Two kinds of B-basis of the algebraic hyperbolic space

In this paper, two new kinds of B-basis functions called algebraic hyperbolic (AH) Bezier basis and AH B-Spline basis are presented in the space (?)k=span{1,t,...,tk-3,sinht,cosht}, in which K is an arbitrary integer larger than or equal to 3. They share most optimal properties as those of the Bezier basis and B-Spline basis respectively and can represent exactly some remarkable curves and surfaces such as the hyperbola, catenary, hyperbolic spiral and the hyperbolic paraboloid. The generation of tensor product surfaces of the AH B-Spline basis have two forms: AH B-Spline surface and AH T-Spline surface.     

Shape modification of Bézier curves by constrained optimization

The Bézier curve is one of the most commonly used parametric curves in CAGD and Computer Graphics and has many portant problem, and is also an important research issue in CAD/CAM and NC technology fields. This work investigates the curves to satisfy the given constraints and modify the shape of the curves optimally. Practical examples are also given.     

基于约束优化的有理Bezier曲线形状修改

研究了基于某种约束条件的有理Bezier曲线的形状修改,约束条件为曲线通过某个单点或多个点,或在端点处满足某种切矢条件。方法是修改控制点。目的是使得修改前后的曲线的控制点的改变量最小。给出了具体控制点的扰动的计算公式,且给出了具体实例。     

圆锥曲线的有理三次Bezier表示

给出圆锥曲线上的两个控制点,利用有理曲线升阶方法,求出有理三次B6zier曲线的另外两个控制顶点以及权因子γ的值,从而达到用有理三次B6zier曲线对已给定的圆锥曲线的精确表示,如双曲线弧、抛物线弧和椭圆弧的表示。并给出了数值实例。     

基于MACRO的非圆二次旋转曲线轮廓的数控加工研究

针对常规手工编程中难以加工非圆二次旋转曲线的问题,对华中数控系统中典型的非圆二次函数公式曲线轮廓的车削加工进行研究。首先根据加工轮廓确定中心在坐标原点,且不倾斜的曲线方程,在solidworks软件中创建表达式,应用规律曲线参数模块绘制出曲线图形;然后将表达式中的方程进行坐标旋转及平移转换,绘制出与加工图纸一致的曲线轮廓;最后采用分析归纳法得出二次旋转曲线的宏程序模块,并给出该宏程序在旋转双曲线和椭圆曲面零件加工中的编程应用。实践表明,该宏程序对数控编程基础人员灵活应用非圆二次旋转曲线轮廓的编程方法与技巧有实际的指导意义。     

Convexity-preserving interpolation of trigonometric polynomial curves with a shape parameter

In computer aided geometric design(CAGD) ,it is often needed to produce a convexity-preserving interpolating curve according to the given planar data points. However,most existing pertinent methods cannot generate convexity-preserving in-terpolating transcendental curves;even constructing convexity-preserving interpolating polynomial curves,it is required to solve a system of equations or recur to a complicated iterative process. The method developed in this paper overcomes the above draw-backs. The basic idea is:first to construct a kind of trigonometric polynomial curves with a shape parameter,and interpolating trigonometric polynomial parametric curves with C2(or G1) continuity can be automatically generated without having to solve any system of equations or do any iterative computation. Then,the convexity of the constructed curves can be guaranteed by the appropriate value of the shape parameter. Performing the method is easy and fast,and the curvature distribution of the resulting interpolating curves is always well-proportioned. Several numerical examples are shown to substantiate that our algorithm is not only correct but also usable.     

高强度聚焦超声手术平台的Bezier曲线定位规划

提出了一种定位区域球方法来表示高强度聚焦超声手术平台在定位运动时肿瘤在其工作空间中的位置和姿态. 针对该简化肿瘤模型, 使用最近邻近查询方法确定了治疗头和超声焦点在定位到肿瘤目标过程中必须经过的中间位姿和目标位姿. 根据确定的位姿, 把组合Bezier曲线的连续条件和SO(3)的De Casteljau算法结合, 构造出了一条在衔接位姿C2连续的组合Bezier曲线路径用于定位, 并且根据一例肝脏肿瘤病例对各种连续路径作了详细分析.     

Shape memory behavior of SMPU knitted fabric

A preliminary investigation of shape memory (SM) effects of SMPU (shape memory polyurethane) knitting fabric is presented in this paper. Three SMPU knitted fabrics series with different content of SMPU fibers: 100% SMPU, 50% SMPU and 50% cotton, 16% SMPU and 84% cotton are designed and manufactured in our lab. Their shape memory behaviors at different temperatures are characterized in terms of bagging. Our experimental results showed that shape memory effect can be improved with increasing content of SMPU fibers. A comparison between Lycra and SMPU knitted fabrics was also made to validate the shape memory effects of SMPU knitted fabrics.     

