A method of approximate calculation of eigenvalues and eigenvectors of an oscillatory matrix

2002 ◽  
pp. 275-281
Keyword(s):  
Approximate Calculation ◽  
Eigenvalues And Eigenvectors

Improved first-order approximation of eigenvalues and eigenvectors

AIAA Journal ◽  
1998 ◽  
Vol 36 ◽  
pp. 1721-1727
Author(s):  
Prasanth B. Nair ◽  
Andrew J. Keane ◽  
Robin S. Langley
Keyword(s):  
Order Approximation ◽  
Eigenvalues And Eigenvectors ◽  
First Order ◽  
First Order Approximation

Approximate Calculation of Pressure Drop in Laminar Flow of Generalized Newtonian Liquid Through Channel of Noncircular Cross Section

1994 ◽  
Vol 59 (3) ◽  
pp. 603-615 ◽  
Author(s):  
Václav Dolejš ◽  
Ivan Machač ◽  
Petr Doleček
Keyword(s):  
Pressure Drop ◽  
Laminar Flow ◽  
Numerical Solution ◽  
Cross Section ◽  
Approximate Calculation ◽  
Newtonian Liquid ◽  
Straight Channel ◽  
Suggested Procedure ◽  
Noncircular Cross Section ◽  
Calculation Results

The paper presents a modification of the equations of Rabinowitsch-Mooney type for an approximate calculation of pressure drop in laminar flow of generalized Newtonian liquid through a straight channel whose cross section forms a simple continuous area. The suitability of the suggested procedure of calculation of pressure drop is demonstrated by the comparison of calculation results with both the published and original results of numerical solution and experiments.

scholarly journals Matching Point Clouds with STL Models by Using the Principle Component Analysis and a Decomposition into Geometric Primitives

2021 ◽  
Vol 11 (5) ◽  
pp. 2268
Author(s):  
Erika Straková ◽  
Dalibor Lukáš ◽  
Zdenko Bobovský ◽  
Tomáš Kot ◽  
Milan Mihola ◽  
...  
Keyword(s):  
Point Cloud ◽  
Principal Component ◽  
Point Clouds ◽  
Component Analysis ◽  
Language Models ◽  
Computational Time ◽  
Dominant Eigenvalue ◽  
Eigenvalues And Eigenvectors ◽  
Correct Model ◽  
Geometric Primitives

While repairing industrial machines or vehicles, recognition of components is a critical and time-consuming task for a human. In this paper, we propose to automatize this task. We start with a Principal Component Analysis (PCA), which fits the scanned point cloud with an ellipsoid by computing the eigenvalues and eigenvectors of a 3-by-3 covariant matrix. In case there is a dominant eigenvalue, the point cloud is decomposed into two clusters to which the PCA is applied recursively. In case the matching is not unique, we continue to distinguish among several candidates. We decompose the point cloud into planar and cylindrical primitives and assign mutual features such as distance or angle to them. Finally, we refine the matching by comparing the matrices of mutual features of the primitives. This is a more computationally demanding but very robust method. We demonstrate the efficiency and robustness of the proposed methodology on a collection of 29 real scans and a database of 389 STL (Standard Triangle Language) models. As many as 27 scans are uniquely matched to their counterparts from the database, while in the remaining two cases, there is only one additional candidate besides the correct model. The overall computational time is about 10 min in MATLAB.

scholarly journals The approach of a vortex pair to a plane surface in inviscid fluid

1979 ◽  
Vol 92 (3) ◽  
pp. 497-503 ◽  
Author(s):  
P. G. Saffman
Keyword(s):  
Approximate Calculation ◽  
Plane Surface ◽  
Vortex Pair ◽  
Plane Wall ◽  
Inviscid Fluid ◽  
Viscous Effects ◽  
Axis Ratio ◽  
Local Rate

It is shown that a symmetrical vortex pair consisting of equal and opposite vortices approaching a plane wall at right angles must approach the wall monotonically in the absence of viscous effects. An approximate calculation is carried out for uniform vortices in which the vortices are assumed to be deformed into ellipses whose axis ratio is determined by the local rate of strain according to the results of Moore & Saffman (1971).

Multi-Location Inventory Model Considering Bidirectional and Unidirectional Transshipments Simultaneously

2013 ◽  
Vol 694-697 ◽  
pp. 2742-2745
Author(s):  
Jin Hong Zhong ◽  
Yun Zhou
Keyword(s):  
Process Model ◽  
Approximate Calculation ◽  
Inventory Model ◽  
Inventory System ◽  
Death Process ◽  
Birth And Death Process ◽  
Inventory Models ◽  
Continuous Review ◽  
Poisson Demand ◽  
Queue Theory

Abstract. A cross-regional multi-site inventory system with independent Poisson demand and continuous review (S-1,S) policy, in which there is bidirectional transshipment between the locations at the same area, and unidirectional transshipment between the locations at the different area. According to the M/G/S/S queue theory, birth and death process model and approximate calculation policy, we established inventory models respectively for the loss sales case and backorder case, and designed corresponding procedures to solve them. Finally, we verify the effectiveness of proposed models and methods by means of a lot of contrast experiments.

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