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By Marnaghan F. D., Wintner A.

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3. Random Numbers. Since the "quality" of random numbers used for computations is checked by means of special tests it is of no importance how they were generated if only they satisfy the accepted set of tests. We may even calculate them by means of a prescribed formula. But such a formula must, of course, be a very ingenious one. The numbers calculated by means of some formula and simulating the values of the random variable l' are called pseudo-random numbers. The term "simulating" means that 2&ยท these numbers satisfy a set of tests as if they represented the values of this random variable.

We now ha ve to find out how to select a random direction of a neutron after scattering. As the problem is symmetrical about the z-axis, the direction is completely defined by an angle 'P between the neutron velocity and the Ox-axis. It can be proved* that the requirement of equal probability of all directions is equivalent in this case to the requirement that the cosine of this angle 11 == cos (f) be uniformly distributed over the interval (-1, 1). Formula (24) for a == -1, b = 1 yields the expression for drawing I-L values: fl == 21' - 1.

It is more expedient to use the so-called pseudo-random jt, numbers. 3. Random Numbers. Since the "quality" of random numbers used for computations is checked by means of special tests it is of no importance how they were generated if only they satisfy the accepted set of tests. We may even calculate them by means of a prescribed formula. But such a formula must, of course, be a very ingenious one. The numbers calculated by means of some formula and simulating the values of the random variable l' are called pseudo-random numbers.

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A Canonical Form for Real Matrices under Orthogonal Transformations by Marnaghan F. D., Wintner A.


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