Asian-European Journal of Mathematics

This work aims to study the existence and the regularity of positive solutions to a p-Laplacian system with nonlinearities of growth conditions. We focus on positive ground-state solutions and we assume that the nonlinearities are controlled by general polynomial functions, and we use a variational method to apply the mountain pass theorem which guarantees the existence of a super-solution in the sense of Hernandez, then we construct some compact operator T and some invariant set K where we can use the Leray–Schauder fixed point theorem. By the end of this paper, we establish an -estimation which allows to derive a property of regularity for such positive solutions.

For a ring endomorphism α, we introduce and investigate skew Hurwitz serieswise Armendariz (or SHA) rings which are a generalization of α-rigid rings and determine the radicals of the skew Hurwitz series ring (HR, α), in terms of those of R. We prove that several properties transfer between R and the extensions, in case R is an SHA-ring. We also construct various types of nonreduced SHA-rings.

This paper presents one-step numerical schemes for solving quantum stochastic differential equation (QSDE). The algorithms are developed based on the definition of QSDE and the solution techniques yield rapidly convergent sequences which are readily computable. As well as developing the schemes, we perform some numerical experiments and the solutions obtained compete favorably with exact solutions. The solution techniques presented in this work can handle all class of QSDEs most especially when the exact solution does not exist.

In this paper, we state three theorems for the inverse Laplace transform and using these theorems we obtain new integral identities involving the products of the Wright and Mittag-Leffler functions. The relationships of these integral identities with the Stieltjes transform are also given.

In this paper, we are concerned with the asymptotic behavior of certain solutions of third-order nonlinear differential equations with quasiderivatives. More precisely, the necessary and sufficient conditions for the existence of some types of nonoscillatory solutions with a specified asymptotic property as t → ∞ are given. In order to prove some of our results, we use a topological approach based on the Banach fixed point theorem.

Lie symmetry group method is applied to study the Born–Infeld equation. The symmetry group is given, and similarity solutions associated to the symmetries are obtained. Finally the Hamiltonian equations including Hamiltonian symmetry group and conservation laws are determined.

Duality principles in Gabor theory play a fundamental role for analyzing Gabor systems. In this paper, we obtain some results of duality principles for g-frames. Let {γ_j ∈ B(H, H_j) : j ∈ ℕ} and {η_i ∈ B(H, H_i) : i ∈ ℕ} be g-orthonormal bases for H with respect to {H_i}_i∈ℕ. For a g-Bessel sequence Λ = {Λ_i ∈ B(H, H_i) : i ∈ ℕ}, we define . Then we describe some properties of the sequence . We also characterize the sequence when Ψ = {Ψ_i ∈ B(H, H_i) : i ∈ ℕ} is a dual g-frame of {Λ_i}_i∈ℕ.

In distribution theory, the product of two distributions can only be defined under certain conditions. In this paper, by using Fisher's definition, it is proved that if G_m,s(x) denotes the distribution (ln^m+1x_-)^(s), then the noncommutative neutrix product exists and

Let 𝔽_q be a finite field and 𝔽_qⁿ be an extension, where a Type I optimal normal basis exists. Suppose n = mk. We provide a bound for the complexity of the normal basis of 𝔽_q^m over 𝔽_q generated by the trace of the dual element of the generator of a Type I optimal normal basis of 𝔽_qⁿ over 𝔽_q. Further, we show that our bounds are better than the known bounds under certain conditions on m and k.

In this paper, we have introduced a new concept of a modular pair in terms of maximal elements of lower cone (L) and minimal elements of upper cone (U) in posets. The relation between our definition and the existing definitions of modular pairs in posets has been studied for different classes of posets. We succeeded in characterizing a modular pair by means of forbidden configuration in general posets. We have obtained several characterizations of modular pairs in atomistic and semi-orthogonal posets. We have also introduced ∇-relation in posets.

The notion of Stonity of a pseudo-complemented Almost Distributive Lattice A is introduced and several properties of the Stonity S(A) of A are proved. Mainly, it is proved that the Stonity S(A) is the largest sub-ADL of A which is a Stone ADL and that S(A) is independent of the pseudo-complementation on A.

In this paper, we introduce a subclass of meromorphically univalent functions involving q-hypergeometric function. We derive results based on partial sums of functions belonging to this class.

A subgroup H of a group G is said to be K-ℙ-subnormal inG [A. F. Vasilyev, T. I. Vasilyeva and V. N. Tyutyanov, On finite groups with almost all K-ℙ-subnormal Sylow subgroups, in Algebra and Combinatorics: Abstracts of Reports of the International Conference on Algebra and Combinatorics on Occasion the 60th Year Anniversary of A. A. Makhnev (Ekaterinburg, 2013), pp. 19–20] if there exists a chain of subgroups H = H₀ ≤ H₁ ≤ ⋯ ≤ H_n = G such that either H_i-1 is normal in H_i or |H_i : H_i-1| is a prime, for i = 1, …, n. In this paper, we describe finite groups in which every second maximal subgroup is K-ℙ-subnormal.

Let 𝔻^k denote the unit polydisk in ℂ^k, k ≥ 1, and H(𝔻^k) the set of all holomorphic functions on 𝔻^k. Now, let v : 𝔻^k → (0, ∞) be a weight and the Banach space of holomorphic functions f on 𝔻^k such that sup_{z ∈ 𝔻^k} v(z)|f(z)| < ∞. A holomorphic self-map ϕ : 𝔻^k → 𝔻^k induces the linear composition operator C_ϕ : H(𝔻^k) → H(𝔻^k), f ↦ f ◦ ϕ. We investigate under which conditions on the symbol ϕ and the weight v the operator C_ϕ acting on is a bellwether for boundedness of composition operators, where C_ϕ being a bellwether means that C_ϕ acts boundedly on if and only if all composition operators act boundedly on .

In this paper, we establish Stone like duality between the class of relatively complemented almost distributive lattices and the class of locally Boolean spaces.

We study corner spaces on singular manifolds, in particular, with conical or edge singularities, and singularities of second-order. We characterize the nature of discrete asymptotics, and we establish other elements of the analysis in these spaces which are necessary in the corner pseudo-differential calculus.

In this paper, we introduce the notion of Gorenstein n-flat modules and Gorenstein n-absolutely pure modules. First, we prove that the direct limit of Gorenstein n-flat modules over a right n-coherent ring is again a Gorenstein n-flat module. Also we prove that over a right n-coherent ring, any pure submodule of a Gorenstein n-flat module is a Gorenstein n-flat module. Finally, the class of all Gorenstein n-flat left modules over a ring R is a Kaplansky class and then we prove that all left modules over a right n-coherent ring have Gorenstein n-flat covers.

In this paper, we introduce the concept of a complete almost distributive lattice (ADL), a zone and a dual zone in a complete ADL and derive their important properties.