The Direct-Requirements Table

The dollar flow matrix in Tables 4.2 and 4.4a can be normalized to yield a table of coefficients that represents the fractions of a dollar required by a sector to produce a dollar of output. This is done as follows dividing any element Xkj in the use table by the output of a sector gives the dollar input from industry k required for 1 output from industry j (6). This is defined as the direct coefficient  

In tabular form, the direct coefficients of an entire economy are referred to as direct-requirements tables. Table 4.9 is the direet-requirements table for the four-sector economy illustrated in Table 4.2. Each column shows the inputs to the industry named at the top of the column required from the industry in each row at the left for 1 of column industry output 

Industry k Dollar input from k needed to produce 1 output from industry j 

For example, to produce 1 output, the plastics and synthetic materials industry 28 requires input from 58 industries. It requires the most input from industrial and other chemicals (33.2 cents), paper and allied products (1.1 cents), and wholesale and retail trade (4.3 cents). Table 4.11 lists the five largest suppliers of sectors 8,9-1- 10, 24, 27A, and 28, as well as 29A and 29B, in terms of dollar of direct input per total dollar output. 

The direct-requirements table permits the estimation of changes in output directly required of any industry k due to changes in total output of industries supplied by industry k. Assuming that the direct coefficients remain constant, this is accomplished as follows  

---

Table 4.10, which may be found in Appendix C, is the direct-requirements table of the U.S. economy in 1987. Note that special industries 82-85 are not... 

Table 4.9 is obtained by using Eq. (4.8). For example, the direct requirement of the energy industry for service is 0.185, which is obtained by dividing 12 billion of service industry input by the total output of the energy sector, 65 billion. Table 4.9 shows that in addition to service costs of 18.5 cents, the energy sector needs 35.4 cents of input from itself, 44.6 cents of value added (mostly employee compensation), and 1.5 cents from basic industry to produce 1 of output. 

The total-requirements table for the U.S. economy for 1987 is given as Table 4.15 (see Appendix C). The elements of this table are obtained by inverting the I - D matrix, where D is found from Table 4.10. Each column shows the output required both directly and indirectly from the industry named at the left of each row per dollar of delivery to final demand by the industry named at the head of the column. Returning to our automobile example, a 10 million increase in final demand for the products of industry 59A requires an increase of 0.0.3769 X 10,000,000 = 376,900 in total output in both direct and indirect requirements for products of industry 27A. This is about eight times the direct-requirement increase of 45,200 computed by using the direct requirement only. 

Help Sharppencil construct the transactions table, direct-requirements table, and total-requirements table. 

Full notiHcation is required 60 days before a substance is to be supplied to the EC at an amount of one tonne a (or 5 tonnes cumulative). The information required for the notiHcation (the Base Set ) is specified in Annex VII of the Directive (see Table 34.1). It consists of the identity of the substance, commercial information, recommendations for safe handling and use, physico-chemical properties, animal toxicology, mutagenicity studies, ecotoxicology, recommendations for disposal, the proposed classification and labelling and a draft MSDS for dangerous substances. 

Further information must be submitted when the amount of substance supplied to the EC reaches the Level 1 and Level 2 trigger points. The possible studies are given in Annex VIII of the Directive (see Tables 34.4 and 34.5) although those required will depend on the particular substance. Level 1 testing may be required at 10 tonnes a (or 50 tonnes cumulative), but will definitely be required (if not already done) at 100 tonnes annually (or 500 tonnes cumulative). Level 2 testing will be required at 1000 tonnes a (or 5000 tonnes cumulative). 

Prostaglandins arise from unsaturated C20 carboxylic acids such as arachidonic acid (see Table 26 1) Mammals cannot biosynthesize arachidonic acid directly They obtain Imoleic acid (Table 26 1) from vegetable oils m their diet and extend the car bon chain of Imoleic acid from 18 to 20 carbons while introducing two more double bonds Lmoleic acid is said to be an essential fatty acid, forming part of the dietary requirement of mammals Animals fed on diets that are deficient m Imoleic acid grow poorly and suffer a number of other disorders some of which are reversed on feed mg them vegetable oils rich m Imoleic acid and other polyunsaturated fatty acids One function of these substances is to provide the raw materials for prostaglandin biosynthesis... 

Ring-Substituted Derivatives The ring-chlorinated derivatives of benzyl chloride, benzal chloride, and benzotrichloride are produced by the direct side-chain chlorination of the corresponding chlorinated toluenes or by one of several indirect routes if the required chlorotoluene is not readily available. Physical constants of the main ring-chlorinated derivatives of benzyl chloride, benzal chloride, and benzotrichloride are given in Table 4. 

For estimating purposes for direct-heat drying applications, it can be assumed that the average exit-gas temperature leaving the sohds bed wih approach the final solids discharge temperature on an ordi-naiy unit carrying a 5- to 15-cm-deep bed. Calculation of the heat load and selec tion of an inlet-air temperature and superficial velocity (Table 12-32) will then permit approximate sizing, provided an approximation of the minimum required retention time can be made. 

When tested in accordance with the methods given in Table 20.1 the properties of the commercial butane and commercial propane shall be in accordance with the limiting requirements given in that table. For gauge vapor pressure, either the direct measurements method described in BS 3324 or the calculation procedure described in Appendix C of this standard shall be used. 

Most plant sites have access to a public supply of water. Until recently this was legally required to be no more than wholesome and palatable . Water suppliers are now responsible for meeting the EC s Directives (see Table 31.1). Wherever possible, all drinking-water taps should be served directly from the incoming main, and the plant engineer s sole responsibility is to ensure that no deterioration takes place within his system. 

To illustrate the correct approach, consider applications in which a material is used in sheet form, as in automotive body panels, and suppose that the service requirements are for stiffness and strength in flexure. First imagine four panels with identical dimensions that were manufactured from the four materials given in Table 3-1. Their flexural stiffnesses and strengths depend directly on the respective material s modulus and strength. All the other factors are shared in common with the other materials, there being no significantly different Poisson ratios. Thus, the relative panel properties are identical with the relative material properties illustrated in Fig. 3-3. Obviously, the metal panels will be stiffer and... 

There have been a number of amending directives since the base directives were issued these are summarised in Table 1.4. Directive 2007/47/EC is the most important as it contains significant amendments to all three base directives. It builds on the practical experience gained in implementing the directives, and sets out to simplify and harmonise the language of the directives so as to ensure consistent interpretation and application of the requirements in all Member States. Among other items addressed,... 

Although the decomposition of a data table yields the elution profiles of the individual compounds, a calibration step is still required to transform peak areas into concentrations. Essentially we can follow two approaches. The first one is to start with a decomposition of the peak cluster by one of the techniques described before, followed by the integration of the peak of the analyte. By comparing the peak area with those obtained for a number of standards we obtain the amount. One should realize that the decomposition step is necessary because the interfering compound is unknown. The second approach is to directly calibrate the method by RAFA, RBL or GRAFA or to decompose the three-way table by Parafac. A serious problem with these methods is that the data sets measured for the sample and for the standard solution should be perfectly synchronized. 

---