Variable transformer

Many forms and sizes of magnetic stirring apparatus are available commercially. These include those fitted with an electric hot plate attached to the flat top the hot plate is controlled by an energy regulator or variable transformer (Variac). 

Fig. II, 17, 2 illustrates a fractional distillation unit f for use with glass helices. The column is provided with an electrically-heated jacket the resistance shown in the Figure may be replaced by a variable transformer. The still head is of the total-condensation variable take-off type aU the vapour at the top of the column is condensed, a portion of the condensate is returned to the column by means of the special stopcock (permitting of...

The flask (150, 250 or 500 ml.) is provided vdth a cylindrical extension at the bottom forming a boiling tube the latter is heated electrically and the heat input is controlled by a resistance or variable transformer. 

If crystallisation commences as soon as the solvent cools or if large quantities of hot solution are to be filtered, the funnel (and fluted filter paper) should be warmed externally during the filtration (hot water funnel). Three types of hot water funnel are illustrated in Fig. 11,1, 6 no flames should be present whilst inflammable solvents are being filtered through the funnel of Fig. 11, 1, 6, a. Alternatively, the funnel may be surrounded by an electric heating mantle (see Section 11,57) the heat input may be controlled by a variable transformer. When dealing with considerable volumes of aqueous or other solutions which do not deposit crystals rapidly on cooling, a Buchner funnel may be used for filtration (see detailed account in Section 11,1 and Fig. 11 1, 7, c). The filter paper... 

Pressure. Most pressure measurements are based on the concept of translating the process pressure into a physical movement of a diaphragm, bellows, or a Bourdon element. For electronic transmission, these basic elements are coupled with an electronic device for transforming a physical movement associated with the element into an electronic signal proportional to the process pressure, eg, a strain gauge or a linear differential variable transformer (LDVT). 

This suggests drat could be a useful variable transformation. Then the... 

The submitters used a transformer purchased from the Franklin Transformer Company, Minneapolis, Minnesota, for 25-30. It was provided with taps so that secondary voltages of 5500, 6600, 7700, 8800, 9900, and 11,000 could be obtained. These transformers do not always deliver the rated voltage and hence should be calibrated by actual measurement. The checkers used a luminous tube transformer obtained from the Jefferson Electric Company, Bellwood, Illinois, Cat. No. 721-411. Cap. 825 VA. Primary 115 V.A.C. 60 cycles. Secondary 15,000 V. 60 M.A. Price 19.60. The variable transformer used to regulate the voltage should be rated at 7.5 amperes and may be a Varitran, Adjustavolt, or Variac. 

One or two minutes of a Stir-O-Vac operated through a variable transformer at full voltage is required. 

Variable transformer/rectifier sets rated at 12-50 V and current sufficient to give 15-50 A/dm supply d.c. power. 

Heating mantles. These consist of a flexible knitted fibre glass sheath which fits snugly around a flask and contains an electrical heating element which operates at black heat. The mantle may be supported in an aluminium case which stands on the bench, but for use with suspended vessels the mantle is supplied without a case. Electric power is supplied to the heating element through a control unit which may be either a continuously variable transformer or a thyristor controller, and so the operating temperature of the mantle can be smoothly adjusted... 

The requirement of Postulate 3 that the equations of motion be form-invariant (i.e., that fix ) and A u(x ) satisfy the same equation of motion with respect to a as did fx) and Au x) with respect to x demands that the field variables transform under such transformations according to a finite dimensional representation of the Lorentz group. In other words it demands that transform like a spinor... 

For convenience, mass fraction units are used for [I] and [M] instead of moles per unit volume to eliminate density, which is assumed constant. With an appropriate variable transformation and series expansion, the analytical solution of differential Equation 10 can be derived. The solution is as follows. 

To benchmark our learning methodology with alternative conventional approaches, we used the same 500 (x, y) data records and followed the usual regression analysis steps (including stepwise variable selection, examination of residuals, and variable transformations) to find an approximate empirical model, / (x), with a coefficient of determination = 0.79. This model is given by... 

We replace the integral from Si to S2 by a sum over a regular grid. We do this by applying first a variable transformation (to be specified by some criteria) such that after this transformation an equidistant grid can be used. An estimate of the discretization error is possible by means of tricky and non-trivial application of analysis. Details on this are given in the appendix, which is a rather important part of this paper. 

The next step on the way to an expansion of 1/r in a Ganssian basis is to replace the integral (2.2) by a snm. Before we divide the range between and t2 into n intervals, we apply a variable transformations, such that after this transformation an equidistant grid can be used. 

We next approximate the integral (3.3) by a numerical integration after performing the variable transformation (2.11) with 7=1. This means we first replace (3.3) by... 

An equidistant integration grid may not be the best choice. Let us therefore consider that we perform a variable transformation in the integral before we discretize. 

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