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.
n.
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.
is obtained and some sufficient conditons for a linear mapping to be an ε-approximate orthogonality preserving mapping are given. Secondly, the stability of an ε-approximate orthogonality preserving linear mapping is discussed. Lastly, the perturbations of ε-approximate orthogonality preserving linear mappings are studied.
which may be non doubling. The only condition that μ must satisfy is μ(B(x,r))≤C0 rn for all 
, r>0 and some fixed n∈(0,d]. In this paper, the authors establish the boundedness of the commutator generated by the Lipβ(μ)(0<β) function and the Marcinkiewicz integral with kernel satisfying certain slightly stronger Hörmander-type condition, respectively, from Lp(μ) to Lq(μ) with 1<p≤n/β and 1/q=1/p-β/n, from the space Lp(μ) to Lipβ-n/p(μ) and from the space Ln/β(μ) to RBMO(μ). Some of the results are also new even for the classical Marcinkiewicz integral.
This is a strong converse inequality of type B.
, we give a new proof of the well-known fact that if the ideal class number of a real quadratic function field 
equals to 1, then D must be P or QR, where P,Q,R∈ are monic and irreducible, and Q,R have odd degrees.
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).
(f(x)=ax2+bx+c∈Z[x] is an irreducible quadratic polynomial) is not a square for sufficiently large n.
