Automatic G arc spline interpolation for closed point set

A method for generating an interpolation closed G¹ arc spline on a given closed point set is presented. For the odd case, i.e. when the number of the given points is odd, this paper disproves the traditional opinion that there is only one closed G¹ arc spline interpolating the given points. In fact, the number of the resultant closed G¹ arc splines fulfilling the interpolation condition for the odd case is exactly two. We provide an evaluation method based on the arc length as well such that the choice between those two arc splines is made automatically. For the even case, i.e. when the number of the given points is even, the points are automatically moved based on weight functions such that the interpolation condition for generating closed G¹ arc splines is satisfied, and that the adjustment is small. And then, the G¹ arc spline is constructed such that the radii of the arcs in the spline are close to each other. Examples are given to illustrate the method.     

G 2 interpolation and blending on surfaces

We introduce a method for curvature-continuous (G ²) interpolation of an arbitrary sequence of points on a surface (implicit or parametric) with prescribed tangent and geodesic curvature at every point. The method can also be used forG ² blending of curves on surfaces. The interpolation/blending curve is the intersection curve of the given surface with a functional spline (implicit) surface. For the construction of blending curves, we derive the necessary formulas for the curvature of the surfaces. The intermediate results areG ² interpolation/blending methods in IR².     

G2连续的低次避障代数样条曲线

为便于机器人在避障时能高速前进,把整体G2连续的低次避障曲线从参数形式拓展到代数样条形式上。首先,对导向折线段中除去首末线段的其他线段插入中点,以生成一组控制多边形;然后,根据各控制多边形和与之对应的障碍物,得到既能使曲线规避所有障碍物,又能使曲线在整体上保持G2连续的形状因子。低次避障代数样条曲线不仅能够直接得到与给定点之间的位置关系,还具有次数低、连续阶高、计算简单、保形性好和便于控制的优点。曲线在次数为3时更是具有局部可调性,其在设计时的灵活度得以增加。     

Bivariate C cubic spline space over a nonuniform type-2 triangulation and its subspaces with boundary conditions

In this paper, we discuss the algebraic structure of bivariate C¹ cubic spline spaces over nonuniform type-2 triangulation and its subspaces with boundary conditions. The dimensions of these spaces are determined and their local support bases are constructed.     

深海适冷菌Pseudoalteromonas sp. SM9913胞外多糖对Pb2+和Cu2+的吸附性能研究

采用深海适冷菌Pseudoalteromonas sp. SM9913分泌的胞外多糖（EPS）分别对Pb²⁺和Cu²⁺进行吸附,研究了多糖用量、pH、吸附时间和共存离子对EPS吸附性能的影响及EPS对Pb²⁺和Cu²⁺的吸附热力学.结果表明,EPS对Pb²⁺和Cu²⁺的吸附量随EPS投加量的增加而减小.EPS对Pb²⁺和Cu²⁺的最佳吸附pH分别为4.5～5.5和4.5～6.0. EPS对Cu²⁺的吸附平衡时间为90　min,对Pb²⁺的吸附平衡时间则长达180　min.共存离子Ca²⁺、Mg²⁺、Na⁺、K⁺的加入均降低了EPS对Pb²⁺的吸附量,Ca²⁺、Mg²⁺的加入降低了EPS对Cu²⁺的吸附量,但低浓度的Na⁺和实验范围浓度的K⁺不仅没有降低反而增加了EPS对Cu²⁺的吸附量.Freundlich和Dubinin-Radushkevich方程均能较好地描述SM9913胞外多糖吸附Pb²⁺和Cu²⁺的热力学过程,由Dubinin-Radushkevich方程得到SM9913胞外多糖对Pb²⁺和Cu²⁺的最大吸附量分别为243.3 mg/g (10℃) 和36.7 mg/g (40℃).胞外多糖吸附金属离子前后的红外光谱分析表明,多聚糖中C—O—C、乙酰基和羟基是起主要吸附作用的官能团.     

3个控制顶点的类三次Bézier螺线

目的 为了使得过渡曲线的设计更为简单高效。提出基于3个控制顶点的类三次Bézier螺线。方法 通过对基函数的研究首先构造了3条在一定条件下曲率单调递减的类三次Bézier曲线,并由参数的对称性得另3条曲率单调递增的曲线。它们具有端点性、凸包性、几何不变性等三次Bézier曲线的基本性质,特点是只有3个控制顶点。接着严格地证明了此类曲线曲率单调的充分条件。 结果 有两条曲线比三次Bézier曲线的曲率单调条件范围大,且类三次Bézier螺线与三次Bézier螺线存在一定的位置关系。这6条曲线中有4条曲线的一个端点处曲率为零,可组合成4对类三次Bézier螺线来构造两圆弧间半径比例不受限制的S型和C型G²连续过渡曲线;剩下的两条曲线在两圆弧半径相差较大的情况下都可做不含曲率极值点的过渡曲线。最后用实例表明了此类曲线的有效性。结论 在过渡曲线设计中基于3个控制顶点的类三次Bézier螺线比三次Bézier螺线更为简单高效。     

Single quantum dot-micelles coated with gemini surfactant for selective recognition of a cation and an anion in aqueous solutions

The synthesis of quantum dot coated with cetyltrimethyl ammonium bromide (CTAB) and gemini surfactant [C₁₂H₂₅N⁺(CH₃)₂(CH₂)₄(CH₃)₂N⁺C₁₂H₂₅]·2Br⁻ (C_12-4-12) in aqueous solution have been described. It is characterized by photoluminescent spectroscopy, UV–vis spectroscopy and transmission electron microscopy (TEM), etc. In comparison with CTAB-coated QDs, the QDs coated with C_12-4-12 respond selectively to both transition metal ion copper and fluoride ion in aqueous media. When Cu²⁺ is bound to C_12-4-12-coated QD micelles, the fluorescence intensity is quenched. Linear relationships are found between the relative fluorescence intensity and the concentration of Cu²⁺ in the range 0–500 μM, which is best described by a Stern–Volmer-type equation. Meanwhile, it is found that F⁻ enhanced the luminescence of the C_12-4-12-coated QD micelles in a concentration dependence that is described by a Langmuir binding isotherm equation in the range 0–300 μM. The limits of detection of Cu²⁺ and F⁻ are 1.1 and 0.68 μM, respectively. The possible mechanism is discussed.     

Some quadrature formulas for functions partially holomorphic with respect to each variable in a Jordan polydomain in C 2 and a complex double integral formula

In this paper, quadrature formulas with remaining term in integral form for functions partially holomorphic with respect to each variable in a Jordan polydomain in C ² and a complex double integral formula are given. For this, we used the Cauchy Integral formula for Jordan polydomain in C ².