Es wird ebenfalls gezeigt, daB die gemeinsame Wirkung von Ultraschall-und elektrischen Stromen es ermoglicht, Wolfram durch eine einzige Reduktion zu einem Grad zu deformieren, der als Rekord gelten kann, 85% oder dariiber. Insbesondere 1aBt sich ein Draht yon 0,41 mm Dnrchmesser in einem einzigen Durchgang zu einem flachen Band von 70 pm Dicke auswalzen.

We prove two theorems on upper and lower bounds for probabilities in the multidimensional case. We generalize and improve the Prokhorov multidimensional analog of the Chebyshev inequality and establish a multidimensional analog of the generalized Kolmogorov probability estimate.In [1], using quadratic forms, Prokhorov obtained a multidimensional analog of the Chebyshev inequality. We generalize this analog by using the result concerning the refinement of Kolmogorov lower bounds for probabilities and further development of Chebyshev ideas obtained by the author in [2]. In this paper, we prove two theorems on estimates for the probabilities of values taken by multidimensional random variables. Theorem on Upper Bound for Probabilities in Multidimensional Case. L e t ξ = ξ ( ω ) be a real multidimensional random variable, let ϕ( ξ ( ω ) ) be a real single-valued scalar function of a multidimensional random variable, and let α be a nonzero exponent (integer or fractional, positive or negative). Then the following inequality is true:

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As is known [1], the concept of "supercentfifuge" includes tubular supercentrifuges and liquid separators. The rotors of these pieces of equipment are often of a complex shape in the form of long thick-walled cylinders.The strength of the rotors of supercentrifuges is usually calculated on the basis of the theory of rapidly rotating thick-walled shells [2]. We will use the condition for the failure of a cylindrical steel rotor after having extended it to a more general case (i.e., by not restricting the Poisson's ratio to the specific value ~t = 0.3 [2]):