We study properties of a C2-cofinite vertex operator algebra V = ⊕ ∞ i=0Vi of CFT type. If it is also rational (i.e. all modules are completely reducible) and V ′ ∼= V , then the rigidity of the tensor category of modules has been proved by Huang [11], where V ′ denotes the restricted dual of V . However, when we treat irrational C2cofinite VOAs, the rigidity is too strong, because it is almost...

We discuss aspects of the L–Stokes theorem on certain manifolds with singularities. We show that the L–Stokes theorem does not hold on real projective varietes, even for isolated singularities. For a complex projective variety of complex dimension n, with isolated singularities, we show that the Laplacians of the de Rham and Dolbeault complexes are discrete operators except possibly in degrees ...

The fundamental goal of this paper aims to bridge the large gap between the shape versatility of arbitrary topology and the geometric modeling limitation of conventional tensor-product splines for solid representations. Its contribution lies at a novel shape modeling methodology based on tensorproduct trivariate splines for solids with arbitrary topology. Our framework advocates a divide-andcon...

let $r$ be a ring and $m$ a right $r$-module with $s=end_r(m)$. a module $m$ is called semi-projective if for any epimorphism $f:mrightarrow n$, where $n$ is a submodule of $m$, and for any homomorphism $g: mrightarrow n$, there exists $h:mrightarrow m$ such that $fh=g$. in this paper, we study sgq-projective and$pi$-semi-projective modules as two generalizations of semi-projective modules. a m...

Let H be a Hilbert space, U an unitary operator on H and K a cyclic subspace for U . The spectral measure of the pair (U,K) is an operator-valued measure μK on the unit circle T such that ∫ T zdμK(z) = ( PKU k ) ↾K , ∀ k ≥ 0 where PK and ↾ K are the projection and restriction on K, respectively. When K is one dimensional, μ is a scalar probability measure. In this case, if U is picked at random...

This paper presents a novel image space path planning method that takes mechanical constraints into consideration. The aim is to synthesize sub-goal images that can be used as reference inputs for image-based visual servoing systems. Synthesized images are constructed based on screw decompositions represented in a projective space. The projective representation allows image synthesis for threed...