THE RELATIONSHIP BETWEEN PROJECTIVE GEOMETRIC AND RATIONAL QUADRATIC B-SPLINE CURVES

For two rational quadratic B-spline curves with same control vertexes, the cross ratio of four eollinear points are represented; which are any one of the vertexes, and the two points that the ray initialing from the vertex intersects with the corresponding segments of the twocurves, and the point the ray intersecting with the connecting line between the two neighboring vertexes. Different from rational quadratic Beeier curves, the value is generally related with the loeation of the ray, and the necessary and sufficient condition o5 the ratio being independent of the ray‘s loeation is showed. Alsn another cross ratio o5 the following four collinear points are suggested, i.e. one vertex, the points that the ray from the initlal vertex intersects respectivdy with the curve segmentt the line connecting the segments end points, and the line connecting the two neighboring vertexes. This cross ratio is concerned only whh the ray‘s location, butnot with the weights of the curve. Furthermore, the cross ratio is projective invariant under the projective transformation between the two segments.     

关于具有二次相关性收获率的捕食与被捕食系统极限环的存在性分析

讨论了一类两种群具有二次相关性收获率的捕食与被捕食系统,利用常微分定性方法和分支理论,得到了系统平衡点处的性态和极限环的存在性条件,并用Matlab软件对其进行数值模拟,推广了相关文献中两种群捕食模型定性分析的相应结论.     

Real Hypersurfaces Having Many Pseudo-hyperplanes

Abstract

Let nand dbe natural integers satisfying n ≥ 3 and d ≥ 10. Let Xbe an irreducible real hypersurface Xin ? ⁿ of degree dhaving many pseudo-hyperplanes. Suppose that Xis not a projective cone. We show that the arrangement ? of all d ? 2 pseudo-hyperplanes of Xis trivial, i.e., there is a real projective linear subspace Lof ? ⁿ (?) of dimension n ? 2 such that L ? Hfor all H ∈ ?. As a consequence, the normalization of Xis fibered over ?¹in quadrics. Both statements are in sharp contrast with the case n = 2; the first statement also shows that there is no Brusotti-type result for hypersurfaces in ? ⁿ , for n ≥ 3.     

Statistical Computations on Biological Rhythms I: Dissecting Variable Cycles and Computing Signature Phases in Activity-Event Time Series

We propose a computational methodology to compute and extract circadian rhythmic patterns from an individual animal’s activity-event time series. This lengthy dataset, composed of a sequential event history, contains an unknown number of latent rhythmic cycles of varying duration and missing waveform information. Our computations aim at identifying the onset signature phase which individually indicates a sharp event intensity surge, where a subject-night ends and a brand new cycle’s subject-day begins, and collectively induces a linearity manifesting the individual circadian rhythmicity and information about the average period. Based on the induced linearity, the least squares criterion is employed to choose an optimal sequence of computed onset signature phases among a finite collection derived from the hierarchical factor segmentation (HFS) algorithm. The multiple levels of coding schemes in the HFS algorithm are designed to extract contrasting patterns of aggregation against sparsity of activity events along the entire temporal axis. This optimal sequence dissects the whole time series into a sequence of rhythmic cycles without model assumptions or ad hoc behavioral definitions regarding the missing waveform information. The performance of our methodology is favorably compared with two popular approaches based on the periodogram in a simulation study and in real data analyses. The computer code and data used in this article are available on the JCGS webpage.     

Dual bases for Wang-Bézier basis and their applications

This paper presents the dual bases for Wang-Bézier curves with a position parameter L, which include Bézier curve, Wang-Ball curve and some intermediate curves. The Marsden identity and the transformation formulas from Bézier curve to Wang-Bézier curve are also given. These results are useful for the application of Wang-Bézier curve and their popularization in Computer Aided Geometric Design.     

电催化氧化技术处理苯酚废水研究

电化学氧化法可有效处理挥发酚类废水,而阳极材料性能直接制约其电氧化效率.本文分别针对不锈钢、柔性石墨和SnO2 /Ti复合材料测定了其析氧过电位,并以不锈钢、柔性石墨为阳极材料,在 5~6V直流电压下,对合成苯酚废水进行了电化学氧化处理.结果表明:析氧过电位次序为SnO2 /Ti>柔性石墨 >不锈钢,处理后水的COD值接近或小于 100mg·L-1,且出水的苯酚浓度小于 0. 5mg·L-1.     

LiBr分子基态光谱常数和分子常数研究

采用高精度的量子化学从头计算多参考组态相互作用方法和相关一致基, 计算了LiBr分子基态的光谱常数和势能曲线. 为获得更准确的结果, 计算中还考虑了二阶Douglas-Kroll-Hess相对论修正对LiBr分子基态的平衡键长、谐振频率和离解能影响. 将计算得到的势能曲线拟合为Murrell-Sorbie解析势能函数形式, 并进一步计算得到LiBr分子基态的其它光谱常数,ωeχe, αe, Be, D0. 比较发现它们与实验值符合的非常好. 通过求解核运动径向Schrodinger方程, 找到了LiBr分子基态的全部振动态. 还计算了每一个振动态的振动能级、经典转折点和惯性转动常数, 这些结果与已有的实验值一致.     

测量圆盘转动惯量产生误差的曲线研究

结合三线摆实验的基本过程,进行实验数据的采集。利用投影法来测量圆盘的转角大小,借助于matlab的cftool工具箱,对数据进行曲线拟合,对测出来的二组数据拟合,得到转角与百分差曲线图。通过误差的大小比较,得出圆盘转动惯量测量值与理论值的百分差随转角变化最接近于三次曲线。     

平面C-B样条的奇拐点分析

平面C-B样条曲线是三次均匀B样条的推广.通过移动C-B样条曲线段的一个控制点而固定其余三个控制点的方法,讨论了在曲线上形成零曲率点的移动控制点的轨迹,得到了C-B样条曲线段的尖点判别曲线、拐点判别区域,同时也给出了在曲线段上生成重结点的移动控制点的轨迹区域.