略论利玛窦向东方文人介绍世界地图和演绎法思维的意义

考察利玛窦的西学输入给17世纪以后东亚文人所带来的学术意义。首先,考察动摇了中华中心主义世界观的世界地图——《坤舆万国全图》的意义,其次通过对欧几里得《几何原本》的翻译和介绍,讨论以演绎推理为根据的西方学问的明证性。然而,与利玛窦所料想的不同,原来中国并非没有和实用性无关的数理,因此在结论中,也将谈到邵雍的伏羲64卦方圆图给研究二进制的莱布尼茨带来的共鸣。

A Geometric Model of Multiaxial Warp-knitted Preform for Composite Reinforcement

A new geometric model of Multiaxial Warp-Knitted (MWK) performs, which is based on the experimental observations and analysis of basic stitch, is developed to relate the geometric parameters and process variables. The fiber volume fraction and fibre orientation of MWK reinforced composites are described in terms of structural and processing parameters in the model. And this model provides a basis for the prediction of mechanical behavior of the MWK reinforced composites.

On Common Eigenvector of Parametric Interaction Hamiltonian and Number-Difference Operator Derived by Virtue of Entangled State Representation

By virtue of the properties of bipartite entangled state representation we derive the common eigenvector of the parametric Hamiltonian and the two-mode number-difference operator. This eigenvector is superposition of some definite two-mode Foek states with the coefficients being proportional to hypergeometric functions. The Gauss contiguous relation of hypergeometrie functions is used to confirm the formal solution.

Interactive point cloud blending by drag-and-drop

With the rapid development of 3D digital photography and 3D digital scanning devices, massive amount of point samples can be generated in acquisition of complex, real-world objects, and thus create an urgent need for advanced point-based processing and editing. In this paper, we present an interactive method for blending point-based geometries by dragging-and- dropping one point-based model onto another model’s surface metaphor. We first calculate a blending region based on the polygon of interest when the user drags-and-drops the model. Radial basis function is used to construct an implicit surface which smoothly interpolates with the transition regions. Continuing the drag-and-drop operation will make the system recalculate the blending regions and reconstruct the transition regions. The drag-and-drop operation can be compound in a constructive solid geometry (CSG) manner to interactively construct a complex point-based model from multiple simple ones. Experimental results showed that our method generates good quality transition regions between two raw point clouds and can effectively reduce the rate of overlapping during the blending.

Non-hypergeometric Type of Polynomials and Solutions of Schrodinger Equation with Position-Dependent Mass

Using the coordinate transformation method, we study the polynomial solutions of the Schr6dinger equation with position-dependent mass （PDM）. The explicit expressions for the potentials, energy eigenvalues, and eigenfunctions of the systems are given. The issues related to normalization of the wavefunetions and Hermiticity of the Hamiltonian are also analyzed.

Fundamental Groups of Triangle Geometries

In this paper , depending on the theory of buildings, we obtain a kind of method completely different from past ones, to compute topological fundamental groups of some triangle geometries. This method will enable us to easily compulte topological fundametal groups of infinitely finite triangle geometries.

朵云书翰

篆书中堂苏轼《念奴娇·赤壁怀古》海琨(河南):这幅大篆作品,中锋用笔,线条凝练圆润,结字大小错落、参差有致,通篇布局严谨而又流畅,有西周金器铭文之妙。文中“风”、“傑”、“谈”、“笑”、“橹”、“滅”的金文篆法,未知作者据之何本?在此请教。

G^1 Continuous Condition of B-Spline Surfaces with Double Knots

The conditions for G1 continuity between two adjacent bicubic B-spline surfaces with double interior knots along their common boundary curve are obtained in this paper, which are directly represented by the control points of the two B-spline surfaces. As stated by Shi Xi-quan and Zhao Yan, a local scheme of constructing G1 continuous B-spline surface models with single interior knots does not exist; we may achieve a local scheme of (true) G1 continuity over an arbitrary B-spline surface network using these conditions.

守山阁学人群体的崛起与明清“西学”的延续性:以《几何原本》为例

一般以为明末利玛窦、徐光启引进“西学”以后,“利徐之学”在清代曾经中断,似乎只在“鸦片战争”以后,晚至“戊戌”时期的康、梁一辈学者,才重新开始“西学”启蒙运动。然而,清中叶以降江南地区学术传承脉络证明:以钱熙祚、顾观光、张文虎、李善兰为核心的学者群体在1837年即通过抄录、校勘、刊刻“守山阁丛书”,研究和传承明末耶稣会士翻译的天文、地理、数学等著作,并为战后之“西学”复兴做了铺垫。“守山阁丛书”及一系列包含“西学”书目之丛书的刊刻与发行,证明江南地区的乾嘉学者有一种内在和纯学术的热情。如同笛卡尔、帕斯卡哲学提倡“几何学精神”一样,李善兰、伟烈亚力续译《几何原本》(1858)后九卷,接续利玛窦、徐光启的“所以然”的“metaphysical study”,表现了“西学”启蒙运动的延续性。19世纪30年代起,“守山阁丛书”刊刻实践,以及与之相关的墨海书馆、江南制造局、京师同文馆、广方言馆译书活动,是一种延续性事业,更是“戊戌变法”中“西学”宣传运动的基础。总之,“守山阁丛书”学人群体的学术自觉,并不能以“冲击—反应论”的模式来解释,而需要某种形式的“内在理路”来说明。

A Formula Containing Four Independent Bases and Its Applications

A transformation formula containing four independent bases is found by a special inversion formula and it is applied to derive a few summation formulas for basic hypergeometric series only by elementary method. The hypergeometric series, the limits of those formulas are also obtained.

