Rounding procedure

If the rounding procedures used for the display did not mask the effect, the math packs that are in use would come up with seemingly nonsensical results now and then, e.g., instead of a straight 6 one might obtain 5.9999999999999 or 6.0000000000001 those who do their own programming in BASIC, for example, are aware of this. 

Other topics to be reviewed include maintenance and upcoming work. A routine rounds procedure is shown in Figure 6.6. It is to be followed by the outside operator at the start and end of each shift. 

The CSI for a package, overpack or freight container should be rounded up to the first decimal place. For example, if the value of N is 11, then 50/N is 4.5454 and that value should be rounded up to provide a CSI = 4.6. The CSI should not be rounded down. To avoid disadvantages by this rounding procedure with the consequences that only a smaller number of packages can be transported (in the given example the number would be 10), the exact value of the CSI may be taken. 

If we would have rounded one decimal place more, 5.136 will become 5, we would have generated an additional Oa = I/V12 equals 0.288 and the standard deviation in the final result would be a = V(0.05 + 0.288 ) equals 0.294. By rounding so roughly, the standard deviation is nearly completely determined by the rounding procedure. 

The Petroleum Measurement Tables published in 1980, except for Tables 33 and 34 (which are being reissued without change), represent a major conceptual departure from previous versions. Inherent in the Petroleum Measurement Tables is the recognition of the present and future position of computers in the petroleum industry. The actual standard represented by the Petroleum Measurement Tables is neither the hardcopy printed tables nor the set of equations used to represent the density data but is an explicit implementation procedure used to develop computer subroutines for Tables 3,6,23,24,53, and 34. The standardization of an implementation procedure implies the standardization of the set of mathematical expressions, including calculational sequence and rounding procedures, used within the computer code. Absolute adherence to the outlined procedures will ensure that all computers and computer codes of the future, meeting the stated specifications and restrictions, will be able to produce identii results. Hence, the published implementation procedures are the primary standard, the... 

Reactor Operations Department routine rounds procedures are used to collect predictive maintenance information. Motor stator temperatures and bearing temperatures are recorded periodically on the operator s round sheets. Lube oil sampling for tfie Bingham pumps is performed using DPSOL 105-6101A, "Sample-Analysis Schedule and Control-Routine" (Reference 13) DPSOL 6101B, "Sample Description And Location" (Reference 14) and DPSOL 6101C, "Sample Analysis Schedule and Control-Data Sheet and Schedule" (Reference 15). 

In fig. 2 an ideal profile across a pipe is simulated. The unsharpness of the exposure rounds the edges. To detect these edges normally a differentiation is used. Edges are extrema in the second derivative. But a twofold numerical differentiation reduces the signal to noise ratio (SNR) of experimental data considerably. To avoid this a special filter procedure is used as known from Computerised Tomography (CT) /4/. This filter based on Fast Fourier transforms (1 dimensional FFT s) calculates a function like a second derivative based on the first derivative of the profile P (r) ... 

As a first step in the direction outlined here some manufacturers and BAM last year discussed the problems and the possible procedures of such a system of quality assurance. As a result of this meeting round robin tests for the harmonization of the measurements of film system parameters and a possible procedure of surveillance of the quality of film systems were proposed. Closely related to these the BAM offers to perform the classification of film systems. But as during the production of films variations of the properties of the different batches cannot be avoided, the results of measurements of films of a single batch will be restricted to this charge, while only the measurements and mean of several batches of a film type will give representative values of its properties. This fact is taken into account already in section 4 of the standard EN 584-1 which can be interpreted as a kind of continuous surveillance. In accordance with this standard a film system caimot be certified on the base of measurements of a single emulsion only. 

A first comprehensive round robin test described in 4.1 which is open to all interested parties will be followed periodically by round robin tests in a reduced extent to ensure the further harmonisation of measurement procedures. The check of measurering equipments and procedures is an inalienable requirement for the further steps for providing the users with constant film quality. Together with sample tests performed by BAM as indicated in section 4.2 and and the production control by the manufacturer it will be possible to survey the film systems whether they meet the requirements of one of the film classes of EN 584-1. 

In case of mixed systems the procedure must be varied and it would be restricted to the special film systems of interest, of course. Mixed systems would be used by inspection companies and industrial users who normally do not dispose of the equipment for measurements as mentioned above. In these cases instead of a round robin test only periodical measurements of the properties of these mixed film systems by an independent third party institution can be used for film classification and continuous surveillance. 

All numerical computations inevitably involve round-off errors. This error increases as the number of calculations in the solution procedure is increased. Therefore, in practice, successive mesh refinements that increase the number of finite element calculations do not necessarily lead to more accurate solutions. However, one may assume a theoretical situation where the rounding error is eliminated. In this case successive reduction in size of elements in the mesh should improve the accuracy of the finite element solution. Therefore, using a P C" element with sufficient orders of interpolation and continuity, at the limit (i.e. when element dimensions tend to zero), an exact solution should be obtaiiied. This has been shown to be true for linear elliptic problems (Strang and Fix, 1973) where an optimal convergence is achieved if the following conditions are satisfied ... 

