In this paper we obtain new results on the uniform convergence on matrices and a new version of the matrix theorem of the Hahn-Schur summation theorem in effect algebras.

We investigate the existence of solutions and their stability for elliptic Dirichlet problems with nonlinearity of a convex-concave type. By relating the primal action and the dual action functionals on certain subsets of their domains we get the existence of solutions which are further stable with respect to a numerical parameter. We allow also for the differential operator to depend on a numerical parameter.

This paper is concerned with transformations for complex discrete linear Hamiltonian systems and complex discrete linear symplectic systems. A general complex discrete trigonometric system is studied and a criterion for it is established. Based on these results, the Prüfer and trigonometric transformations for complex discrete linear Hamiltonian systems and complex discrete linear symplectic systems are formulated. The relative existing results in real cases are extended.

The author shows that if the dual of a Musielak–Orlicz sequence space lΦ is a stabilized asymptotic l∞, space with respect to the unit vector basis, then lΦ is saturated with complemented copies of l1 and has the Schur property. A sufficient condition is found for the isomorphic embedding of lp spaces into Musielak–Orlicz sequence spaces.

This paper study nearly extremal Cohen–Macaulay and Gorenstein algebras and characterise them in terms of their minimal free resolutions. Explicit bounds on their graded Betti numbers and their multiplicities are obtained.

For a prime p and integers a and b, we consider Salié sums

where χ2(x) is a quadratic character and x¯ is the modular inversion of x, that is, xx¯≡ 1 (mod p). One can naturally associate with Sp (a, b) a certain angle θp(a, b) ∈ [0, π]. We show that, for any fixed ε > 0, these angles are uniformly distributed in [0, π] when a and b run over arbitrary sets , ℬ ⊆ {0, 1, …, p − 1} such that there are at least p1+ε quadratic residues modulo p among the products ab, where (a, b) ∈  × ℬ.

Suppose that H is a closed subgroup of a locally compact group G. We show that a unitary representation U of H is the restriction of a unitary representation of G if and only if a dual representation Û of a crossed product C*(G) ⋊ (G/H) is regular in an appropriate sense. We then discuss the problem of deciding whether a given representation is regular; we believe that this problem will prove to be an interesting test question in non-Abelian duality for crossed products of C*-algebras.

An infinite class of identities relating infinite products is proved. It is shown that this class contains a famous identity of Jacobi.

We show that the λ-multiplier convergence of operator series depends completely upon the AK property of the sequence space λ, and thus present a lot of new important theorems.

We show that nontrivial classical pretzel knots L (p, q, r) are hyperbolic with eight exceptions which are torus knots. We find Conway polynomials of n-pretzel links using a new computation tree. As applications, we compute the genera of n-pretzel links using these polynomials and find the basket number of pretzel links by showing that the genus and the canonical genus of a pretzel link are the same.

In this paper, composition operators acting on Bergman-Orlicz spaces

are studied, where ψ is a non-constant, non-decreasing convex function defined on (-∞, ∞) which satisfies the growth condition . In fact, under a mild condition on ∞, we show that every holomorphic-self map ∞ of induces a bounded composition operator on and C∞ is compact on if and only if it is compact on .

An iteration method for the matrix equation A×B = C is constructed. By this iteration method, the least-norm solution for the matrix equation can be obtained when the matrix equation is consistent and the least-norm least-squares solutions can be obtained when the matrix equation is not consistent. The related optimal approximation solution is obtained by this iteration method. A preconditioned method for improving the iteration rate is put forward. Finally, some numerical examples are given.

Two integral inequalities of Ostrowski type for the Stieltjes integral are given. The first is for monotonic integrators and Hölder continuous integrands while the second considers the dual case, that is, for monotonic integrands and Hölder continuous integrators. Applications for the mid-point inequality that are useful in the numerical analysis of Stieltjes integrals are exhibited. Some connections with the generalised trapezoidal rule are also presented.

Finite groups in which a given property of two-generator subgroups is a transitive relation are investigated. We obtain a description of such groups and prove in particular that every finite soluble-transitive group is soluble. A classification of finite nilpotent-transitive groups is also obtained.