Minimal enclosing parallelepiped in 3D

We investigate the problem of finding a minimal volume parallelepiped enclosing a given set of n three-dimensional points. We give two mathematical properties of these parallelepipeds, from which we derive two algorithms of theoretical complexity O(n⁶). Experiments show that in practice our quickest algorithm runs in O(n²) (at least for n10⁵). We also present our application in structural biology.     

A New Method for the Construction of Multivariate Minimal Interpolation Polynomial

The extended Hermite interpolation problem on segment points set over n-dimensional Euclidean space is considered. Based on the algorithm to compute the Gröbner basis of Ideal given by dual basis a new method to construct minimal multivariate polynomial which satisfies the interpolation conditions is given.     

A New Non-Overlapping Domain Decomposition Method for a 3D Laplace Exterior Problem

We propose a method for solving three-dimensional boundary value problems for Laplace’s equation in an unbounded domain. It is based on non-overlapping decomposition of the exterior domain into two subdomains so that the initial problem is reduced to two subproblems, namely, exterior and interior boundary value problems on a sphere. To solve the exterior boundary value problem, we propose a singularity isolation method. To match the solutions on the interface between the subdomains (the sphere), we introduce a special operator equation approximated by a system of linear algebraic equations. This system is solved by iterative methods in Krylov subspaces. The performance of the method is illustrated by solving model problems.     

透平机械内部三维可压缩Navier-Stokes方程的流面方法和维数分裂算法

在这篇文章中,运用经典的张量分析方法,把流动区域用-个二维流形序列分割成一系列流层之并,推得在流层内半测地坐标之下的Navier-Stokes方程,在流形的法线方向应用向后Euler差分,推导了两维流形上的可压缩Navier-Stokes方程,和流函数满足的方程.在这个基础上,提出了一种维数分裂法的新算法.这种方法不同于区域分解法.对于三维问题,在区域分解法中我们必须在每个子区域上仍解三维问题,但是在这种新方法中,只需要在每个子区域上求解二维问题,不过是几个二维流形上的NS方程.文中还给出了-个透平机械内部流动的数值计算实例.     

3D Filtering of Images Corrupted by Additive-Multiplicative Noise

Doklady Mathematics - A novel method for filtering images contaminated by mixed (additive-multiplicative) noise is substantiated and implemented for the first time. The method includes several...     

计算柱面上对面积的曲面积分的一种新方法

给出了利用对弧长的曲线积分计算柱面上对面积的曲面积分的一种新方法,其计算公式为∫∫_Σf(x,y,z)dS=∫_(L*)ds∫z_1(x,y) z_2(x,y)f(x,y,z)dz,其中积分曲面Σ为垂直于xoy坐标面的柱面片,L*为Σ在xoy坐标面上的投影曲线(平面曲线),z=z1(x,y),z=z2(x,y)分别为过Σ的下边界曲线和上边界曲线的任一不同于Σ的曲面的方程.     

A Fast Implicit Numerical Method for Time Dependent Viscous Flows

The iterative method used by Esch (1964) and Pearson (1964, 1965a, b), for the solution of an implicit finite difference approximation to the Navier Stokes equation, is analysed. A more general iteration method is suggested that may require many iteration parameters, and it is shown how these parameters can be computed. It was found that when the non-dimensional number vΔt/2L² is small, a single optimum iteration parameter exists (v being the kinematic viscosity, Δt the time step and L a characteristic length). An approximate expression for the “best” parameter is developed, and a procedure is described for improving that estimate. With the improved estimate and extrapolation in time, convergence is achieved in one or two iterations per time step on the average. In some cases the time step used was 200 times bigger than the time step required for stability of explicit schemes.     

A Weierstrass Representation for Minimal Surfaces in 3-Dimensional Manifolds

In this paper we will discuss a Weierstrass type representation for minimal surfaces in Riemannian and Lorentzian 3-dimensional manifolds.     

第一类曲面积分的一种解法

运用第一类曲线积分方法解决一类特殊的第一类曲面积分问题,并举例说明此方法的简便性.     

一种新型的四相水平集图像分割方法

水平集方法在图像分割和计算机视觉领域有很广泛的应用,在传统的水平集方法中,水平集函数需要保持符号距离函数.现有的活动轮廓模型、GAC模型、M-S模型、C-V模型等在演化过程中均需要对水平集函数进行重新初始化,使其保持符号距离函数,然而这样会引起数值计算的错误,最终破坏演化的稳定性,另外这些模型只适用于灰度值较为均匀的图像,对灰度值不均匀的图像不能进行理想的分割·针对这些问题,结合C-V模型的思想,提出了一种带有正则项的四相水平集分割模型,其中正则项被定义为一个势函数,具有向前向后扩散的作用,使水平集函数在演化过程中保持为符号距离函数,避免了水平集函数重新初始化的过程.最后对该模型进行数值实现,实验表明了新模型的可行性和有效性.     

