Ховый метод измерени я коэфициента отражния

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A new method of measuring the reflectivity factor

A new method is given of measuring reflectivity and compared with methods known up to now, which are characterized briefly. The applicability and suitability of the given method is shown on an example of measurement of the reflectivity of germanium in the ultra-violet and visible regions.

     

Spectrophotometric determination of molybdenum in steel,tantalum, niobium or tungsten

A rapid, accurate spectrophotometric method for the determination of 0.001–0.1% of molybdenum in steel, tantalum, niobium or tungsten is presented. The molybdenum is isolated, when required, by solvent extraction with α-benzoinoxime-chloroform solution or cupferron- chloroform solution and then determined by the thiocyanate method. Conditions for obtaining high sensitivity by quantitative reduction of molybdenum (VI) to molybdenum (V) with tin(II) chloride have been established. It has been shown that fading of the molybdenum(V)-thiocyanate color can be minimized by adding hydroquinone to prevent air oxidation of molybdenum (V).     

Spectrophotometric determination of traces of several metals in ferrous and nonferrous metals and alloys after isolation by iodide extraction

Methods are presented for the determination of traces of lead, cadmium, indium, bismuth, copper, and antimony in most of the important metals and alloys used in industry. The trace metals are isolated by hexone extraction of their iodides from 5% hydrochloric acid solution and then determined spectrophotometrically. The attractive feature of the proposed procedures is that the method used for each of the trace metals is applicable to all of the matrix metals and alloys being considered.     

The inhibition of factor inhibiting hypoxia-inducible factor (FIH) by beta-oxocarboxylic acids

Cyclic beta-oxocarboxylic acids inhibit factor inhibiting hypoxia-inducible factor via ligation to the active site iron.     

Chebyshev expansions and rational approximations

Let A(z) = A_m(z) + a_mz^mB(z,m) where A_m(z) is a polynomial in z of degree m-1. Suppose A(z) and B(z,m) are approximated by main diagonal Padé approximations of order n and r respectively. Suppose that the number of operations needed to evaluate both sides of the above equations by means of the Padé approximations and polynomial noted are the same. Thus 4n = 3m + 4r. We address ourselves to the question of which procedure is more efficient? That is, which procedure produces the smallest error? A variant of this problem is the situation where A(z) and B(z,m) are approximated by their representations in infinite series of Chebyshev polynomials of the first kind truncated after n and r terms respectively. Here n = m + r.Let F(z) have two different series type representations in overlapping or completely disjoint regions of the complex z-plane. Suppose that for each representation there is a sequence of rational approximations of the same type, say of the Padé class, which converge for |arg z| < π except possibly for some finite set of points. Assume that the number of machine operations required to make evaluations using the noted approximations are the same. Again, we ask which procedure is best? Other variants are studied.General answers to the above questions are not known. Instead, we illustrate the ideas for a number of the rather common special functions.     

A note on evaluation of coefficients in the polynomials of Padé approximants by solving systems of linear equations

This is a sequel to my previous paper concerning the determination of the coefficients in the polynomials which define Padé fractions, where the coefficients are found by solving systems of linear equations. The present note uses the same models and computer as before, but the computations are far more extensive so as to reveal more pointedly the effects of round off error in the coefficients as the order of the system increases. Only the main diagonal Padé entries are studied numerically. The numerics are achieved using two routines in LINPACK one of which evaluates a condition number for the matrix. This is advantageous if one suspects ill conditioning. In our previous paper, it was shown that though the relative errors in the numerator and denominator polynomials increase as the order of the system increases, the effect on the Padé approximant is virtually nil at least for the size of the variable x and the order n considered. Of course, ultimately so as to render the without bound, we should expect so much contamination due to round off so as to render the results meaningless. All of this is illustrated with numerics. Heuristic procedures based on the numerical data developed are presented to warn of deterioration due to round off.