曲面体纹理映射技术的研究

当使用单幅图像对曲面体表面进行颜色纹理映射时,需要根据曲面体的参数方程反求顶点的纹理坐标,求解过程依赖于具体的曲面体方程,计算过程复杂,针对这个问题,本文提出了一种统一纹理映射方法,使得在划分曲面体的网格顶点时就直接计算了纹理坐标,计算公式统一,便于绘制颜色纹理与凹凸纹理.     

均匀三次B样条曲面顶点反求的整体算法

本文推导出一个由均匀三次B样条曲面上型值点反求网格顶点的整体算法公式,明显地展示出型值点与网格顶点间的函数关系.如果给定曲面上m×n个型值点,再按边界条件给最外层网格顶点赋值,则其余m×n个网格顶点全部可由该式解出.计算过程很简单.克服内存不足的几种措施也在此作了介绍.     

CE-Bézier可展曲面的设计与形状调整

为了解决工程中可展曲面位置与形状难以调整和控制的问题,基于3D射影空间中点和平面间的对偶性这一重要思想,提出了2种直接、简单有效的可展曲面设计新方法.首先,构造了一组含有2个形状参数α、γ的三次多项式调配函数,并定义了一种带2个形状控制参数的CE-Bézier曲线族,然后利用这种带参数的CE-Bézier调配函数生成了具有CE-Bézier基的控制平面,并由该控制平面来进行可展曲面的设计,同时给出了在CE-Bézier基函数下可展曲面的参数表示形式.由新方法生成的可展曲面不仅具有灵活的局部形状可调性和更强的描述能力,而且保留了Bézier曲面的特性,特别是当α、γ都取值为1时,所生成的可展曲面即为Bézier可展曲面.2种可展曲面设计方法的应用实例表明,该设计方法不仅简单、有效,而且易于控制曲面形状,从而为可展曲面的设计提供了一种新途径.     

新型曲面四边形边界元精细后处理方法研究

为了精确计算三维静电场的电场强度和电位分布,提出了新型曲面四边形边界元方法．在该方法中,对模型边界面进行二阶四边形单元剖分,对二阶单元顶点上的节点号重新编号,以单元的顶点为求解点,根据二阶四边形曲面参数方程,结合面积比值法定义的曲面单元顶点的形状函数,计算曲面单元顶点的函数值．与一阶平面四边形边界元相比,新型曲面边界元法在没有增加计算节点的情况下,由于采用更接近实际边界的曲面积分,计算精度将明显提高．但由于边界面采用二阶单元粗略剖分,单元数量相对较少,剖分后的模型较粗糙．虽然顶点节点上的函数值比较精确,但只能以平面线性单元的形式显示,离实际模型边界差别较大．本文就此提出边界元精细后处理方法．在该方法中,对曲面单元两边按一定步长等分,再根据曲面的参数方程把曲面单元精细显示出来．单元上新建节点的函数值可由曲面单元顶点上的函数值和面积比值法定义的形状函数插值得到．最后形成经精细显示后的新型曲面边界元方法．算例表明,经精细显示后边界面比未处理前更接近实际边界．     

二色有向图及二色有向自补图的计数与构造

通过构造一种新的群,解决了二色有向图及二色有向自补图的计数问题.获得了有 m 个顶点的一种颜色和 n 个顶点的另一种颜色的二色有向图的计数发生函数B_(m,n)(x)及二色有向自补图的数目分别是 B_(m,n)(x)=Z(S_m*S_n;1+x)和 Z(S_m*S_n;0,2,0,2,…).并构造出 m=n=2的全部76个二色有向图及全部12个二色有向自补图.     

