Discretization correction of general integral PSE Operators for particle methods

The general integral particle strength exchange (PSE) operators [J.D. Eldredge, A. Leonard, T. Colonius, J. Comput. Phys. 180 (2002) 686–709] approximate derivatives on scattered particle locations to any desired order of accuracy. Convergence is, however, limited to a certain range of resolutions. For high-resolution discretizations, the constant discretization error dominates and prevents further convergence. We discuss a consistent discretization correction framework for PSE operators that yields the desired rate of convergence for any resolution, both on uniform Cartesian and irregular particle distributions, as well as near boundaries. These discretization-corrected (DC) PSE operators also have no overlap condition, enabling the kernel width to become arbitrarily small for constant interparticle spacing. We show that, on uniform Cartesian particle distributions, this leads to a seamless transition between DC PSE operators and classical finite difference stencils. We further identify relationships between DC PSE operators and operators used in corrected smoothed particle hydrodynamics and reproducing kernel particle methods. We analyze the presented DC PSE operators with respect to accuracy, rate of convergence, computational efficiency, numerical dispersion, numerical diffusion, and stability.     

A measure of 2D shape-of-object dissimilarity

We describe an approach for measuring 2D shape-of-object dissimilarity. The shape of the different objects to be compared is mapped to a representation invariant under translation, rotation, and area. Thus, the shapes will have the same amount of information to describe them (equal number of pixels). The measure of dissimilarity is based on the transformation of one shape into another. This transformation is performed by moving pixels. Thus, the shape difference could be ascertained by counting how many pixels we have to move and how far to change one shape into another. When the shape transformation is performed, the distribution of the shape difference is computed, which permits an improvement in shape comparison.     

14C激发态中子晕

利用¹³C(d,p)¹⁴C反应实验数据,抽取转移反应重叠函数渐近归一化常数,计算了¹⁴C的1^－和0^－激发态的最后一个中子的密度分布的均方根半径和在核外的几率.研究结果表明,¹⁴C的1^－和0^－激发态为中子晕态.     

Dual geometry of Cartan distribution

The paper is devoted to the study of intrinsic geometry of a Cartan distribution \(\mathcal{M}\) in projective space P_2m . We essentially use the hyperband distribution \(\mathcal{H}\) and P_2m associated with \(\mathcal{M}\). Using the duality theory, we construct, in the 4th differential neighborhood, a series of normalizations of \(\mathcal{M}\). We also consider dual affine connections \(\mathop \nabla \limits^1 \) and \(\mathop \nabla \limits^2 \) induced by the dual normalization of the Cartan distribution \(\mathcal{M}\).     

基金评审中的归一化分析方法与应用

本以国家自然科学基金评审为主要研究对象，提出平均非共识度和最大非共识度的概念，针对项目评分的最大非共识度分布不一致的问题，应用优化理论、归一化方法等，建立了确定平均非共识度和最大非共识度的优化模型与算法，克服了因最大非共识度的不同影响项目评审公正性的弊端，经国家自然科学基金委员会部分学科的应用，收到很好效果。     

Algebra over estimation algorithms: Normalization and division

An algebra over recognition algorithms supplemented with a normalization operation (under various definitions) and the division operation is investigated. Correctness criteria for various algebraic closures are obtained.     

谈谈物理实验课的教学管理

为了提高物理实验课的教学质量．有必要加强实验教学的规范化、制度化建设。我们对此作了初步的实践和探索。     

A formalization of Sambins's normalization for GL

Sambin [6] proved the normalization theorem (Hauptsatz) for GL, the modal logic of provability, in a sequent calculus version called by him GLS. His proof does not take into account the concept of reduction, commonly used in normalization proofs. Bellini [1], on the other hand, gave a normalization proof for GL using reductions. Indeed, Sambin's proof is a decision procedure which builds cut-free proofs. In this work we formalize this procedure as a recursive function and prove its recursiveness in an arithmetically formalizable way, concluding that the normalization of GL can be formalized in PA. MSC: 03F05, 03B35, 03B45.