The volume of an isotropic random parallelotope

1979 ◽  
Vol 16 (1) ◽  
pp. 84-94 ◽  
Author(s):  
Harold Ruben
Keyword(s):  
Multivariate Statistics ◽  
Orthogonal Projection ◽  
Actual Distribution ◽  
Linear Subspaces ◽  
Radial Projection ◽  
Isotropic Random

The p-content of the p-parallelotope ∇p, n determined by p independent isotropic random points z1, …, zp in ℝn (1 < p ≦ n) can be expressed as a product of independent variates in two ways, by successive orthogonal projection onto linear subspaces and by radial projection of the points, enabling calculation of the actual distribution as well as the moments of ∇p, n. This is done explicitly in several cases. The results also have interest in multivariate statistics.

The volume of an isotropic random parallelotope

1979 ◽  
Vol 16 (01) ◽  
pp. 84-94 ◽  
Author(s):  
Harold Ruben
Keyword(s):  
Multivariate Statistics ◽  
Orthogonal Projection ◽  
Actual Distribution ◽  
Linear Subspaces ◽  
Radial Projection ◽  
Isotropic Random

The p-content of the p-parallelotope ∇ p, n determined by p independent isotropic random points z 1, …, zp in ℝ n (1 &lt; p ≦ n) can be expressed as a product of independent variates in two ways, by successive orthogonal projection onto linear subspaces and by radial projection of the points, enabling calculation of the actual distribution as well as the moments of ∇ p, n . This is done explicitly in several cases. The results also have interest in multivariate statistics.

scholarly journals Projections of fractal percolations

2013 ◽  
Vol 35 (2) ◽  
pp. 530-545 ◽  
Author(s):  
MICHAŁ RAMS ◽  
KÁROLY SIMON
Keyword(s):  
Hausdorff Dimension ◽  
Orthogonal Projection ◽  
Cantor Sets ◽  
Orthogonal Projections ◽  
Radial Projection ◽  
Random Cantor Sets ◽  
Distance Set ◽  
Distance Sets

AbstractIn this paper we study the radial and orthogonal projections and the distance sets of the random Cantor sets $E\subset { \mathbb{R} }^{2} $, which are called Mandelbrot percolation or percolation fractals. We prove that the following assertion holds almost surely: if the Hausdorff dimension of $E$ is greater than $1$ then the orthogonal projection to every line, the radial projection with every centre, and the distance set from every point contain intervals.

Multivariate Statistics with Psychiatric Applications

1973 ◽  
Vol 18 (7) ◽  
pp. 325-326
Author(s):  
STANLEY A. MULAIK
Keyword(s):  
Multivariate Statistics

Modification of tundish design to improve quality of slabs, casted at CCM No. 4 of EVRAZ NTMK

2020 ◽  
Vol 76 (6) ◽  
pp. 559-563
Author(s):  
I. M. Zakharov ◽  
V. A. Smirnov ◽  
D. V. Sushnikov ◽  
A. G. Lyzhin ◽  
E. A. Lavrova ◽  
...  
Keyword(s):  
Basic Number ◽  
Metal Level ◽  
Surface Layers ◽  
Secondary Oxidation ◽  
Strip Rolling ◽  
Actual Distribution ◽  
Ultrasonic Control ◽  
Analysis Of Results ◽  
Water Simulation

A technology of continuous casting of steel has a large effect on its contamination. In particular, proper organization of metal flows in tundish and mold is very important. After completion a series of casting through a tundish and drop of metal level in it, it possible, that the slag flows from the surface layers of the tundish to capture the metal. An analysis of results of ultrasonic control of finished strip showed, that the basic number of the revealed defects was obtained during strip rolling out of the last slabs of the last heat in a series for a tundish. Metallographic studies determined, that the defects were located in the slab axis zone and filled by macro-inclusions of complex composition. To determine the actual distribution of metal flows, a water simulation of them was accomplished for the existing design of the EVRAZ NTMK tundish. It was determined, that at the drop of metal level in a tundish, a capture of slag from the metal reservoir and its transfer into the main bath of the tundish takes place due to whirligig flows. Following the weight metal consumption, the zone of slag inclusions distribution enlarges. Besides, denudation of the metal mirror in the metal reservoir takes place, resulted in metal secondary oxidation. Based on the results of the simulation, it was proposed to modify the design of the “turbostop”, which is installed in the metal reservoir of the tundish. Besides, it was proposed to remove the dividers installation in the tundish. It was noted, that the proposed steps enable to ensure a minimal level of rejections.

Orthogonal Projection DOA Estimation with a Single Snapshot

2013 ◽  
Vol E96.B (5) ◽  
pp. 1215-1217 ◽  
Author(s):  
Ann-Chen CHANG ◽  
Chih-Chang SHEN
Keyword(s):  
Orthogonal Projection ◽  
Doa Estimation ◽  
Single Snapshot

Detection of Small Target on the Sea Surface Using Orthogonal Projection

2014 ◽  
Vol 35 (1) ◽  
pp. 24-28
Author(s):  
Yong Yang ◽  
Shun-ping Xiao ◽  
De-jun Feng ◽  
Wen-ming Zhang
Keyword(s):  
Orthogonal Projection ◽  
Sea Surface ◽  
Small Target

Determination of Pyridostigmine Bromide in Presence of its Related Impurities by Four Modified Classical Least Square Based Models: A Comparative Study

2020 ◽  
Vol 17 (1) ◽  
pp. 87-94
Author(s):  
Ibrahim A. Naguib ◽  
Fatma F. Abdallah ◽  
Aml A. Emam ◽  
Eglal A. Abdelaleem
Keyword(s):  
Comparative Study ◽  
Least Squares ◽  
Orthogonal Projection ◽  
Predictive Ability ◽  
Least Square ◽  
Projection To Latent Structures ◽  
Preprocessing Method ◽  
Spectral Residual ◽  
Latent Structures

: Quantitative determination of pyridostigmine bromide in the presence of its two related substances; impurity A and impurity B was considered as a case study to construct the comparison. Introduction: Novel manipulations of the well-known classical least squares multivariate calibration model were explained in detail as a comparative analytical study in this research work. In addition to the application of plain classical least squares model, two preprocessing steps were tried, where prior to modeling with classical least squares, first derivatization and orthogonal projection to latent structures were applied to produce two novel manipulations of the classical least square-based model. Moreover, spectral residual augmented classical least squares model is included in the present comparative study. Methods: 3 factor 4 level design was implemented constructing a training set of 16 mixtures with different concentrations of the studied components. To investigate the predictive ability of the studied models; a test set consisting of 9 mixtures was constructed. Results: The key performance indicator of this comparative study was the root mean square error of prediction for the independent test set mixtures, where it was found 1.367 when classical least squares applied with no preprocessing method, 1.352 when first derivative data was implemented, 0.2100 when orthogonal projection to latent structures preprocessing method was applied and 0.2747 when spectral residual augmented classical least squares was performed. Conclusion: Coupling of classical least squares model with orthogonal projection to latent structures preprocessing method produced significant improvement of the predictive ability of it.

Exploring good cycling cities using multivariate statistics

2019 ◽  
Vol 40 (4) ◽  
pp. 526-543 ◽  
Author(s):  
Andrew J. Collins ◽  
Craig A. Jordan ◽  
R. Michael Robinson ◽  
Caitlin Cornelius ◽  
Ross Gore
Keyword(s):  
Multivariate Statistics
Sign in / Sign up

Export Citation Format

Share Document