MATLAB中隐函数绘图方法探究

MATLAB作为一种功能强大的仿真软件,在科学计算和工程绘图方面也有广泛的应用。针对隐函数求解不便并且图形难以手工绘制的问题,该文研究用MATLAB软件绘制二维隐函数曲线和三维隐函数曲面的方法：利用软件提供的ezplot函数可以直接绘制二维隐函数曲线,并讨论了二维隐函数带变量使用的情况;采用等值面计算函数isosurface和面元渲染函数patch可以分步实现三维隐函数曲面的绘图。根据上述方法给出一些具体应用实例和绘图结果。实践表明,MATLAB软件能有效解决比较复杂的隐函数绘图问题。     

4次带参Bézier可展曲面的设计

摘要： 为了方便解决工程中可展曲面位置与形状难以调节和控制的问题,提出了2种带形状参数的Bézier可展曲面设计新方法. 基于3D射影空间中点和平面间的对偶性,利用一种带形状参数的4次λ Bézier调配函数生成了具有4次λ Bézier基的控制平面,并由该平面进行包络和脊线可展曲面的设计,同时给出了在4次λ Bézier基函数下2种可展曲面的参数表示形式. 该方法生成的可展曲面不仅具有良好的形状可调性,而且保留了Bézier曲面的许多特性, 特别当参数λ取值为0时, 所生成的可展曲面即为3次Bézier可展曲面. 最后,对所设计的可展曲面进行了形状与性质分析,并给出了可展曲面间G2光滑拼接的条件. 实例结果表明,所提方法不仅直接、简单有效,而且易于控制可展曲面的形状,从而为可展曲面的设计提供了一种有效的新途径.
关键词： 中图分类号： 文献标志码： A


Abstract：     

几类图的同构因子分解

本文解决了以下几类图的同构因子分解问题:1.G=C_n×P_s,n为偶数,k为C_n每点的度数,ks+2s-2为素数;2.G=C_n×P_s,其中j_rn/2,s为偶数,rs+s-1为素数;3.G=C_n×C_s,其中n为偶数,2r+1为素数。     

基于BPLI从二维平行轮廓线重建三维表面的新算法

系统分析了BPLI方法的基本原理,在保持BPLI解决分支问题和对应问题的优越性的基础上提出系列新算法：首先提出一种新的轮廓线分段匹配算法,简化了轮廓线细化工作并提高了匹配效果;其次,提出一种求解空间多边形三角剖分的新算法,消除了退化区域。这些工作还使得新算法进行三维表面重构有效地提高了计算效率。     

构建基于曲面的秘密共享方案

为了解决密码系统中二元参数密钥的秘密共享问题,引入多维空间参数曲面的概念,按照门限秘密共享的思想和参数曲面上整数点可微的研究思路,利用两条曲面曲线的交点来构建(2,n)情形的门限体制,通过曲面上参数曲线的切向量张成的超切面与曲面曲线的交点来构建(s,n)(n≥3)情形的门限体制.结果表明,该门限方案满足重构要求和安全性要求,是一个直观完备的秘密共享方案,它较Blakley门限方案更具体实用,且易于实现.     

Voronoi样本与ACO星系团样本的比较

提出以Ｖｏｒｏｎｏｉ镶嵌作为分析宇宙大尺度结构的工具,并以此讨论了星系的类似Ｖｏｒｏｎｏｉ镶嵌的分布,同时运用Ｖｏｒｏｎｏｉ镶嵌模拟星系分布,通过比较模拟样本与星系团实际样本的异同,表明二者具有极其相似的分布特性,论证了利用Ｖｏｒｏｎｏｉ镶嵌研究宇宙大尺度结构的合理性与优越性。     

最小Q-特征值第二小的给定悬挂点数的非二部单圈图

图的最小Q-特征值常被用来衡量一个图的非二部程度,受到研究者的广泛关注。在路Pn-k-2的一端接出一个圈C3,另一端接出k个悬挂边,所得的n阶图记为Ukn(3)。范益政等人最近证明Ukn(3)是最小Q-特征值达到最小的图。在他们的基础上,证明C13(n-k-1)是最小Q-特征值达到第二小的图,其中C13(n-k-1)是将Ukn(3)的一条悬挂边移至与悬挂邻点相邻的非悬挂点上所得的图。     

