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Consider a finite set of segments on a plane with endpoints in the general position. In [1] Sylvester posted a problem of finding the measure of the set of lines intersecting all of this segments. In ...
Using the results presented in the previous lecture, namely the generalization of the Tsirelson's theorem [2] to mixed volumes, we calculate the mixed volume of the closed convex hulls of the two orth...
Let K be a convex compact subset of a separable Hilbert space H. One of the most important geometric characteristics of K is its intrinsic volumes. In the finitedimensionalcase (K ? R^d), the intrinsi...
Geometrically continuous splines are piecewise polynomials defined on a collection of patches stitched together through transition maps. In this talk, we introduce an algebraic framework to study geom...
扩展有限元法(XFEM)是目前裂纹分析的主流数值方法。2009年起,ABAQUS、ANSYS等主流商业软件集成XFEM并应用于裂纹问题,标志着该方法被工业界广泛接受。然而,在实际应用中XFEM仍然受到两方面的困扰:总体方程高度病态和动力学计算时能量难以守恒。基于“困难的根源在于单位分解插值引入的额外自由度”这一判断和认识,我们提出了一种无额外自由度的改进型扩展有限元方法,有效解决了现有方法总体刚度...
本报告讨论Hamilton系统辛算法的KAM稳定性,给出辛算法应用于近可积系统时不变环面的存在性证明和数值逼近结果。具体地,近可积系统用辛算法离散化,假设系统的可积部分满足Ruessmann非退化条件,当时间步长足够小且Hamilton函数足够光滑时,离散系统存在不变环面,它们在相应空间中占据一个大测度Cantor集。进而假设系统的可积部分满足Kolmogorov非退化条件,则在Hausdorff...
Given a graph G with weight function w and an acyclic edge subset E', the partial inverse spanning tree problem on (G, w; E') is to find a new weight function w* so that E' can be extended to a maximu...
Improving the sensitivity of protein-protein interaction detection and protein structure probing is a principal challenge in cross-linking mass spectrometry (XL-MS) data analysis. In this talk, we pro...
In this talk, we define a new class of differential fields called separably differentially closed fields and show their several characterizations by comparing them with differentially closed fields of...
In this work, the cooperation between coherent control and noises in open spin systems is studied, aiming to demonstrate that such cooperation can provide new possibilities for parametrization in quan...
In this work, synthesis of robust memory modes for linear quantum passive systems in the presence of unknown inputs has been studied, aimed at facilitating secure storage and communication of quantum ...
In the study of incompressible fluid, one fundamental phenomenon that arises in a wide variety of application is dissipation enhancement by so-called mixing flow. In this talk, I will give a brief int...
We consider the Cauchy problem for the defocusing cubic NLS on R3T1 and establish almost sure scattering for random initial data. The main obstacle to extend the classical almost sure scattering resul...
The Morse boundary of a proper geodesic metric space is a generalization of the Gromov boundary of a hyperbolic space. It is a quasi-isometry invariant to study "hyperbolic directions" in the space. T...
In this paper, we will provide the the finite element method for the electro-osmotic flow in micro-channels, in which a convection-diffusion type equation is given for the charge density ρe. A time-di...

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