalized) dicyclic groups. We find explicit formulas for these quantities and we provide another example of a class of groups whose (cyclic) subgroup commutativity degree vanishes asymptotically.

In the paper by M. Filipczak, G. Ivanova and J. Wódka, Comparison of some families of real functions in porosity terms, Math. Slovaca 67(5) (2017), 1155–1164, it was proved that the family of quasi-continuous Świątkowski functions is porous but not strongly porous in the space of quasi-continuous functions. We improved this result. We found the unique number q = 2/3 such that the family of quasi-continuous

In this paper, we study a parameter that is a relaxation of an important domination parameter, namely the paired domination. A set D of vertices in G is a semipaired dominating set of G if it is a dominating set of G and can be partitioned into 2-element subsets such that the vertices in each 2-set are at most distance two apart. The semipaired domination number, γpr2(G), is the minimum cardinality

Let pod(n) denote the number of partitions of an integer n wherein the odd parts are distinct. Recently, a number of congruences for pod(n) have been established. In this paper, we establish the generating function of pod(5n + 2) and then prove new infinite families of congruences modulo 5 and 9 for pod(n) by using the formulas for t3(n) and t5(n), where tk (n) is the number of representations of n

This paper deals with Cauchy problems and nonlocal problems for non-linear Stieltjes differential equations corresponding to a certain function g. We establish existence and uniqueness results for nonlinear equations with initial value or nonlocal conditions in the space ℬ𝒞g ([0, H], ℝ) using fixed point methods and g-topology theory. We introduce the concepts of Ulam-Hyers (UH) and generalized Ulam-Hyers-Rassias

We introduce a new subring (L) of (L) for a completely regular frame L and characterize pseudocompact frames via these subrings. Also we obtain several sufficient conditions on L which guarantee that the cozero part of generates L. Further, we prove that the Stone-Čech compactification βL of L is determined by these subrings whenever L is pseudocompact or strongly zero-dimensional. Finally, we have conjectured

Based on the recent development of the theory of measures of noncompactness, we first show a representation theorem of measures of noncompactness defined on Banach spaces. Then, in terms of measure of noncompactness, we present some new characterizations of the existence of global attractors for norm-to-weak continuous semigroups, and a fixed point theorem for norm-to-weak continuous mappings.

In this paper, we present a new characterization for a trans-Sasakian 3-manifold to be proper. More precisely, we prove that if a compact trans-Sasakian 3-manifold has η-parallel Ricci operator, then the manifold is homothetic to a cosymplectic or a Sasakian 3-manifold or is of type (0, β) with ∇β = ξ(β)ξ.

We consider metric spaces over the ring of integers. For any generating set S of ℤ, it is shown that the metric dimension of the metric space X = X(ℤ, S) is not greater than 2 max S. The resolving set of metric space X = X(ℤ, S) is determined. If S = {−m, −(m − 1), . . . , −1, 1, . . . , m − 1, m}, then the metric dimension of the metric space X = X(ℤ, S) is m + 1. We determine the basis of the metric

Let be a commutative ring with unity, be -algebras, be ()-bimodule and be ()-bimodule. The -algebra is a generalized matrix algebra defined by the Morita context . In this article, we study multiplicative generalized Lie triple derivation on generalized matrix algebras and prove that every multiplicative generalized Lie triple derivation on a generalized matrix algebra has the standard form.

In this paper, we use the idea of normal family to investigate the situation when a power of a combination of transcendental meromorphic function with its shift shares small function with it’s derivative and obtain three results which improve and generalize the recent result due to Lü and Yi [12]. Also we exhibit some examples to fortify the condition of our results.

In this paper, we establish the existence of solutions and multiplicity properties for generalized Yamabe equations on Riemannian manifolds. Problems of this type arise in conformal Riemannian geometry, astrophysics, and in the theories of thermionic emission, isothermal stationary gas sphere, and gas combustion. The abstract results of this paper are illustrated with Emden-Fowler equations involving

It is well known that every asymmetric normed space is a T0 paratopological group. Since all Ti axioms (i = 0, 1, 2, 3) are pairwise non-equivalent in the class of paratopological groups, it is natural to ask if some of these axioms are equivalent in the class of asymmetric normed spaces. In this paper, we will consider this question. We will also show some topological properties of asymmetric normed

Let X be a C1 vector field of a compact connected boundaryless smooth smooth Riemannian manifold M with dimM ≥ 3. We show the following: (i) if the chain recurrence set 𝓡(X) is robustly measure expansive, then it is Axiom A without cycles; and (ii) if the homoclinic class H(Orb(p), X) that contains a hyperbolic periodic orbit Orb(p) is generic-robustly measure expansive, then it is hyperbolic.

In this paper, firstly we proved a general theorem dealing with absolute Riesz summability factors of infinite series under weaker conditions. And secondly we applied it to the trigonometric Fourier series. Also we have obtained some new and known results.

In this note we investigate contractibility properties in the class of the so-called DF-algebras. We also give a complete characterization of contractible Köthe co-echelon algebras.

In this note we present a new characterization of the pointwise multipliers of the space BMOA.

For a set Ω = {1, 2, . . . , n} where n = 2k ≥ 6, let Ω{k} denote the set of all subsets of Ω of size k. We examine the binary codes from the row span of biadjacency matrices of bipartite graphs with bipartition (Ω{k}, Ω{k+1}) and two vertices as k-subsets and (k+1)-subsets of Ω being adjacent if they have one element in common. We show that S2k is contained in the automorphism group of the graphs

In this paper, we consider a singular even-order Hamiltonian system on the union of two intervals together with appropriate boundary and transmission conditions. For investigating the spectral properties of the problem we pass to the inverse operator with an explicit form and we prove some completeness theorems.