In recent years, with the development of 3D data acquisition equipments, the study on reverse engineering becomes more and more important. However, the existing methods for parameterization are hard to ensure that the parametric domain is rectangular, and the parametric curve grid is regular. In order to overcome the limitations, we present a novel method for parameterization of triangular mesh...

A new procedure for testing quasi-independence in an ordinal triangular contingency table is proposed as a generalization of Pearson's chi square test. The test is asymptotically equivalent in terms of power to the corresponding restricted likelihood ratio test for contiguous alternatives. Numerical results are also included in this study.

We make a local semi-analytical study of a quasi-periodic perturbation of the Sun-Jupiter RTBP Hamiltonian in a neighbourhood of the triangular points. First, we construct a suitable normal form of the Hamiltonian around the invariant torus that replaces L5. Then, we use this (high order) normal form to give a description of the local non-linear dynamics.

Let H be a finite Hopf algebra with CH,H = C −1 H,H . The duality theorem is shown for H, i.e., (R#H)#H ∗̂ ∼= R ⊗ (H⊗̄H ) as algebras in C. Also, it is proved that the Drinfeld double (D(H), [b]) is a quasi-triangular Hopf algebra in C. 2000 Mathematics subject Classification: 16w30.

We classify the orbits of coquasi-triangular structures for the Hopf algebra E(n) under the action of lazy cocycles and the Hopf automorphism group AutHopf (E(n)). Using this result we show that for any triangular structure R on E(n) the Brauer group BM(k,E(n), R) is the direct product of the Brauer-Wall group of the base field k and the group Symn(k) of symmetric matrices of order n with entri...

We numerically demonstrate ultraflattened chromatic dispersion with low losses in microstructured optical fibers (MOFs). We propose using two different MOF structures to get this result. Both structures are based on a subset of a triangular array of cylindrical air holes; the cross sections of these inclusions are circular, and a missing hole in the fiber's middle forms the core. In this MOF st...

Let H be a finite Hopf algebra with CH,H = C −1 H,H . The duality theorem is shown for H, i.e., (R#H)#H ∗̂ ∼= R ⊗ (H⊗̄H ) as algebras in C. Also, it is proved that the Drinfeld double (D(H), [b]) is a quasi-triangular Hopf algebra in C. 2000 Mathematics subject Classification: 16w30.

We consider a black hole in a heat bath, and the whole system which consists of the black hole and the heat bath is isolated from outside environments. When the black hole evaporates, the Hawking radiation causes an energy flow from the black hole to the heat bath. Therefore, since no energy flow arises in an equilibrium state, thermodynamic state of the whole system is not in an equilibrium. T...

We prove that a triangular grid without local cuts is (almost) always Hamiltonian. This suggests an efficient scheme for rendering triangulated manifolds by graphics hardware. We also show that the Hamiltonian Cycle problem is NP-Complete for planar subcubic graphs of arbitrarily high girth. As a by-product we prove that there exist tri-Hamiltonian planar subcubic graphs of arbitrarily high gir...