一种半参数ROC曲面估计方法

ROC曲面是诊断医学统计学里评估有多类诊断结果的诊断测试方法准确性的一个重要工具,也是近年来的一个研究热点.本文提出一种半参数的ROC曲面估计方法.该方法可以借助于许多统计软件里的逻辑斯蒂回归程序进行计算,所以它的实施较为方便.相关统计模拟显示,本文提出的方法与传统的非参数方法相比,有效性得到了显著提高.而与参数方法相比,当参数模型假设是正确时仍比参数方法有略高的有效性;而当参数模型假设不正确时,本文提出的半参数方法明显优于参数方法.     

Two Sample Tests for Mean 3D Projective Shapes from Digital Camera Images

In this article, we extend mean 3D projective shape change in matched pairs to independent samples. We provide a brief introduction of projective shapes of spatial configurations obtained from their digital camera images, building on previous results of Crane and Patrangenaru (J Multivar Anal 102:225–237, 2011). The manifold of projective shapes of k-ads in 3D containing a projective frame at five given landmark indices has a natural Lie group structure, which is inherited from the quaternion multiplication. Here, given the small sample size, one estimates the mean 3D projective shape change in two populations, based on independent random samples of possibly different sizes using Efron’s nonparametric bootstrap. This methodology is applied in three relevant applications of analysis of 3D scenes from digital images: visual quality control, face recognition, and scene recognition.     

第一类曲面积分的新方法

从一个具体的物理问题入手,探讨了如何将第一类曲面积分转化为两个第一类曲线积分的累次形式,从而给出了这两类积分之间的关系,并通过举例说明该公式可以用来直观简便地计算第一类曲面积分.     

A Note on Minimal Surfaces in Euclidean 3-Space

In this note, a construction of minimal surfaces in Euclidean 3-space is given. By using the product of Weierstrass data of two known minimal surfaces, one gets a new Weierstrass data and a corresponding minimal surface from the Weierstrass representation.     

A New Regularity Criterion for the 3D MHD Equations Involving Partial Components

In this paper, we establish a new regularity criterion for the 3D incompressible MHD equations involving partial components of the velocity gradient and magnetic fields.     

A Spectrally Minimal Realization Formula for H^{\infty}({\mathbb{D}})

In this article we prove a representation theorem for functions, such that the realization formula is spectrally minimal in the following sense: the spectrum of the main operator in the realization intersects the unit circle precisely at those points where the given function has no holomorphic extension. We also extend this result to operator-valued H ^∞ functions. Received: March 12, 2007. Revised: April 12, 2007. Accepted: May 7, 2007.     

A Parallel Preconditioned Iterative Realization of the Panel Method in 3D

The parallel version of precondition iterative techniques is developed for matrices arising from the panel boundary element method for three-dimensional simple connected domains with Dirichlet boundary conditions. Results were obtained on an nCube-2 parallel computer showing that preconditioned iterative methods are very well suited also in three-dimensional cases for implementation on an MIMD computer and that they are much more efficient than usual direct solution techniques.     

Computing the Detour and Spanning Ratio of Paths, Trees, and Cycles in 2D and 3D

The detour and spanning ratio of a graph G embedded in measure how well G approximates Euclidean space and the complete Euclidean graph, respectively. In this paper we describe O(nlog n) time algorithms for computing the detour and spanning ratio of a planar polygonal path. By generalizing these algorithms, we obtain O(nlog ² n)-time algorithms for computing the detour or spanning ratio of planar trees and cycles. Finally, we develop subquadratic algorithms for computing the detour and spanning ratio for paths, cycles, and trees embedded in , and show that computing the detour in is at least as hard as Hopcroft’s problem. This research was partly funded by CRM, FCAR, MITACS, and NSERC. P.A. was supported by NSF under grants CCR-00-86013 EIA-99-72879, EIA-01-31905, and CCR-02-04118, by ARO grants W911NF-04-1-0278 and DAAD19-03-1-0352, and by a grant from the U.S.-Israeli Binational Science Foundation. R.K. was supported by DFG grant Kl 655/14-1. M.S. was supported by NSF Grants CCR-97-32101 and CCR-00-98246, by a grant from the U.S.-Israeli Binational Science Foundation (jointly with P.A.), by a grant from the Israeli Academy of Sciences for a Center of Excellence in Geometric Computing at Tel Aviv University, and by the Hermann Minkowski–MINERVA Center for Geometry at Tel Aviv University. Some of these results have appeared in a preliminary form in [2, 20].