非连通图(K1∨(P(1)n∪ P(2)n)) ∪ P(3)n及(K1∨(P(1)n∪ P(2)n)) ∪ P(3)n∪ St(n)的优美性

 给出了非连通图(K₁∨(P⁽¹⁾_n∪ P⁽²⁾_n)) ∪ P⁽³⁾_n和(K₁∨(P⁽¹⁾_n∪ P⁽²⁾_n)) ∪ P⁽³⁾_n∪ St(n),且对其优美性进行了研究。证明了如下结论：设 n 为任意正整数,则当n≥4时,非连通图 (K₁∨(P⁽¹⁾_n∪ P⁽²⁾_n)) ∪ P⁽³⁾_n和(K₁∨(P⁽¹⁾_n∪ P⁽²⁾_n)) ∪ P⁽³⁾_n∪ St(n)均是优美图;其中,Pn 是 n 个顶点的路,Kn 是n个顶点的完全图, St(n) 是 n+1 个顶点的星形树,G₁ ∨ G₂ 是图 G1 与 G2 的联图。     

An algorithm for the spectral immunity of binary sequence with period 2<Superscript><Emphasis Type="Italic">n</Emphasis></Superscript>

To resist the fast algebraic attack and fast selective discrete Fourier transform attacks, spectral immunity of a sequence or a Boolean function was proposed. At the same time, an algorithm to compute the spectral immunity of the binary sequence with odd period N was presented, here N is a factor of 2 ⁿ ? 1, where n is an integer. The case is more complicated when the period is even. In this paper, we compute linear complexity of every orthogonal sequence of a given sequence using Chan-Games algorithm and k - error linear complexity algorithm. Then, an algorithm for spectral immunity of binary sequence with period N = 2 ⁿ is obtained. Furthermore, the time complexity of this algorithm is proved to be O(n).     

A quantum algorithm for the dihedral hidden subgroup problem based on lattice basis reduction algorithm

To optimize the algorithms for the dihedral hidden subgroup problem, we present a new algorithm based on lattice basis reduction algorithm. For n 〈 120, we reduce the dihedral hidden subgroup problem to shortest vector problem. A subroutine is given to get a transition quantum state by constructing a phase filter function, and then the measurement basis are derived based on the lattice basis reduction algorithm for solving low density subset sum problem. Finally, the parity of slope s is revealed by the measurement. This algorithm needs preparing mn quantum states, m qubits to store and O（n2） classical space, which is superior to existing algorithms.     

ATHK1 acts downstream of hydrogen peroxide to mediate ABA signaling through regulation of calcium channel activity in Arabidopsis guard cells

Plants gradually develop their ability to tolerate environmental water deficit as part of the evolutionary process.Abscisic acid(ABA) plays a critical role during drought and osmotic stress.Several histidine protein kinases are regarded as osmotic sensors or regulators in the adaptive response of plants to water deficit.In this study,we report that ATHK1,which was previously shown to function as an osmotic regulator,is involved in ABA-induced stomatal signaling in Arabidopsis.Mutants null for ATHK1 expression were unable to transmit normal ABA responses in guard cells,including inducing stomatal closure,producing hydrogen peroxide and activating calcium influx.Moreover,patch clamp and confocal analysis demonstrated that ATHK1 may function downstream of hydrogen peroxide in ABA-induced stomatal closure,by regulating calcium channel activity and calcium oscillation in Arabidopsis guard cells.     

