Product graph

Fig. 2 An example of the search space. The search space (c) is defined as the graph product of two enumeration trees for subsequences (a) and for subgraphs (b). (c) Covers all possible frequent subgraph-subsequence pairs...

The recursion rules in Proposition 2 make us keep all instances explicidy in the graph product T xTs. That is, Q SM must be kept and be passed to subsequent nodes. This is a space-consuming procedure, because two enumeration trees are practically very huge. Thus, we can consider a depth-first traversal of the graph product T x T by simplifying recursion rules in Proposition 2 into those in the following Proposition 4 (see Note 6). 

United States Department of Agriculture (2013). Coconut Oil Production by Country. Available at http //www.indexmundi.com/agriculture/ commodity=coconut-oil graph=production, last accessed September 4, 2013. 

The graph gives the yields that the refiner would obtain at the outlet of the atmospheric distillation unit allowing him to set the unit s operating conditions in accordance with the desired production objectives. 

The use of larger particles in the cyclotron, for example carbon, nitrogen or oxygen ions, enabled elements of several units of atomic number beyond uranium to be synthesised. Einsteinium and fermium were obtained by this method and separated by ion-exchange. and indeed first identified by the appearance of their concentration peaks on the elution graph at the places expected for atomic numbers 99 and 100. The concentrations available when this was done were measured not in gcm but in atoms cm. The same elements became available in greater quantity when the first hydrogen bomb was exploded, when they were found in the fission products. Element 101, mendelevium, was made by a-particle bombardment of einsteinium, and nobelium (102) by fusion of curium and the carbon-13 isotope. 

Correlation with markets for other products is particularly useful for a new product. For example, market growth history of an older product, eg, nylon, can be plotted on a graph to predict the probable growth for a newer product, eg, polyester fibers. Data for both products may be plotted on the same chart, though not necessarily to the same scale and with the time scale shifted to bring the respective curves in parallel. 

Each reactant and product appears in the Nemst equation raised to its stoichiometric power. Thermodynamic data for cell potentials have been compiled and graphed (3) as a function of pH. Such graphs are known as Pourbaix diagrams, and are valuable for the study of corrosion, electro deposition, and other phenomena in aqueous solutions.Erom the above thermodynamic analysis, the cell potential can be related to the Gibbs energy change... 

Breakeven charts present a snapshot of the present situation by means of graphs which are generally drawn in the manner shown in Figs. 9-2, 9-3, and 9-4. Since the lines are straight, this implies that Cs, Cy , and Aee will remain constant over the range of variation of R, which is of interest. The values would be based on the production rate currently achieved (or scheduled), since all the data are available from... 

Crystallizers with Fines Removal In Example 3, the product was from a forced-circulation crystallizer of the MSMPR type. In many cases, the product produced by such machines is too small for commercial use therefore, a separation baffle is added within the crystallizer to permit the removal of unwanted fine crystalline material from the magma, thereby controlling the population density in the machine so as to produce a coarser ciystal product. When this is done, the product sample plots on a graph of In n versus L as shown in hne P, Fig. 18-62. The line of steepest ope, line F, represents the particle-size distribution of the fine material, and samples which show this distribution can be taken from the liquid leaving the fines-separation baffle. The product crystals have a slope of lower value, and typically there should be little or no material present smaller than Lj, the size which the baffle is designed to separate. The effective nucleation rate for the product material is the intersection of the extension of line P to zero size. 

In this equation, all of the terms except y +i and x but including x, are constant. Hence the relationship between and x is linear with a slope of L j(L + D) and a line representing the relationship on a graph of y vs jc must pass tlrrough y = jcd when x — jcd, since tire vapour and the liquid have the same composition in the product. This is called the rectifying operating line in a graphical representation of tire distillation process. 

While the F-N curve is a cumulative illustration, the risk profile shows the expected frequency of accidents of a particular category or level of consequence. The diagonal line is a line of constant risk defined such that the product of expected frequency and consequence is a constant at each point along the line. " As the consequences of accidents go up, the expected frequency should go down in order for the risk to remain constant. As the example illustrates, if a portion of the histogram sticks its head up above the line (i.e., a particular type of accident contributes more than its fair share of the risk), then that risk is inconsistent with the risk presented by other accident types. (Note There is no requirement that you use a line of constant risk other more appropriate risk criteria for your application can be easily defined and displayed on the graph.)... 

If air quality data at a receptor for any one averaging time are lognormally distributed, these data will plot as a straight line on log probability graph paper (Fig. 4-9) which bears a note Sg = 2.35. Sg is the standard geometric deviation about the geometric mean (the geometric mean is the Nth root of the product of the n values of the individual measurements). 

With the same scanning capability, it is much faster and often more useful to simply scan one line on a sample. The data is again output to a color CRT, but it is presented as the modulation of the y-amplitude, which is determined by the intensity of the X-ray signal production ftom the ROI of the element of interest. As the probe scans along the line, the CRT plots a graph of the elemental counting rates versus distance. Here again, it is usually possible to plot the data from many ele-... 

Figure 1. Graph of the Reciprocal of the Diffusivity against the Product of the Cube Root of the Molar volume and the Square Root of the Molecular Weight...

The preceding graph shows the time-dependent concentrations of each component. The profile for B drops nearly linearly with time and that of product rises the same way The concentration of A is very small until most of B is used up and then it rises sharply with time. 

Productivity is addressed under Continuous improvement and in order to improve productivity you will need to collect data generally in the form of resource/part produced. Resource can be hours, costs, weight, or volume of material consumed. Graphs showing the productivity trend over time for plants, products, and processes would satisfy this requirement. 

Records can take various forms reports containing narrative, computer data, forms containing data in boxes, graphs, tables, lists, and many others. Where forms are used to collect data, they should carry a form number and name as their identification. When completed they should carry a serial number to give each a separate identity. Records should also be traceable to the product or service they represent and this can be achieved either within the reference number or separately, providing the chance of mistaken identity is eliminated. The standard does not require records to be identifiable to the product involved but unless you do make such provision you will not be able to access the pertinent records or demonstrate conformance to specified requirements. 

Both factors depend on the respective partial vapor pressures of water and carbon dioxide and upon the distance to the radiation source. The partial vapor pressure of carbon dioxide in the atmosphere is fairly constant (30 Pa), but the partial vapor pressure of water varies with atmospheric relative humidity. Duiser (1989) published graphs plotting absorption factors (a) against the product of partial vapor pressure and distance to flame (Px) for flame temperatures ranging from 800 to 1800 K. 

The graph in Fig. 10.12 shows that the purity decreases very quickly below acceptable levels as retention factor of the more retained enantiomer decreases. Flowever, with minor adjustment of the SMB internal flow rates, a variation of more than 10 % of the retention factor of the more retained enantiomer still meets required purity, productivity, and eluent consumption. Control of critical parameters such as retention factors can be made without modification of the feed and eluent flowrates. 

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