Discard

Figure 1.8 Optimization discards many structural features, leaving an optimized structure.

Fourier transform is widely used for signal analysis purposes and is satisfactory when applied to signals where stationary features are of particular interest. However, it turns out to be very poor when dealing with defect detection, where it is the non stationary characteristics of the signal which has to be highlighted. The main reason is that in the Fourier analysis, the time parameter is discarded. 

For that reason, we chose to build a "detection cartography" out of the 16 scalo-grams, by selecting one particularly pertinent scale for detection, and discarding all the... 

The following device, discarding to an attribute suitable - not suitable is the installation for the testing of welding by friction (figure 7). The given device allows carrying out the... 

The solution adopted by us is the use of computer simulations of mathematical models of the process and the mock-up situations. Eventually, simulation techniques will become so accurate, that the mock-up step can be discarded. For the time being it is reasonable to use such models to generate corrections for smaller differences between mock-up and process. 

Taking advantage of the synnnetry of the crystal structure, one can list the positions of surface atoms within a certain distance from the projectile. The atoms are sorted in ascending order of the scalar product of the interatomic vector from the atom to the projectile with the unit velocity vector of the projectile. If the collision partner has larger impact parameter than a predefined maximum impact parameter discarded. If a... 

The idea may be illustrated by considering first a method for increasing the acceptance rate of moves (but at the expense of trying, and discarding, several other possible moves). Having picked an atom to move, calculate the new trial interaction energy for a range of trial positions t = 1.. . k. Pick the actual attempted move from this set, with a probability proportional to the Boltzmann factor. This biases the move selection. 

When the correct solvent for recrystallisation is not known a procedure similar to that given on pp. 15-16 should be followed, but on the semi-micro scale not more than 10 mg. of the solid should be placed in the tapered-end test-tube (Fig. 29(B)) and about o i ml. of the solvent should be added from the calibrated dropping-pipette (Fig. 30(B)). If the compound dissolves readily in the cold, the solvent is unsuitable, but the solution should not be discarded. [In this case recourse should be had to the use of mixed solvents (p. 18). For example if the substance is very soluble in ethanol, water should be added from a calibrated pipette with shaking to determine whether crystallisation will now take place, indicated by a cloudiness or by the separation of solid.]... 

If the solid does not dissolve in the cold solvent gently heat the mixture over a micro-Bunsen burner or in a small water-ba until the liquid boils. Continue to add o-i ml. portions of solvent until the solid dissolves. [If more than about i ml. of solvent is required, the solvent is considered unsatisfactory.] If a clear solution is obtained, cool the tube and scratch it below the surface of the solution with a very fine glass rod and proceed as suggested on p. 16. In general, the products from the choice of solvent investigation are not discarded but added to the main bulk of the crude product for recrystallisation. 

Ethyl bromide soon distils over, and collects as heavy oily drops under the water in the receiving flask, evaporation of the very volatile distillate being thus prevented. If the mixture in the flask A froths badly, moderate the heating of the sand-bath. When no more oily drops of ethyl bromide come over, pour the contents of the receiving flask into a separating-funnel, and carefully run oflF the heavy lower layer of ethyl bromide. Discard the upper aqueous layer, and return the ethyl bromide to the funnel. Add an equal volume of 10% sodium carbonate solution, cork the funnel securely and shake cautiously. Owing to the presence of hydrobromic and sulphurous acids in the crude ethyl bromide, a brisk evolution of carbon dioxide occurs therefore release the... 

Fit securely to the lower end of the condenser (as a receiver) a Buchner flask, the side-tube carrying a piece of rubber tubing which falls well below the level of the bench. Steam-distil the ethereal mixture for about 30 minutes discard the distillate, which contains the ether, possibly a trace of unchanged ethyl benzoate, and also any biphenyl, CeHs CgHs, which has been formed. The residue in the flask contains the triphenyl carbinol, which solidifies when the liquid is cooled. Filter this residual product at the pump, wash the triphenyl-carbinol thoroughly with water, drain, and then dry by pressing between several layers of thick drying-paper. Yield of crude dry product, 8 g. The triphenyl-carbinol can be recrystallised from methylated spirit (yield, 6 g.), or, if quite dry, from benzene, and so obtained as colourless crystals, m.p. 162. ... 

Steam-distil the ethereal solution and discard the distillate. The residue in the flask is triphenyl-carbinol and solidifies on cooling. Filter at the pump, wash with water, drain and dry. Yield of crude product 0 6 g. Recrystallise when dry from benzene to obtain colourless crystals m.p. 162°. 

A 1500 ml. flask is fitted (preferably by means of a three-necked adaptor) with a rubber-sleeved or mercury-sealed stirrer (Fig. 20, p. 39), a reflux water-condenser, and a dropping-funnel cf. Fig. 23(c), p. 45, in which only a two-necked adaptor is shown or Fig. 23(G)). The dried zinc powder (20 g.) is placed in the flask, and a solution of 28 ml. of ethyl bromoacetate and 32 ml. of benzaldehyde in 40 ml. of dry benzene containing 5 ml. of dry ether is placed in the dropping-funnel. Approximately 10 ml. of this solution is run on to the zinc powder, and the mixture allowed to remain unstirred until (usually within a few minutes) a vigorous reaction occurs. (If no reaction occurs, warm the mixture on the water-bath until the reaction starts.) The stirrer is now started, and the rest of the solution allowed to run in drop-wise over a period of about 30 minutes so that the initial reaction is steadily maintained. The flask is then heated on a water-bath for 30 minutes with continuous stirring, and is then cooled in an ice-water bath. The well-stirred product is then hydrolysed by the addition of 120 ml. of 10% sulphuric acid. The mixture is transferred to a separating-funnel, the lower aqueous layer discarded, and the upper benzene layer then... 

The analogous procedure for a multivariate problem is to obtain many experimental equations like Eqs. (3-55) and to extract the best slopes from them by regression. Optimal solution for n unknowns requires that the slope vector be obtained from p equations, where p is larger than n, preferably much larger. When there are more than the minimum number of equations from which the slope vector is to be extracted, we say that the equation set is an overdetermined set. Clearly, n equations can be selected from among the p available equations, but this is precisely what we do not wish to do because we must subjectively discard some of the experimental data that may have been gained at considerable expense in time and money. 

One litre of commercial absolute alcohol (or any ethyl alcohol of 99 per cent, purity or better) is treated with 14 g. of clean, dry sodium when the sodium has completely reacted, 40 g. of pure ethyl formate are added. The mixture is refluxed for 2-3 hom , and the dry alcohol is distilled oflF as in Method 2 the first 25 ml. of distillate are discarded. The super-dry alcohol contains about 0 03 per cent, of water. 

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