Pad£ approximants

The reaction solution Is filtered through a Cellte pad (approximately 5 cm thick on a 32-cm Buchner funnel), and the solid Is washed repeatedly with tetrahydrofuran (1.5 L). The combined filtrates are concentrated under reduced pressure at a temperature not above 30°C. To the concentrate is added 1.5 L of ether. The solution Is stirred for 15 min, again filtered through Cellte, and concentrated at 30 C (Note 11). 

Figure 9. Plot of the correlation energy, given by the [2/1] PadS approximant to the third-order energy, against basis set size for beryllium-like ions.

In Section I we gave some boundary conditions on the behavior of diatomic potential functions. As a standard approach, the Pad approximant, which approximates a given diatomic potential function, is chosen in such a manner that these limitations are satisfied (Jordan et al., 1974 Jordan, 1975 Engelke, 1978 Yorish and Shcherbak, 1979). There exist two types of Pad6 approximants in the Dunham (D) version. They are as follows ... 

Such forms of the Pad approximants in D-version are caused by the molecular dissociation energy limit. For type I, we have only the diagonal Pad6 approximants. In the literature, there have been adopted two numerical procedures of finding coefficients. The first, developed by Jordan et al. (1974) and Jordan (1975), consists in the following procedure The coefficients a, 2 and M i are determined by the requirement that Eq. (10) must reproduce the first terms of the D-expansion. Then in that framework for [2/2],( D) and (3/3] ( d) we obtain (Jordan et al., 1974)... 

Figure 10. The full width at half maximum (ro/A) of the stochastic lineshape function a(

A short silica gel pad approximately 10 cm in length by 5 cm in diameter is recommended. Isolation of the product by distillation (bp 111-120°C, bath temperature 150°C) resulted in significant material loss presumably due to its thermal decomposition.6... 

G.A. Baker and P. Graves-Morris, Pad Approximants, Addison-Wesley, Reading, 1981. 

The greater our effort, the greater the error of our result. The error is equal to 13%for2L+l = 17, then it goes to 22% for 2L + 1 = 19, and finally, it attains 36% for 2L + 1 = 21. Despite of these hopeless results, it turns out that the problem is easy for the Pad approximants." They were already much better for L = 3. 

THPC—Amide—PoIy(vinyI bromide) Finish. A flame retardant based on THPC—amide plus poly(vinyl bromide) [25951-54-6] (143) has been reported suitable for use on 35/65, and perhaps on 50/50, polyester—cotton blends. It is appUed by the pad-dry-cure process, with curing at 150°C for about 3 min. A typical formulation contains 20% THPC, 3% disodium hydrogen phosphate, 6% urea, 3% trimethylolglycouril [496-46-8] and 12% poly(vinyl bromide) soUds. Approximately 20% add-on is required to impart flame retardancy to a 168 g/m 35/65 polyester—cotton fabric. Treated fabrics passed the FF 3-71 test. However, as far as can be determined, poly(vinyl bromide) is no longer commercially available. 

These problems can be dealt with by usiag artificial test cloths impregnated with various approximations of natural soils such as vacuum cleaner dust, dirt from air conditioner filters, clays, carbon black, fatty acids, dirty motor oil, and artificial sebum, either alone or ia combination (37,94—98). The soils are appHed by sprayiag, immersion, or padding. If the soils are carefully appHed, reproducible results can be obtained. Soil test cloths can be of great help ia detergency studies, when used with an understanding of their limitations. 

Equation 4.83 states that there are four variables involved. We have already determined the load variable, F, earlier. The load is applied at a mean distanee, /r, of 150 mm representing the eouple length, and is normally distributed about the width of the foot pad. The standard deviation of the eouple length, cr, ean be approximated by assuming that 6cr eovers the pad, therefore ... 

Once the grout materials have cured (dependent on grout composition and site conditions, but commonly approximately 24 h), a locking protective cover is installed in concrete over the top of the riser pipe. A concrete pad is commonly installed around the protective cover with its upper surface sloped away from the cover to shed precipitation and/or surface water (Figure 1). 

---