Furthermore, \ textstyle \ Lambda ( B ) has the interpretation of being the expected number of points of the Poisson process located in the bounded region \ textstyle B, namely
12.
The Radon measure \ textstyle \ Lambda maintains its previous interpretation of being the expected number of points of \ textstyle { N } located in the bounded region \ textstyle B, namely
13.
Sonoluminescence in this respect is what is physically termed a bounded phenomenon meaning that the sonoluminescence exists in a bounded region of parameter space for the bubble; a coupled magnetic field being one such parameter.
14.
For a Poisson process in the plane, this implies that the probability of having " n " points or nodes in a bounded region "'B "'is given by
15.
Typical problems about an arrangement in " n "-dimensional real space is to say how many regions there are, or how many faces of dimension 4, or how many bounded regions.
16.
Theodor Estermann ( 1902 1991 ) proved in his book " Complex Numbers and Functions " the following statement : Let K \ subset G be a bounded region with continuous boundary \ partial K.
17.
Here A is the area of the region bounded by a closed Jordan curve of length ( perimeter ) L in the plane, R is the circumradius of the bounded region, and r is its inradius.
18.
In a chaotic recurrence relation, the variable " x " stays in a bounded region but never converges to a fixed point or an attracting cycle; any fixed points or cycles of the equation are unstable.
19.
One easy consequence of the theorem stated above is that if there are no " refractory " cells initially then the pattern will die out in any bounded region ( whether the total grid is finite or infinite in extent ).
20.
Because S _ { x _ 0 } is a bounded region, the maximum modulus principle is applicable and implies that | gh _ \ epsilon | \ leq 1 for all z \ in S _ { x _ 0 }.
