非球面最适球面的确定方法——三点法

根据非球面生产的实际情况．指出非球面最适球面的确定方法．详细分析最适球面的计算方法．并对一抛物面进行了实例计算，通过与最小二乘法的计算结果比较．指出该方法具有计算简单、与加工工艺过程相符合等特点。     

大口径方形离轴非球面的非球面度计算与应用研究

采用不同的数值计算方法求解了大口径(340mm×340mm)方形离轴非球面的最接近球面曲率半径和非球面度,得出了各种不同的磨削量及其对应的分布结构。对不同的最接近球面及非球面度所适用的加工工艺和检测方法进行了分析和评价。这对离轴非球面的加工和检测具有一定的指导意义。     

The Effects of Chemical Bonding at Subatomic Resolution: A Case Study on α-Boron

Similar to classical asphericity shifts, aspherical deformations of the electron density in the atomic core region can result in core asphericity shifts in refinements using a Hansen-Coppens multipolar model (HCM), especially when highly precise experimental datasets with resolutions far beyond sin(θ)/λ ≤ 1.0 Å⁻¹ are employed. These shifts are about two orders of magnitude smaller than their counterparts caused by valence shell deformations, and their underlying deformations are mainly of dipolar character for 1st row atoms. Here, we analyze the resolution dependence of core asphericity shifts in α-boron. Based on theoretical structure factors, an appropriate Extended HCM (EHCM) is developed, which is tested against experimental high-resolution (sin(θ)/λ ≤ 1.6 Å⁻¹) single-crystal diffraction data. Bond length deviations due to core asphericity shifts of α-boron in the order of 4–6·10⁻⁴ Å are small but significant at this resolution and can be effectively compensated by an EHCM, although the correlation of the additional model parameters with positional parameters prevented a free refinement of all core model parameters. For high quality, high resolution data, a proper treatment with an EHCM or other equivalent methods is therefore highly recommended.     

Asphericity in the Fermi Surface and Fermi Energy of Na-K, Na-Rb and Na-Cs Binary Alloys

Detailed theoretical investigations into asphericity in the Fermi surface (FS) and Fermi energy (FE) ofNa1_xKx, Na1_xRbx, and Na1_xCsx binary solid solutions are carried out for the first time. The alloying behavior ofthe K, Rb, and Cs with the Na generates the Fermi surface distortion (FSD) of bce simple metals. The FS of Na-K,Na-Rb, and Na-Cs solid solution is a distorted sphere with the largest deviation along [110]. We have found that theimpact of local-field correction function on FSD is maximun at [100] point and minimum at [111] point. The exchangeand correlation effect is found to suppress the value of FE.     

计算机控制光学表面成形法初值的确定

介绍了计算机控制光学表面成形法的原理,分析了几种非球面度的测量方法,研究了非球面度的不同计算方法对采用计算机控制光学表面成形法加工非球面的影响。从光学零件加工的角度对计算机控制光学表面成形法初值的确定进行了探讨。     

光学非球面元件非球面度计算方法

详细介绍光学非球面元件非球面度计算的牛顿迭代法、近似法、最小二乘法3种方法，并根据工程实践比较了3种方法的优缺点，得出了工程应用中的结论：近似法适用于一些相对孔径较小的非球面，否则误差会较大；牛顿迭代法的精度较高，但计算量大也最复杂，且不能直接得到最接近参考圆的圆心位置坐标；最小二乘法的计算方法简单，不涉及求导、积分、迭代，适合编写计算程序，且可直接得到最接近参考圆的圆心位置坐标。     

On the residual finiteness and other properties of (relative) one-relator groups

A relative one-relator presentation has the form where is a set, is a group, and is a word on . We show that if the word on obtained from by deleting all the terms from has what we call the unique max-min property, then the group defined by is residually finite if and only if is residually finite (Theorem 1). We apply this to obtain new results concerning the residual finiteness of (ordinary) one-relator groups (Theorem 4). We also obtain results concerning the conjugacy problem for one-relator groups (Theorem 5), and results concerning the relative asphericity of presentations of the form (Theorem 6).

     

Asymptotic hereditary asphericity of metric spaces of asymptotic dimension 1

Asymptotic hereditary asphericity (AHA) is a coarse property introduced by Januszkiewicz and ?wia?tkowski in the context of systolic complexes and groups. We show, that spaces of asymptotic dimension 1 are all AHA.     

On the fundamental group of real toric varieties

LetX (Δ) be the real toric variety associated to a smooth fan Δ. The main purpose of this article is: (i) to determine the fundamental group and the universal cover ofX (Δ), (ii) to give necessary and sufficient conditions on Δ under which π₁(X(Δ)) is abelian, (iii) to give necessary and sufficient conditions on Δ under whichX(Δ) is aspherical, and when Δ is complete, (iv) to give necessary and sufficient conditions forC _Δ to be aK (π, 1) space whereC _Δ is the complement of a real subspace arrangement associated to Δ.     

干涉条纹密度的计算及其应用研究

采用光的干涉方法检测曲面光学表面的加工质量时,都需要事先设计好系统光路的最佳检测技术参数,并能对检测的难度进行有效的评估,从而确保检测的精度。该研究采用了一种计算干涉条纹密度的新方法,对任意光学曲面检测的难度进行评估,并用于确定球面参考光点光源的最佳位置。以非球面为例,计算了非球面的最接近球面的半径和最大非球面度以及非球面检测时球面参考光点光源的最佳位置,说明了计算干涉条纹密度方法在确定干涉检测系统光路调试最佳条件的优越性,可为各种干涉检测系统的设计以及优化调试过程提供理论依据和分析指导。