化学改性活性炭对Cu(Ⅱ)离子吸附性能的研究

将市售粉状活性炭用16%硝酸进行氧化,再用0.1mol.L-1的氢氧化钠进行处理,制得化学改性活性炭,并对其吸附性能进行了研究.实验结果表明,改性后的活性炭较改性前对Cu2 离子的吸附能力提高60%以上.     

一种食饵捕食系统的定性分析

讨论了一类食饵捕食系统。主要利用线性变分矩阵的方法讨论了系统平衡点的性态，并用数学分析的方法证明了方程逆时针方向周期解的存在性，最后对结论相应的生态学意义给予了说明。     

高应变率下Zr基非晶合金的单轴压缩断裂行为

采用分离式Hopkinson压杆装置(SHPB)和扫描电镜(SEM)技术研究了不同高应变率下Zr基非晶合金样品(Zr55Cu30Al10Ni5)的变形行为和断口形貌。研究发现与准静态压缩形变相比,高应变率水平(3400 s-1和1900 s-1)下,非晶合金样品断裂应力显著降低,最大降低约达40%。扫描电镜形貌观察表明,非晶合金的高速断裂发生在一条主剪切带上,主剪切面偏离45°最大切应力面。同时断口形貌为明显的脉络花样,并覆盖有大量液滴状和不规则形状熔融物,表明高应变率下断裂表面温升较准晶态断裂有所增加。     

计及SVC影响的10kV配电线路的理论线损计算

将目前的10kV理论线损分析方法扩展到包含静止无功补偿器(SVC)的计算中。在线性控制方式的基础上，建立SVC补偿容量的表达式，并配合迭代算法进行求解。从而能够计算整个10kV配电线路的理论线损．并在实际线路上进行了试算。方法简单实用，为进一步优化分析提供了根据。     

基于支持向量机的siRNA降解效率预测

为了辅助siRNA的设计,从已发表文献中共收集到573个siRNA的实验数据,使用基于统计学习理论的支持向量机(SVM)方法,提取了siRNA序列的碱基对关联性(BBC)特征,然后使用十倍交叉验证方法,对siRNA沉默目标基因的效率进行了预测.结果表明,基于支持向量机,选用多项式核作为核函数的算法具有最高的AUC值(0.73,ROC曲线图)和最高的r值(0.43,Pearson相关系数分析),优于以前基于打分的算法.结果说明,在以后的siRNA的设计中应该更多关注碱基之间的关联信息.     

耐水和低游离甲醛脲醛树脂的合成与改性

为寻求合适的工艺条件以提高脲醛树脂胶粘剂的综合性能,采用了降低甲醛/尿素物质的量比、改进合成工艺、加入改性剂等3种途径优化了脲醛树脂的合成方法.实验结果表明:以甲醛和尿素为单体,添加适量的聚乙烯醇和三聚氰胺改性剂,甲醛和尿素最佳物质的量比约为1.5:1,尿素分3次(11.4 g、0.5 g、0.2 g)投料,反应温度控制在(35℃-85℃),反应时间约60min,用聚乙烯醇和三聚氰胺进行改性,可制得综合性能较好的低毒耐水脲醛树脂胶粘剂.产品质量达到国家相关规定指标.     

预应力混凝土梁桥上部结构综合评价方法

建立针对缺损预应力混凝土梁桥上部结构的多层次评估模型,提出模型中各项评价指标并初步确定其分级标准.构造正态关联函数计算确定无下属层元素评价指标与相应各评价等级的关联度,并在对模型中分项层及指标层元素进行评价时,考虑同下属于某元素的各元素的缺损状态进行权重修正计算.采用关联度及结构评定标度共同表征预应力混凝土梁桥上部结构的缺损状态,故该方法可针对预应力结构进行细致的评价,并且结果与现行<公路桥涵养护规范>的评价方法相统一.最后,对吉林省某一实际桥梁缺损状态进行了详细的评估,可作为算例供工程参考.     

New exact solutions of nonlinear differential-difference equations with symbolic computation

In this paper, the Toda equation and the discrete nonlinear Schrdinger equation with a saturable nonlinearity via the discrete ＂ （G′/G＂）-expansion method are researched. As a result, with the aid of the symbolic computation, new hyperbolic function solution and trigonometric function solution with parameters of the Toda equation are obtained. At the same time, new envelop hyperbolic function solution and envelop trigonometric function solution with parameters of the discrete nonlinear Schro¨dinger equation with a saturable nonlinearity are obtained. This method can be applied to other nonlinear differential-difference equations in mathematical physics.     

银行储蓄所储蓄存款余额预测分析

本文采用灰色系统GM预测模型和二次曲线预测模型,分别对银行储蓄所“月日平均余额”和“年月平均余额”进行统计分析,为制定考核标准,预测发展规模提供理论依据.