一种估算砂岩核磁T_2谱新方法

根据核磁共振弛豫机制,基于三维数字岩心技术建立一种估算砂岩核磁共振横向弛豫(T_2)谱的新方法。采用过程模拟法重建砂岩三维数字岩心,通过Delaunay剖分将砂岩微观孔隙结构划分为多个四面体孔隙单元,再用几何方法和Monte Carlo方法相结合求出每个孔隙单元的表面积与体积之比(S/V),进而获得砂岩模拟的核磁T2谱。经过大量模拟试验筛选参数,减小计算误差。考虑单峰态和双峰态核磁T_2谱,模拟结果和实验结果基本吻合。该方法有助于研究粒度分布、孔隙结构等对岩石核磁共振响应的影响。     

非连通图(P1∨Pn)∪Gr和(P1∨Pn)∪(P3∨r)及Wn∪St(m)的优美性

讨论非连通图((P₁∨P_n)∪G_r和(P₁∨P_n)∪(P₃∨_r)及W_n∪St(m)的优美性, 证明了如下结论： 设n,m为任意正整数, s=［n/2］, r=s-1, G_r是任意具有r条边的优美图, 则当n≥4时, 非连通图((P₁∨P_n)∪G_r和(P₁∨P_n)∪(P₃∨_r)是优美图； 当n≥3, m≥s时, 非连通图W_n∪St(m)是优美图. 其中, P_n是n个顶点的路, K_n是n个顶点的完全图, n是K_n的补图, G₁∨G₂是图G₁与G₂的联图, W_n是n+1个顶点的轮图, St(m)是m+1个顶点的星形树.     

Optical turbulence profiling with single star SCIDAR technique

In order to characterize optical turbulence, we have developed a single star SCIDAR （SSS） for measurement of the distribution of Cn^2 with height. The SSS consists of a 40 cm telescope and a CCD camera for fast sampling of stellar scintillation pattern. Spatio- temporal auto and cross-correlation functions of the single star images are computed, providing vertical profiles of optical turbulence intensity C2（h） and wind speed V（h）. Using this new SSS experiment, profiles of turbulence can be obtained from the ground to the top of atmosphere, allowing the determination of seeing, isoplanatic angle and coherence time. Detailed characteristics of atmospheric optical turbulence are important for active and passive imaging, astronomical site testing, adaptive optics, laser communications, target tracking and designation, and laser beam control. We plan to improve the robotization of the SSS to be able to use it routinely even under harsh weather and altitude conditions that we expect to encounter on the high Tibetan plateau or at Dome A in Antarctica. SSS will also be applied for the site testing campaign of the future Chinese extremely large telescope.     

Kinetic analysis and strain-compensated constitutive models of Ti-42.9Al-4.6Nb–2Cr during isothermal compression

The hot deformation behavior of Ti-42.9Al-4.6Nb–2Cr (at. %) was investigated by isothermal compression tests at the deformation temperature range of 1373–1573 K, strain rate range of 0.001–1.0 s⁻¹, up to the strain of 0.69. The flow stress test results of Ti-42.9Al-4.6Nb–2Cr showed negative temperature and positive strain rate sensitivity. Besides, strain had a great effect on the hot deformation behavior of Ti-42.9Al-4.6Nb–2Cr. Kinetic analysis was adopted to assess the hot workability of Ti-42.9Al-4.6Nb–2Cr via apparent activation energy (Q) of hot deformation, strain-rate sensitivity index (m) and strain hardening index (n). The Q value varied from 607.1 ± 0.7 kJ·mol⁻¹ to 512.6 ± 10.8 kJ mol⁻¹ with the increasing of strain from 0.1 to 0.6. The effect of strain on the Q value at the deformation temperatures below 1473 K was mainly related to dynamic recrystallization of γ phase and kinking of γ lamellae, while the Q value at the deformation temperature above 1473 K might be linked to γ→α phase transformation and DRV of α phase. Based on the kinetic analysis, strain-compensated Arrhenius model and Hensel-Spittel model were successfully established to predict the hot workability (flow stress). Average absolute relative errors of established strain-compensated Arrhenius model and Hensel-Spittel model were 7.52% and 11.95%, respectively. Moreover, both established constitutive models can be extrapolated for predicting the flow stress of Ti-42.9Al-4.6Nb–2Cr to larger strain levels.