Further progress in the coordinate equations theory A.V. Shanin Department of Physics, Acoustics division, Moscow State University, Leninskie Gory, Moscow 119992, Russia, e-mail: andrey shanin@mail.ru Abstract A new method is proposed for solving diffraction problems having piecewise linear ideal boundaries. ... The coefficients of these equations are rational matrix functions of the coordinates. ... The coefficients of the equation are rational functions of the coordinates. ...

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... 2 ZERO-ORDERED SEQUENCES OF SPARSE VECTORS Let X = {xk } be a sequence of sparse vectors from Kn, I = {ik } be a sequence of multiindices. ... L ..... uL x1 ..... x1 ..... xn NNp-1 u1 u p-1 xn NNp-1 u1 NN p up-1 ..... up Let's consider a following sequential chain SPN of linked -neurons: u1 = spn1(x), up = spnp(x, up-1), 7 where p = 2, . ... We learn -neurons spn1, . ... Let's consider a following multy-layered network SPNN of -neurons: u1 = spn1(x), up = spnp(x, up-1), where p = 2, . ... SPNp-1(x))...

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