Dilation methods

The eigenenergies and eigenfunctions of resonant eigenstates may be obtained by the complex dilation method[21, 22] which is illustrated in fig. 4. The... 

A number of computer algorithms for measuring perimeter dimension are reviewed by Allen et al. [52], including several computer-based implementations of the divider method. They conclude that Adler and Hancock s [53] distance transform method is a more accurate and faster analysis than the popular dilation method approach to box counting. This is generally considered the preferred method to use for measuring perimeter dimension. 

Adler, J. and Hancock, D. (1994). Advantages of using a discrete distance transform function in the measnrement of fractal dimensions by the dilation method. Powder Technol., 78,191-196. 

Suitable measuring temperatures are 10,15,20,25, 30, 35,40 and increases of 5° up to 60 °C, as required. However, unlike in the dilatation method, it is not necessary to measure at all these temperatures. In general, the temperatures chosen will correspond to those for the long- or short-range dilatation (Section 6.2.4). 

If the hub removal is necessary, such as required on compressor with non-split seals, a tapered hub fit on the shaft should be used. The removable hubs should have tapped puller holes. The shaft should be keyless with the preferred method of installation and removal by use of hydraulic dilation. Two injection ports 180° apart should be used whether injection is through the shaft or through the hub. Shrink fits should be 2 to 2.5 mil/in. of diameter. API 671 rcL ommends 1,5 mil/in. minimum, but experience indicates the heavier shrink may be required. For the juncture rating calculation, a f ra lion value of. 12 is recommended. 

Many antihypertensive drug lower the blood pressure by dilating or increasing the size of the arterial blood vessels (vasodilatation). Vasodilatation creates an increase in the lumen (the space or opening within an arteiy) of the arterial blood vessels, which in turn increases the amount of space available for the blood to circulate Because blood volume (the amount of blood) remains relatively constant, an increase in the space in which the blood circulates (ie, the blood vessels) lowers the pressure of the fluid (measured as blood pressure) in the blood vessels. Although the method by which anti-hypertensive drug dilate blood vessels varies, the result... 

Potential methods of measurement for dilatation parameters are the damping of transverse and longitudinal surface waves and the damping of vibrating bubbles. For theory and measuring techniques see Wiistneck and Kretzschmar [47]. 

Hsu and Berger [43] used the maximum bubble pressure method (MBP) to study the dynamic surface tension and surface dilational viscosity of various surfactants including AOS and have correlated their findings to time-related applications such as penetration and wetting. A recent discussion of the MBP method is given by Henderson et al. [44 and references cited therein]. 

Method 1. Treat 2 - 0 g. of the mixture of amines with 40 ml. of 10 per cent, sodium hydroxide solution and add 4 g. (3 ml.) of benzenesulphonyl chloi de (or 4 g. of p-toluenesulphonyl chloride) in small portions. Warm on a water bath to complete the reaction. Acidify the alkaline solution with dilute hydrochloric acid when the sulphonamides of the primary and secondary amines are precipitated. Filter off the solid and wash it with a little cold water the tertiary amine wiU be present in the filtrate. To convert any disulphOnamide that may have been formed from the primary amine into the sulphonamide, boil the solid under reflux with 2 0 g. of sodium dissolved in 40 ml. of absolute ethyl alcohol for 30 minutes. Dilute with a little water and distil off the alcohol filter off the precipitate of the sulphonamide of the secondary amine. Acidify the filtrate with dUute hydrochloric acid to precipitate the derivative of the primary amine. Recrystallise the respective derivatives from alcohol or from dilate alcohol, and identify them inter alia by a determination of the m.p. 

