By Spencer D.C.
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Extra resources for Deformation of structures on manifolds defined by transitive, continuous pseudogroups (Ann. of Math., 1962-1965)
A) Let p ~ (x) == 2/n in the interval (0, :n/2). The Iormula for drawing ; can he obtained from Eq. (24) with a:=:O and b ~= n/2: S ~ rr:'(/2. N O\V formula (35) takes tho form N I~ 2~ ~ sink j=1 Let us set N = 10. 001). Intermediate results are listed in Table 1. 952. (h) Now we set p ~ (x) ~ 8x/J1 2 • To draw; \VO use Eq. (23) ~ ) (8xjn 2 ) dx=y, o whence, after simple calculations, we obtain J1 ~=2 -V-V· Eq. (35) takes now the following form 2 N f: • I~""::'- ~ ~ ~ 8N LJ S' j~1 } · 61 Let N =:: 10.
We shall consider the simplest version of the problem of neutron transmission through a plate. 1. Statement of the Problem. Let the flux of neutrons with energy Eo be incident on a homogeneous infinite plate o ~ x ~ h. The angle of incidence is 90 Upon collision with atoms of the plate material neutrons may be either elastically scattered or captured. Let us assume for simplicity that energy of neutrons is not changed in scattering and that any direction of "recoil" of a neutron from an atom is equall y probable (this is sometimes the case in neutron collisions with heavy atoms).
Firstly, is difficult to check the "quality" of generated numbers. drift'' may appear due to some faults (that is, zeros and unities appear in some bits at nonidentical frequencies). Secondly, all calculations in computers arc usually performed twice to exclude the possibility of occasional failure. However, it is impossible to reproduce the same random numbers if they are not stored in the course of computations. But in the case of storing them we again face the situation typical for tables. Generators of this type will undoubtedly prove useful when specialized computers will be designed for solving problems by means of the Monte Carlo method.
Deformation of structures on manifolds defined by transitive, continuous pseudogroups (Ann. of Math., 1962-1965) by Spencer D.C.
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