Random Johnson-Mehl tessellations

1992 ◽  
Vol 24 (4) ◽  
pp. 814-844 ◽  
Author(s):  
Jesper Møller
Keyword(s):  
Euclidean Space ◽  
Second Order ◽  
Poisson Processes ◽  
Dimensional Euclidean Space ◽  
Inhomogeneous Poisson Processes

A unified exposition of random Johnson–Mehl tessellations in d-dimensional Euclidean space is presented. In particular, Johnson-Mehl tessellations generated by time-inhomogeneous Poisson processes and nucleation-exclusion models are studied. The ‘practical' cases d = 2 and d = 3 are discussed in detail. Several new results are established, including first- and second-order moments of various characteristics for both Johnson–Mehl tesselations and sectional Johnson–Mehl tessellations.

Random Johnson-Mehl tessellations

1992 ◽  
Vol 24 (04) ◽  
pp. 814-844 ◽  
Author(s):  
Jesper Møller
Keyword(s):  
Euclidean Space ◽  
Second Order ◽  
Poisson Processes ◽  
Dimensional Euclidean Space ◽  
Inhomogeneous Poisson Processes

A unified exposition of random Johnson–Mehl tessellations in d-dimensional Euclidean space is presented. In particular, Johnson-Mehl tessellations generated by time-inhomogeneous Poisson processes and nucleation-exclusion models are studied. The ‘practical' cases d = 2 and d = 3 are discussed in detail. Several new results are established, including first- and second-order moments of various characteristics for both Johnson–Mehl tesselations and sectional Johnson–Mehl tessellations.

scholarly journals Hybrid Second Order Method for Orthogonal Projection onto Parametric Curve in n-Dimensional Euclidean Space

Mathematics ◽  
2018 ◽  
Vol 6 (12) ◽  
pp. 306 ◽  
Author(s):  
Juan Liang ◽  
Linke Hou ◽  
Xiaowu Li ◽  
Feng Pan ◽  
Taixia Cheng ◽  
...  
Keyword(s):  
Euclidean Space ◽  
Orthogonal Projection ◽  
Second Order ◽  
Dimensional Euclidean Space ◽  
Order Method ◽  
Order Convergence ◽  
Initial Value ◽  
Parametric Curve ◽  
First Order ◽  
Special Cases

Orthogonal projection a point onto a parametric curve, three classic first order algorithms have been presented by Hartmann (1999), Hoschek, et al. (1993) and Hu, et al. (2000) (hereafter, H-H-H method). In this research, we give a proof of the approach’s first order convergence and its non-dependence on the initial value. For some special cases of divergence for the H-H-H method, we combine it with Newton’s second order method (hereafter, Newton’s method) to create the hybrid second order method for orthogonal projection onto parametric curve in an n-dimensional Euclidean space (hereafter, our method). Our method essentially utilizes hybrid iteration, so it converges faster than current methods with a second order convergence and remains independent from the initial value. We provide some numerical examples to confirm robustness and high efficiency of the method.

scholarly journals On a Class of Markov Chains

1971 ◽  
Vol 12 (1) ◽  
pp. 91-97 ◽  
Author(s):  
A. G. Pakes
Keyword(s):  
Time Series ◽  
Euclidean Space ◽  
Markov Chains ◽  
State Space ◽  
Borel Subset ◽  
Second Order ◽  
Dimensional Euclidean Space ◽  
Joint Distributions

Until recently, very little work has been done on the second order properties of Markov chains. Craven [1] has studied the joint distributions of Markov chains having a Borel subset of n-dimensional Euclidean space as state space. His idea was to consider the process as a time series.

scholarly journals Semilinear Second Order Elliptic Oscillation

1979 ◽  
Vol 22 (2) ◽  
pp. 139-157 ◽  
Author(s):  
C. A. Swanson
Keyword(s):  
Partial Differential Equations ◽  
Euclidean Space ◽  
Recent Progress ◽  
Unbounded Domains ◽  
Elliptic Partial Differential Equations ◽  
Second Order ◽  
Dimensional Euclidean Space ◽  
Semilinear Elliptic ◽  
Oscillation Problem ◽  
Image Position

These pages summarize recent progress on the oscillation problem for semilinear elliptic partial differential equations of the form(1)in unbounded domains Ω in n-dimensional Euclidean space Rn. Our attention is restricted to the second order symmetric equation (1), and completeness is not attempted; the emphasis is on results obtained in the last five years.

On Vitali's Theorem for Groups of Motions of Euclidean Space

1999 ◽  
Vol 6 (4) ◽  
pp. 323-334
Author(s):  
A. Kharazishvili
Keyword(s):  
Euclidean Space ◽  
Dimensional Euclidean Space ◽  
Finite Dimensional

Abstract We give a characterization of all those groups of isometric transformations of a finite-dimensional Euclidean space, for which an analogue of the classical Vitali theorem [Sul problema della misura dei gruppi di punti di una retta, 1905] holds true. This characterization is formulated in purely geometrical terms.

Some properties of Wigner coefficients and hyperspherical harmonics

1956 ◽  
Vol 52 (3) ◽  
pp. 424-430 ◽  
Author(s):  
A. P. Stone
Keyword(s):  
Angular Momentum ◽  
Euclidean Space ◽  
Rotation Group ◽  
Dimensional Euclidean Space ◽  
Hyperspherical Harmonics ◽  
Shift Operators ◽  
Analytical Relations

ABSTRACTGeneral shift operators for angular momentum are obtained and applied to find closed expressions for some Wigner coefficients occurring in a transformation between two equivalent representations of the four-dimensional rotation group. The transformation gives rise to analytical relations between hyperspherical harmonics in a four-dimensional Euclidean space.

On inequalities of the Tchebychev type

1963 ◽  
Vol 59 (1) ◽  
pp. 135-146 ◽  
Author(s):  
J. F. C. Kingman
Keyword(s):  
Probability Theory ◽  
Euclidean Space ◽  
Random Variable ◽  
Dimensional Euclidean Space ◽  
Real Random Variable ◽  
Finite Dimensional

1. A type of problem which frequently occurs in probability theory and statistics can be formulated in the following way. We are given real-valued functions f(x), gi(x) (i = 1, 2, …, k) on a space (typically finite-dimensional Euclidean space). Then the problem is to set bounds for Ef(X), where X is a random variable taking values in , about which all we know is the values of Egi(X). For example, we might wish to set bounds for P(X > a), where X is a real random variable with some of its moments given.

Curve following in n—dimensional Euclidean space

SIMULATION ◽  
1973 ◽  
Vol 21 (5) ◽  
pp. 145-149 ◽  
Author(s):  
John Rees Jones
Keyword(s):  
Euclidean Space ◽  
Dimensional Euclidean Space
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