We discuss weak Morita equivalence of the symplectic orbifold groupoids, and show that two symplectic orbifold groupoids are weak Morita equivalent if and only if they have isomorphic orbifold fundamental groups.

This paper provides some functional equations satisfied by the generating functions for unicursal planar maps rooted in a vertex of odd valency with the number of edges, the valencies of rooted vertex and nonrooted odd-valent vertex of the maps as three parameters. Moreover, explicit expressions of these functions are also derived. Two of them is summation-free.

It is proved that every weakly continuous local 3-cocycle of a nest subalgebra of a factor von Neumann algebra with coeffcients on a unital dual bimodule is a 3-cocycle.

Under the frame of the smooth Banach spaces, we introduce the notions of the weakly convex set and the W-sun set and present their properties and applications in approximation problems.

This paper studies the pricing problem of the convertible bond with risk in Jump-diffusion model. Under the hypothesis that the stock price is satisfied to geometic Brown motion , the pricing formulas of the convertible bond are obtained by means of Martingale approach (risk-neutral valuation).

In this paper, the effective sequences in a Hilbert space are discussed and by introducing the adjoint sequence of a sequence, an equivalent characterization of an effective sequence is presented. Next, some properties of linear operators preserving the effectiveness of effective sequences are discussed. It is proved that a linear operator maps every effective sequence as an effective sequence if and only if it is a unitary. Finally, we give a necessary and sufficient condition for a sequence obtained by adding a unit vector into an orthonormal basis to be an effective sequence.

In this note we study the generalized property (ω), a variant of generalized Weyl's theorem, by means of the new spectrum. We establish for a bounded linear operator defined on a Banach space a sufficient and necessary condition for which generalized property (ω) holds. As a consequence of the main result, the stability of generalized property (ω) is considered.

Paraunitary matrices play a very important role in construction of wavelets, multiwavelets and frames. In this paper, we give an explicit algorithm for constructing paraunitary symmetric matrices (p.s.m. for short), whose components are symmetric or antisymmetric polynomials. Based on the constructed p.s.m. and the given orthogonal and symmetric multiwavelets (o.s.m. for short), parametrization of o.s.m. filter banks is given. Appropriately selecting some parameters, we can obtain o.s.m. with some additionally desirable properties such as Armlet. To embody our results, we construct a family of symmetric Chui--Lian Armlet filters.

In this paper, we use a new lemma to investigate the relation between solutions, their 1st, 2nd derivatives, differential polynomial of differential equations with function of small growth.