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.

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

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

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.

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

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

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 .

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.

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

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

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.

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

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

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.

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.

In this addendum we give a few remarks about Subsection 6.2 of the paper “Variations of classical selection principles: An overview,” Quaestiones Mathematicae, https://doi.org/10.2989/16073606.2019.1601646.

A practical number is a positive integer n such that all positive integers less than n can be written as a sum of distinct divisors of n. Leonetti and Sanna proved that, as x → +∞, the central binomial coefficient is a practical number for all positive integers n ≤ x but at most O(x0.88097) exceptions. We improve this result by reducing the number of exceptions to exp (C(log x)4/5 log log x), where

In this paper, we show that the difference between the number of parts in the odd partitions of n and the number of parts in the distinct partitions of n satisfies Euler’s recurrence relation for the partition function p(n) when n is odd. A decomposition of this difference in terms of the total number of parts in all the partitions of n is also derived. In this context, we conjecture that for k > 0,

A commutative non-associative division closed lattice-ordered ring with identity that is not an f -ring is presented. More conditions are provided to ensure that an associative division closed lattice-ordered ring is an f -ring. In particular, for a division closed lattice-ordered ring with identity, if it is Σ-clean or Σ-semiclean, then it is an f -ring. Finally it is shown that a ring with identity

In this paper we consider properties of the class of finitely continuous Darboux functions. In particular, we study some properties of the set of discontinuity points of the function from this class. We show some relations between the family of all Darboux finitely continuous functions and the family of all Darboux strong finitely continuous functions or Baire-one-star Darboux functions.

For k ≥ 1 an integer, a set S of vertices in a graph G with minimum degree at least k − 1 is a k-tuple dominating set of G if every vertex of S is adjacent to at least k − 1 vertices in S and every vertex of V (G) / S is adjacent to at least k vertices in S; that is, |NG[v] ∩ S| ≥ k for every vertex v of G where NG[v] denotes the closed neighborhood of v which consists of v and all neighbors of v.

In this paper, a new identity is established for differentiable mappings. By using the mathematical analysis techniques, some new integral inequalities of Hermite-Hadamard type for differentiable p-convex functions are proved. A comparison of the established results with previously obtained results is demonstrated to show that the results presented in this paper are better than those already exist

Let (M3, g) be a three dimensional almost coKähler manifold such that the Reeb vector field ξ is an eigenvector field of the Ricci operator Q, i.e. Qξ = ρξ, where ρ is a smooth function on M. In this article, we prove that if g represents a Cotton soliton with potential vector field being collinear with ξ, or a gradient Cotton soliton, then M is coKähler or locally conformally flat. Furthermore, when

The aim of this note is to give a simple proof of the fact that the Hilbert transform in is an isometry, using a basis for consisting orthonormal real rational functions.

Let G be a group, let H be a subgroup of G and let Or(G) be the orbit category. In this paper we extend the definition of the relative group homology the- ories of the pair (G, H) defined by Adamson and Takasu to have coefficients in an Or(G)-module. There is a canonical comparison homomorphism defined by Cisneros- Molina and Arciniega-Nevrez from Takasu’s theory to Adamson’s theory. We give a necessary

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