On fundamental groups of Finsler manifolds In memory of the centenary birthday of Professor S.S.Chern

In this paper,we study the growth of fundamental groups of Finsler manifolds.Some relationships between the growth of fundamental groups and the volume growth of universal covers of Finsler manifolds are found.Some estimates of entropies and the number of generators of fundamental groups of Finsler manifolds are given.Moreover,the quasi-isometry and the geometric norm in Finsler geometry are considered.

Ricci Curvature and Fundamental Group

Abstract By refined volume estimates in terms of Ricci curvature, the two results due to J. Milnor （1968） are generalized.

On Some Transformation and Summation Formulae for Bivariate Basic Hypergeometric Series

The purpose of this paper is to establish several transformation formulae for bivariate basic hypergeometric series by means of series rearrangement technique. From these transformations, some interesting summation formulae are obtained.

Effect of the geometric shapes of specimens on impact tensile tests

The geometric shapes of specimens are important in impact tensile tests because geometric shapes determine the stress states of the specimens, and precise geometric shapes can obtain proper material properties without non-material factors. The aim of this study was to investigate the 1D form of the stress by changing the length-to-diameter (L/D) ratios of specimens. The experiments were carried out on a split Hopkinson tensile bar (SHTB)-rotating disk indirect bar-bar tensile impact apparatus. The L/D ratios of the LY12CZ specimens used in the test ranged from 1 to 5. Results show that the specimens can be used to obtain exact parameters of materials under the proposed conditions when the L/D ratio is greater than 2. This is because the longer length will reduce or eliminate the effects of the interfaces.

Transformation Between Eigenfunctions of Three Components of Geometric Momentum on Two-Dimensional Sphere

A technique of coordinate transformation is devised to overcome the computational difficulty associated with the direct transformation between eigenfunctions of three components of the geometric momentum on two-dimensional spherical surface, and the computations are firstly carried out in new coordinates and secondly the results are transformed back into the original coordinates. The eigenfunctions of different components of geometric momentum is explicitly demonstrated to transform under the spatial rotations in the precise way we anticipate.

Cartan-Fubini type extension of holomorphic maps respecting varieties of minimal rational tangents

A fundamental result in the theory of minimal rational curves on projective manifolds is Cartan- Fubini extension theorem proved by Hwang and Mok, which describes the extensibility of biholomorphisms between connected open subsets of two Fano manifolds of Picard number 1 which preserve varieties of minimal rational tangents （VMRT）, under a mild geometric assumption on the second fundamental forms of VMRT＇s. Hong and Mok have developed Cartan-Fubini extension for non-equidimensional holomorphic immersions from a connected open subset of a Pano manifold of Picard number 1 into a uniruled projective manifold, under the assumptions that the map sends VMRT＇s onto linear sections of VMRT＇s and it satisfies a mild geometric condition formulated in terms of second fundamental forms on VMRT＇s. In the current paper, we give a generalization of Hong and Mok＇s result, under the same condition on second fundamental forms, assuming only that the holomorphic immersions send VMRT＇s to VMRT＇s. Our argument is different from Hong and Mok＇s and is based on the study of natural foliations on the total family of VMRT＇s. This gives a substantially simpler proof than Hong and Mok＇s argument.

ARAP++:an extension of the local/global approach to mesh parameterization

Mesh parameterization is one of the fundamental operations in computer graphics(CG) and computeraided design(CAD). In this paper, we propose a novel local/global parameterization approach, ARAP++, for singleand multi-boundary triangular meshes. It is an extension of the as-rigid-as-possible(ARAP) approach, which stitches together 1-ring patches instead of individual triangles. To optimize the spring energy, we introduce a linear iterative scheme which employs convex combination weights and a fitting Jacobian matrix corresponding to a prescribed family of transformations. Our algorithm is simple, efficient, and robust. The geometric properties(angle and area)of the original model can also be preserved by appropriately prescribing the singular values of the fitting matrix. To reduce the area and stretch distortions for high-curvature models, a stretch operator is introduced. Numerical results demonstrate that ARAP++ outperforms several state-of-the-art methods in terms of controlling the distortions of angle, area, and stretch. Furthermore, it achieves a better visualization performance for several applications, such as texture mapping and surface remeshing.