A formula for calculation of the density function of the distance between two independent points randomly and uniformly chosen in a bounded convex domain D is given. The obtained formula permits to find an explicit form of the density function for the domains D with known chord length distributions. In particular, an application of the formula gives explicit expressions for in the cases of a disc, a regular triangle, a rectangle and a regular pentagon.
In this paper, we will discuss a newly constructed subclass of analytic starlike functions by which we will be obtaining sharp upper bounds of the functional for the analytic function belonging to this subclasses.
The power plant tolling contract is one of most complicated derivative instruments among energy derivatives. The paper continues the investigations begun in [1]. Some papers introduce more complicated switching strategies. However, we deal with much simpler dispatch structures, to introduce a new method of evaluation.
In the paper we investigate the multidimensional inverse problem for the system of parabolic equations in an unbounded domain. The proposed problem is reduced to a boundary value problem of infinite elliptic equations and the method of successive approximations allows one to prove the existence and uniqueness theorems for solutions of systems of these elliptic.
The article focuses on the criteria of convergence of series of independent random variables and regularly varying functions. The author examines the convergence of sums of independent random variables in many of the classical limit theorems of probability theory. Limit laws are derived using characteristic functions (or integral Laplace transform). That is, in the transition to the characteristic functions, the transition from a group with addition (and subtraction) to a group with multiplication (and division). This factor is the basis for the research of measurable Cantor groups.
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