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901.
Michael Krivelevich Eyal Lubetzky Benny Sudakov 《Random Structures and Algorithms》2020,56(4):927-947
We consider supercritical bond percolation on a family of high‐girth ‐regular expanders. The previous study of Alon, Benjamini and Stacey established that its critical probability for the appearance of a linear‐sized (“giant”) component is . Our main result recovers the sharp asymptotics of the size and degree distribution of the vertices in the giant and its 2‐core at any . It was further shown in the previous study that the second largest component, at any , has size at most for some . We show that, unlike the situation in the classical Erd?s‐Rényi random graph, the second largest component in bond percolation on a regular expander, even with an arbitrarily large girth, can have size for arbitrarily close to 1. Moreover, as a by‐product of that construction, we answer negatively a question of Benjamini on the relation between the diameter of a component in percolation on expanders and the existence of a giant component. Finally, we establish other typical features of the giant component, for example, the existence of a linear path. 相似文献
902.
Suruchi Singh Swarn Singh 《Numerical Methods for Partial Differential Equations》2020,36(5):1028-1043
A high order modified nodal bi-cubic spline collocation method is proposed for numerical solution of second-order elliptic partial differential equation subject to Dirichlet boundary conditions. The approximation is defined on a square mesh stencil using nine grid points. The solution of the method exists and is unique. Convergence analysis has been presented. Moreover, the superconvergent phenomena can be seen in proposed one step method. The numerical results clearly exhibit the superiority of the new approximation, in terms of both accuracy and computational efficiency. 相似文献
903.
Crisólogo Dolores Flores Martha Iris Rivera López Deborah Moore-Russo 《School science and mathematics》2020,120(2):104-115
Slope is a fundamental mathematics concept in middle and high school that transcends to the university level. An understanding of slope is needed at the university level since slope plays an important role in understanding problems involving variation and change. In this study Mexican curricula documents were examined to determine which conceptualizations of slope are addressed in the intended mathematics curriculum. To explain the results, we use conceptualizations of slope identified in previous research. Our findings reveal that, to a certain extent, the conceptualizations proposed in the Mexican intended mathematics curriculum differ slightly in terms of the emphasis and timing of instruction from what others have identified in the U.S., with slope as a geometric ratio receiving less emphasis in the Mexican curriculum. There was also noted discontinuity within the Mexican curriculum in introducing slope in grade 9 and subsequently introducing of linear functions in grade 10 without explicit mention of slope. Suggestions are made for future studies, both to consider the conceptualizations of slope promoted in the Mexican textbooks and the impact they have in classroom instruction and student learning of slope. 相似文献
904.
本文对可压缩流体力学高精度拉格朗日格式及其保正性质近年来的发展给出回顾与综述.文中分别介绍了一维、二维可压缩流体力学方程中心型拉格朗日格式的设计步骤,回顾了高精度拉格朗日格式以及高精度保正拉格朗日格式的研究进展. 相似文献
905.
906.
907.
主要研究稳定计算近似函数的高阶导数的积分逼近方法,方法因由Lanczos提出故也称为Lanczos算法.利用Legendre多项式的正交性,提出了一类逼近近似函数高阶导数的高精度积分方法,即构造出一系列积分算子D(m)n,h去逼近噪声函数的高阶导数,且这些积分算子具有O(δ2n+2/2n+m+2)的收敛速度,其中δ为近... 相似文献
908.
Zhang Rongpei 《高等学校计算数学学报》2007,(3)
1引言本文讨论下面非线性Schr(?)dinger方程(NLS)方程的初边值问题:i(?)u/(?)t (?)~2u/(?)x~2 2|u~2|u=0,(1) u(x_l,t)=u(x_r,t)=0,t>0,(2) u(x,0)=u_0(x),x_l≤x≤x_r,(3)其中u(x,t)是复值函数,u_0(x)为已知的复值函数,i~2=-1.该问题有着如下的电荷与能量守恒关系: 相似文献
909.
910.
Charlene S. Chua Simon P. A. Higgins Andreas Fouras 《Journal of synchrotron radiation》2010,17(5):624-630
A high‐repetition‐rate mechanical shutter with asynchronous control and sub‐millisecond operation has been developed and tested for specialist X‐ray systems in the field of medical diagnostics and radiation therapy. Capacitor‐coupled linear voice coil actuators are utilized to achieve opening and closing speeds as fast as 700 µs for an aperture height of 4 mm. The design allows for asynchronous control, permitting slave operation of the shutter, a feature that is distinctly suitable for a number of applications including particle image velocimetry, where high‐frame‐rate operation must be accurately synchronized and triggered by the image acquisition sequence of the detector or timing device. The design and construction of the shutter also makes it ideal, with simple and limited modifications, for applications requiring larger apertures, in particular wide beams as found in many synchrotron beamlines. 相似文献