Joint basis

Walczak, B. and Massart, D. L. (2000). Joint basis and joint best-basis for data. In "Wavelets in Chemistry", (B. Walczak, Ed.), pp. 165-176. Elsevier, Amsterdam. 

Elf Aquitaine had established under Sanofi a small conglomerate with profit-making subsidiaries involved in pharmaceuticals and perfumes. But Atochem, set up on a joint basis by Total and Elf, was a loss-making concern, as was Chloe Chimie, a cast-off of Rhone-Poulenc, which retained only 19.50 percent of its capital, while Elf and Total each acquired a 40.25 percent stake in the new chemical entity. 

Joint Basis and Joint Best-basis for Data Sets... 

Of course, the sum of elements of vector v equals the total variance of the data. The elements of vector v can be sorted in decreasing order. The first n coefficients, their sum exceeding a predefined percentage of variance, form the joint basis for all signals. 

Fig. 3 Schematic representation of data compression in the Joint basis.

While dealing with the data set we are interested in finding a joint basis (oi joint best-basis) for compression of the whole set. Only joint basis allows... 

The most efficient method of data set compression in the joint basis is Principal Component Analysis (PCA). Principal Components (PCs) are constructed as a linear combination of original variables to maximize the description of data variance. They are eigenvectors of the auto-covariance matrix of data set. Each eigenvector is associated with the corresponding eigenvalue, which describes its importance in data variance description. For the studied IR library, 57 eigenvectors (principal components) are necessary to describe 95% of data variance, whereas as much as 109 eigenvectors are needed to describe 99% of data variance (see Fig.5). The mean value of RMS... 

Some additional calculations were performed for comparison sake, using as a criterion the RMS error of spectral reconstruction. In particular, each spectrum was compressed to the degree which allows it reconstruction with the RMS = 0.0127. This value corresponds to the mean value of RMS observed for the data compressed by PCA. or in the joint basis accounting for the 99% of data variance. DWT with RMS criterion (where RMS = 0.0127) leads to 66.8 wavelet coefficients. For illustrative purpose the original spectrum and the spectrum reconstructed with RMS = 0.0127 are presented in Fig. 6. 

Joint basis and joint best-basis approaches to data set compression... 

In the discussed approach the compressed data set has uniform representation (see Fig. 2). Compression ratio equals 7.0621 for DWT, and 7.3669 for WPT. Both, joint basis and joint best-basis minimize the storage require-... 

Fig. 12 (a) The top 200 coefficients (.squared) in the joint basis, and the top 200 elements of variance tree in the joint best basis sorted according to their amplitude and (h) cumulative percentage of the explained variance in the join basis, and in the best joint-... 

In parallel to the development of these security architectures, an international effort has led to the creation of Airworthiness Security Process (AWSP) document ED-202/DO-326 [10] that standardizes the development process of aircraft systems with respect to security. This document aims at providing a joint basis for the certification of information security aspects of aircraft systems. Consequently, this document focuses on security aspects that have an effect on the safety of the aircraft, these aspects are called Security for Safety . The document does not deal with other security aspects concerning, for instance, the protection of passenger privacy or the protection of aircraft manufacturer intellectual property. In this paper we restrict ourselves to the modelling and analysis of Security for Safety . 

Instead of characteristic lives for a population of components, cyclic lives are given on a per joint basis, as was done in the past in the development of Sn-Pb reliability models— this allows for the number of most critical joints per component (Ref 16)... 

Dual-beUows assembhes, ie, universal-type expansion joints, are particularly vulnerable to squirm, and can experience elastic squirm at one-fourth the pressure of an individual bellows. When large amounts of offset are encountered, as is often the design basis, a pinwheel effect occurs because of unbalanced pressure forces. This effect tends to rotate the center-spool pipe which may lead to bellows mpture. Eor this reason the center spool should always be stabilized by hinges or tie-rod lugs to prevent such rotation. 

Meniscus surgery can repair or remove the tom cartilage, depending on the nature of the tear. Arthroscopy, a procedure through small skin incisions to visualize and repair the affected joint, is frequentiy employed. This procedure is sometimes performed on an out-patient basis. If repair of the menisci is not possible the surgeon removes as tittle of the meniscus as possible. 

Biphenyl, terphenyl, and their alkyl or hydrogenated derivatives generally serve markets where price and performance, rather than composition, is the customer s primary concern. Performance standards for heat-transfer appHcations are usually set by the fluid suppHer. The biphenyl—diphenyl oxide eutectic (26.5% biphenyl, 73.5% DPO) represents a special case. This composition has become a widely recogni2ed standard vapor-phase heat-transfer medium. It is sold throughout the world under various trademarks. In the United States, Dow (Dowtherm A) and Monsanto (Therminol VP-1) are the primary suppHers. Alkylated biphenyls and partially hydrogenated terphenyls serving the dielectric and carbonless copy paper dye solvent markets likewise are sold primarily on the basis of price and performance characteristics jointly agreed on by producer and user. 

Steam and hot-water coils should be constructed of seamless steel tube and preferably be without joints within the tank. These coils can be either plain or finned tube. However, due to their greater surface area, finned tubes generally have a higher rate of heat transfer than plain tubes. On the basis of cost per unit surface area, finned tubes are less expensive than conventional tubes. There is also an advantage of weight saving, and complete coverage of the base area is not necessarily required to achieve specified temperatures. 

Why Do We Need to Know This Material The second law of thermodynamics is the key to understanding why one chemical reaction has a natural tendency to occur bur another one does not. We apply the second law by using the very important concepts of entropy and Gibbs free energy. The third law of thermodynamics is the basis of the numerical values of these two quantities. The second and third laws jointly provide a way to predict the effects of changes in temperature and pressure on physical and chemical processes. They also lay the thermodynamic foundations for discussing chemical equilibrium, which the following chapters explore in detail. 

Atmospheric emissions of sulphur dioxide are either measured or estimated at their source and are thus calculated on a provincial or state basis for both Canada and the United States (Figure 2). While much research and debate continues, computer-based simulation models can use this emission information to provide reasonable estimates of how sulphur dioxide and sulphate (the final oxidized form of sulphur dioxide) are transported, transformed, and deposited via atmospheric air masses to selected regions. Such "source-receptor" models are of varying complexity but all are evaluated on their ability to reproduce the measured pattern of sulphate deposition over a network of acid rain monitoring stations across United States and Canada. In a joint effort of the U.S. Environmental Protection Agency and the Canadian Atmospheric Environment Service, eleven linear-chemistry atmospheric models of sulphur deposition were evaluated using data from 1980. It was found that on an annual basis, all but three models were able to simulate the observed deposition patterns within the uncertainty limits of the observations (22). 

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