Cuprous cyanide solution. The most satisfactory method is to dissolve the cuprous cyanide (1 mol) in a solution of technical sodium cyanide (2 5-2-6 mols in 600 ml. of water). If it is desired to avoid the preparation of solid cuprous cyanide, the following procedure may be adopted. Cuprous chloride, prepared from 125 g. of copper sulphate crystals as described under 1 above, is suspended in 200 ml. of water contained in a 1-litre round-bottomed flask, which is fitted with a mechanical stirrer. A solution of 65 g. of technical sodium cyanide (96-98 per cent.) in 100 ml. of water is added and the mixture is stirred. The cuprous chloride passes into solution with considerable evolution of heat. As the cuprous cyanide is usually emplo3 ed in some modification of the diazo reaction, it is usual to cool the resulting solution in ice. 

Allyl Chloride. Comparatively poor yields are obtained by the zinc chloride - hydrochloric acid method, but the following procedure, which employs cuprous chloride as a catalyst, gives a yield of over 90 per cent. Place 100 ml. of allyl alcohol (Section 111,140), 150 ml. of concentrated hydrochloric acid and 2 g. of freshly prepared cuprous chloride (Section II,50,i one tenth scale) in a 750 ml. round-bottomed flask equipped with a reflux condenser. Cool the flask in ice and add 50 ml. of concen trated sulphuric acid dropwise through the condenser with frequent shaking of the flask. A little hydrogen chloride may be evolved towards the end of the reaction. Allow the turbid liquid to stand for 30 minutes in order to complete the separation of the allyl chloride. Remove the upper layer, wash it with twice its volume of water, and dry over anhydrous calcium chloride. Distil the allyl chloride passes over at 46-47°. 

Place 125 ml. of glacial acetic acid, 7 -5 g. of purifled red phosphorus (Section II,50,d) and 2 5 g. of iodine in a 500 ml, round-bottomed flask fitted with a reflux condenser. Allow the mixture to stand for 15-20 minutes with occasional shaking until aU the iodine has reacted, then add 2 5 ml. of water and 50 g, of benzilic acid (Section IV,127). Boil the mixture under reflux for 3 hours, and filter the hot mixture at the pump through a sintered glass funnel to remove the excess of red phosphorus. Pour the hot filtrate into a cold, weU-stirred solution of 12 g. of sodium bisulphite in 500 ml, of water the latter should be acid to litmus, pro duced, if necessary, by passing sulphur dioxide through the solution. This procedure removes the excess of iodine and precipitates the diphenyl-acetic acid as a fine white or pale yellow powder. Filter the solid with suction and dry in the air upon filter paper. The yield is 45 g., m.p. 

Alternatively, use the following procedure in which triethylamine replaces potassium acetate as the basic catalyst. Place 2 1 g. (2-0 ml.) of purified benzaldehyde, 2 0 ml. of anhydrous triethylamine and 5 0 ml. of A.R. acetic anhydride in a 200 ml. round-bottomed flask, equipped with a short reflux condenser and a calcium chloride drying tube. Boil the solution gently for 24 hours—heating may be interrupted. Incorporate a steam distillation apparatus in the flask and steam distil until the distillate is no longer cloudy (about 100 ml.) and then collect a further 50 ml. of the distillate di ard the steam distillate. Transfer the residue in the flask to a 400 ml. beaker, add water until the vplume is about 200 ml., then 0 2 g. of decolourising carbon, and boil for a few minutes. Filter the hot solution, and acidify the hot filtrate with 1 1 hydrochlorioiaoid... 

This procedure is used to separate crystallized product from solvent or to remove crap and solids from a liquid. Figure 8 shows the proper apparatus to use. The collecting flask is called a side arm flask and to that extended nipple (tee heel) is attached a vacuum source. The thing that is shoved through the rubber stopper is called a Buchner funnel and is usually made of white porcelain or, preferably, PP. The Buchner funnel, when viewed from above, can be seen to have lots of pin holes in the bottom surface of its reservoir. Over this surface is layered a single sheet of rounded filter paper or paper towel. 

GENERAL PROCEDURE The Alcoholic alkaline solution is prepared by prolonged stirring of 8.8g (or 4.4g) of KOH pellets in 30mL of alcohol. The alkaline solution is placed in a round-bottom flask provided with a reflux condenser (microwave or conventional systems). Then 4.0g of Safrole (or eugenol) is added and the solution heated."... 

Alkvl Azides from Alkyl Bromides and Sodium Azide General procedure for the synthesis of alkyl azides. In a typical experiment, benzyl bromide (360 mg, 2.1 mmol) in petroleum ether (3 mL) and sodium azide (180 mg, 2.76 mmol) in water (3 mL) are admixed in a round-bottomed flask. To this stirred solution, pillared clay (100 mg) is added and the reaction mixture is refluxed with constant stirring at 90-100 C until all the starting material is consumed, as obsen/ed by thin layer chromatographv using pure hexane as solvent. The reaction is quenched with water and the product extracted into ether. The ether extracts are washed with water and the organic layer dried over sodium sulfate. The removal of solvent under reduced pressure affords the pure alkyl azides as confirmed by the spectral analysis. ... 

Apparabus 1-1 One-necked, round-bottomed flask for the hydrolysis procedure see Chapter I, Fig. 3. 

Hove 1. The procedure described in Ref. 1 was modified. To a solution of 2.0 mol of lithium acetylide in 1.2 1 of liquid ammonia in a 4-1 round-bottomed, three-necked flask (see Fig. 2) was added 1.5 mol of freshly distilled benzaldehyde with cooling at about -45°C. After an additional 30 min finely powdered ammonium chloride (2 mol) was introduced in 15 min. The ammonia was allowed to evaporate, then water (1.1 1) was added and the product was extracted with diethyl ether. After drying over magnesium sulfate the extract was concentrated in a water-pump vacuum. High-vacuum distillation,... 

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