In order to study the effect of the cross-section shape of the cavity on the dynamic stress state of the medium we shall calculate the relative radial stresses for the case of the elliptic cross-section cavities with the ratio of the

semiaxis 2 (Fig.

This paper is a short survey on weighted polynomial approximations of functions defined on the real

semiaxis. The function may grow exponentially both at 0 and at +[infinity].

As can be seen from this figure, in the space under consideration, the initial MF produced by the TL group has a negligible polarization, so that its STC represents a strongly elongated ellipse, and the ellipse coefficient (ratio of the smaller

semiaxis of the ellipse to the larger

semiaxis) is about 0.4, which is confirmed by the experimental research.

Ellipse equation as shown in (14), including five parameters: center point coordinate s([x.sub.s], [y.sub.s]), minor

semiaxis b, major

semiaxis a, and intersection angle [[phi].sub.2] with the major axis and axis [x.sub.1].

In the following [R.sub.+] [??] [0, [infinity]) and [R.sub._] = (-[infinity], 0] are

semiaxis of the real axis, [C.sub.+] is an upper half-plane of the complex plane, [bar.m, n] [??] {k [member of] N [union] {0} : m [less than or equal to] k [less than or equal to] n} (m, n [member of] N [union]{0} and m [less than or equal to] n), [[delta].sub.jk] is the Kronecker delta (i.e., [[delta].sub.jk] = 1 if j = k and [[delta].sub.jk] = 0 if j [not equal to] k), and B([H.sub.1], [H.sub.2]) is the set of all linear bounded operators from the Hilbert space [H.sub.1] to the Hilbert space [H.sub.2], B(H) = B(H, H).

Usually the higher

semiaxis (2R) is located in the main traffic direction while the lower

semiaxis is located in the secondary traffic direction.

[L.sub.k] is the k-axis depolarization factor of the oblate spheroidal inclusions ([R.sub.x] = [R.sub.y] > [R.sub.z], where [R.sub.k] is the

semiaxis of the ellipsoid along the k-axis) with aspect ratio [alpha] < 1([alpha] = [R.sub.z]/[R.sub.x]), given by [27]

An n-dimensional ellipsoid is simply a sphere that has been stretched along the n orthogonal

semiaxis of the ellipsoid.

The second term k is calculated according to (10), depending on the tangential modulus of elasticity, the product of the ellipse

semiaxis, the normal load N, and the friction coefficient [mu], considering three different exponents, n, [n.sub.4], and [n.sub.5].

In interpolation, the power was considered as 2, the searching neighborhood was standard, the neighborhoods were at least 10 and neighbors to include was 15, major

semiaxis was 1.52, minor

semiaxis was 1.52, and the angle was 0.

The integral of the function xV(x) over the

semiaxis x [member of] (0, +[infinity]) is finite, hence, according to the general criterion [42-46], the potential supports only a finite number of bound states.

Mahdavi, Neutral functional equations with causal operators on a

semiaxis, Nonlinear Dynamics and Systems Theory 8(2008) 339-348.