Let F_q^{(2\nu +l)} be the (2\nu +l)-dimensional singular symplectic space over the finite field F_q, K be a fixed maximal totally isotropic subspace in F_q^{(2\nu +l)}, and \mathrm{\Omega } be the set of all subspaces of type (1,0,0) not contained in K. In this paper, we construct a class of association schemes by using all subspaces of type (2,0,1) that contain a subspace from \mathrm{\Omega }, and compute all intersection numbers of the constructed schemes.

In this paper, we study the integrals and growth properties of the products multiplying types of polynomials and the Poisson kernel in the half space. By gradually weakening the convergence conditions and redefining the measure, two special cases, namely the growth properties of the integrals multiplying two types of harmonic polynomials and the Poisson kernel, are obtained to solve the Dirichlet boundary value problem of the polyharmonic equation. Moreover, we generalize the results concerning the modified Poisson integral in the half space.

In this paper, we discuss a class of higher order nonlinear nonlocal singularly perturbed boundary value problems with two parameters. Under suitable conditions, we use the fixed-point theorem to study the existence of a generalized solution. Moreover, with the help of the singular perturbation method, we gain the uniformly valid asymptotic representation of the solution.

Let \mathcal{X} be a Banach space with \dim \mathcal{X}\ge 2 and \text{B}(\mathcal{X}) be the Banach algebra of all bounded linear operators on \mathcal{X}, \mathrm{\forall }A,B\in \text{B}(\mathcal{X}). Define a quasi-product by A\circ B=A+B-AB, and (\text{B}(\mathcal{X}),\circ) is a semigroup. In this paper, we mainly discuss the quasi-product automorphisms on \text{B}(\mathcal{X}). It is proved that a bijective map \phi on \text{B}(\mathcal{X}) is a quasi-product automorphism if and only if \phi is a ring automorphism.

For a Morita context ring T=(\genfrac{}{}{0ex}{}{RN}{MS}), the structure of several radicals is given under certain conditions.