Method 2. Place a 3 0 g. sample of the mixture of amines in a flask, add 6 g. (4-5 ml.) of benzenesulphonyl chloride (or 6 g. of p-toluenesulphonyl chloride) and 100 ml. of a 5 per cent, solution of sodium hydroxide. Stopper the flask and shake vigorously until the odour of the acid chloride has disappeared open the flask occasionally to release the pressure developed by the heat of the reaction. Allow the mixture to cool, and dissolve any insoluble material in 60-75 ml. of ether. If a solid insoluble in both the aqueous and ether layer appears at this point (it is probably the sparingly soluble salt of a primary amine, e.g., a long chain compound of the type C,H5(CHj) NH2), add 25 ml. of water and shake if it does not dissolve, filter it off. Separate the ether and aqueous layers. The ether layer will contain the unchanged tertiary amine and the sulphonamide of the secondary amine. Acidify the alkaline aqueous layer with dilate hydrochloric acid, filter off the sulphonamide of the primary amine, and recrystaUise it from dilute alcohol. Extract the ether layer with sufficient 5 per cent, hydrochloric acid to remove all the tertiary amine present. Evaporate the ether to obtain the sulphonamide of the secondary amine recrystallise it from alcohol or dilute alcohol. Finally, render the hydrochloric acid extract alkaline by the addition of dilute sodium hydroxide solution, and isolate the tertiary amine. 

In the corresponding column-standardized biplot of Fig. 31.7 we find all representations of the eight chromatographic methods more or less at the same distance from the origin of space. The circle is distorted because of the large difference between the contributions of the first and second latent variables (95 and 4%) and the choice of a = [3 = 0.5 which has been made at the outset. The combined effect is an apparent dilation of the vertical axis. 

This equation will only apply at points away from the cone to cylinder junction. Bending and shear stresses will be caused by the different dilation of the conical and cylindrical sections. This can be allowed for by introducing a stress concentration factor, in a similar manner to the method used for torispherical heads,... 

Among these techniques, the capacitance dilatometer method may be very sensitive. The change in the sample length produces a capacitance change between the two electrodes of a capacitor one plate of the capacitor is kept in a fixed position while the other is fixed onto one end of the sample. At the maximum elongation of the sample, the two capacitor plates are practically in contact. When the sample contracts the capacitance varies as 1 /AL. One of the main difficulties in this measurement is the realization of a dilatation-free support. 

Nienow and Elson (1988) have reviewed work done mainly by them and their co-workers on the mixing of non-Newtonian liquids in tanks. The above approach for inelastic, shearing thinning liquids has been largely substantiated but considerable doubt has been cast over using this method for dilatant, shear thickening materials. 

In the double-crystal mode, tilts and dilations can only be distinguished by use of more than one reflection and then reconstructing the strain field. A direct method for producing tilt or dilation maps involves the use of an analyser crystal after the specimen. In the true triple-axis geometry (Figrue 10.17), the analyser selects the scattered intensity from a small voltrme of reciprocal space. It is easy to see... 

Another group which is used to mask polar groups in molecules in order to improve GC peak shape is the trimethylsilyl group. Atropine Eye Drops BP are used to dilate the pupil prior to cataract surgery. The 1993 BP method for the analysis of Atropine Eye Drops BP uses derivatisation with a trimethylsilyl group to mask an alchohol group as shown in Figure 11.17. 

Digoxin is indicated in patients with heart failure and atrial fibrillation. It is also most helpful in patients with a dilated heart and third heart sound. It is usually given only when diuretics and ACE inhibitors have failed to control symptoms. Only about 50% of patients with normal sinus rhythm (usually those with documented systolic dysfunction) will have relief of heart failure from digitalis. Better results are obtained in patients with atrial fibrillation. If the decision is made to use a cardiac glycoside, digoxin is the one chosen in most cases (and the only one available in the USA). When symptoms are mild, slow loading (digitalization) with 0.125-0.25 mg per day is safer and just as effective as the rapid method (0.5-0.75 mg every 8 hours for three doses, followed by 0.125-0.25 mg per day). 

Until much more progress is made on these very fundamental approaches, greater accuracy is believed possible in engineering work that is based on the better developed discussion reviewed here. To this end a method has recently been proposed whereby the properties of all four time-independent fluids (Newtonian, pseudoplastic, dilatant, and Bingham plastic) may be quantitatively compared. 

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