Let there be a function f(x), which is a realization of some stationary random function. It is required to find an approximate value of the integral ...

ПОСТАНОВКА ЗАДАЧИВ связи с созданием высокочувствительной измерительной аппара­туры стало возможным определение малых концентраций и потоков радиоактивной примеси в атмосфере. Благодаря этому возникла важ­ная с практической точки зрения задача определения положения и мощ­ности источников примеси, расположенных под землей, по наблюдениям в приземном слое атмосферы. В основу решения этой задачи должна быть положена теория, объясняющая распространение радиоактивной примеси в двухслойной среде земля—атмосфера.

Recently, the formal apparatus of delta functions, i.e., discontinuous functions defined by equalities, has been increasingly applied to the solution of various problems of mathematical physics ...

Let’s consider the following problem in the theory of heat conduction. An initial temperature distribution is given in a space consisting of two media separated by a flat interface. It is required to find the temperature at any point in the space, at any moment of time. The thermal characteristics of each of the two media are assumed to be constant. The formulated problem has been considered by a number of authors for the one-dimensional case. The possibility of solving the multidimensional case using integral equations was pointed out by Münz [4]. In [5], a two-dimensional problem was solved by the method of successive approximations. In the present paper, a closed-form solution of the problem under consideration is given for the two- and three-dimensional case. The solution method can be applied to a number of similar problems.