Automatic reconstruction of 3D objects from 2D orthographic views has been a major research issue in CAD/CAM. In this paper, two accelerating techniques to improve the eÆciency of reconstruction are presented. First, some pseudo elements are removed by depth and topology information as soon as the wire-frame is constructed, which reduces the searching space. Second, the proposed algorithm does not establish all possible surfaces in the process of generating 3D faces. The surfaces and edge loops are generated by using the relationship between the boundaries of 3D faces and their projections. This avoids the growth in combinational complexity of previous methods that have to check all possible pairs of 3D candidate edges.

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We consider an electron with an anomalous magnetic moment g> 2 confined to a plane and interacting with a non-zero magnetic field B perpendicular to the plane. We show that if B has compact support and the magnetic flux in natural units is, the corresponding Pauli Hamiltonian has at least bound states, without making any assumptions about the field profile. Furthermore, in the zero-flux case there is a pair of bound states with opposite spin orientations. Using a Birman-Schwinger technique, we extend the last claim to a weak rotationally symmetric field with, thus correcting a recent result. Finally, we show that under mild regularity assumptions existence of the bound states can also be proved for non-symmetric fields with tails.

The concept of matrix canonical realization of a Lie algebra is introduced. The generators of the Lie algebra of the pseudoorthogonal group n) are recurrently expressed in terms of matrices with polyno-mial elements in a certain number of quantum-mechanical canonical variables p~, qi and they depend on a certain number of free real para-meters. The realizations are, in the well-defined sense, skew-hermitean and Casimir operators are multiples of the identity element. Part of them are usual canonical realizations.

Let G=(V,E) be a locally finite connected weighted graph, and Δ be the usual graph Laplacian. In this article, we study blow-up problems for the nonlinear parabolic equation u_t = Δu + f(u) on G. The blow-up phenomenons for u_t = Δu + f(u) are discussed in terms of two cases: (i) an initial condition is given; (ii) a Dirichlet boundary condition is given. We prove that if f satisfies appropriate conditions, then the corresponding solutions will blow up in a finite time.