On the two-dimensional orthogonal drawing of series-parallel graphs

It has been known that every planar 4-graph has a 2-bend 2-D orthogonal drawing, with the only exception being the octahedron, every planar 3-graph has a 1-bend 2-D orthogonal drawing with the only exception being K₄, and every outerplanar 3-graph with no triangles has a 0-bend 2-D orthogonal drawing. We show in this paper that every series-parallel 4-graph has a 1-bend 2-D orthogonal drawing.     

Approximating tensor product Bézier surfaces with tangent plane continuity

We present a simple method for degree reduction of tensor product Bézier surfaces with tangent plane continuity in L₂-norm. Continuity constraints at the four corners of surfaces are considered, so that the boundary curves preserve endpoints continuity of any order α. We obtain matrix representations for the control points of the degree reduced surfaces by the least-squares method. A simple optimization scheme that minimizes the perturbations of some related control points is proposed, and the surface patches after adjustment are C^∞ continuous in the interior and G¹ continuous at the common boundaries. We show that this scheme is applicable to surface patches defined on chessboard-like domains.     

Some binomial formulas of the generalized Appell form

The authors aim here at finding all the generalizations of the binomial formula that are given by a generating-function of the generalized Appell form for a sequence of Newton polynomials. The formulas obtained include the well-known q-analogue of the binomial formula, several formulas involving hyperbolic functions, a trigonometric analogue, and some formulas involving the geometric and the exponential series.     

On the stability of the linear mapping in Banach modules

We prove the generalized Hyers-Ulam-Rassias stability of the linear mapping in Banach modules over a unital Banach algebra.     

The decomposition theorem for the family of complete quasi-convex mappings

In this paper, we will give a decomposition theorem for some type of holomorphic mappings. This result is the generalization of many known results.     

C语言中定义和引用语句间的内在联系及数组名、指针理解误区探讨

就C语言教学中数组名的量纲、数组名与指针的关系及指针的本质等教材和讲授中容易产生理解误区的内容进行了探讨,总结了C语言中数组定义和引用语句间的内在联系,将其归纳为“升格降格法”用以对数组和指针的使用进行量纲判断．     

Evidence of four light-induced metastable states in iron-nitrosyl complexes

Thermodynamic measurements on irradiated Na₂[Fe(CN)₅NO]⋅ 2H₂O reveal the existence of four light-induced long-lived metastable states, which decay exponentially in time. The activation energies and frequency factors of the four independent states are determined from isothermal calorimetric and differential scanning calorimetric measurements.     

Lifting inequalities for polytopes

We present a method of lifting linear inequalities for the flag f-vector of polytopes to higher dimensions. Known inequalities that can be lifted using this technique are the non-negativity of the toric g-vector and that the simplex minimizes the cd-index. We obtain new inequalities for six-dimensional polytopes. In the last section we present the currently best known inequalities for dimensions 5 through 8.     

Remark on uniqueness of mild solutions to the Navier-Stokes equations

We investigate a limiting uniqueness criterion to the Navier-Stokes equations. We prove that the mild solution is unique under the class , where bmo^-1 is the “critical” space including Lⁿ. As an application of uniqueness theorem, we also consider the local well-posedness of Navier-Stokes equations in bmo^-1.