Suppose that is a meromorphic function, then the order of growth of the function and the exponent of convergence of the zeros of are defined, respectively, as (1.1).
We prove a certain integral representation theorem that is used to determine the degree of growth of the functions in the space B ω α, β ( B n ).
Firstly, due to the type of growth of the functions f and g, we cannot work with the usual H 1 , and then we need fractional Sobolev spaces.
Thus, the behavior of the function (H) where the value of (H) is large (larger than (eta _0theta _0 +1)), is irrelevant to condition (A6)(_{scriptscriptstyle +}), while (A)(_{scriptscriptstyle +}) requires a certain growth of the function (H) where its value is positive.
The inequality (1.1) just indicates that growth of a group is not less than the growth of the function (e^{sqrt{n}}.) All groups from families (mathcal G _{omega }^{(p)}) are residually finite- p) groups (i.e. are approximated by finite- p)-groups).
The alignment-based score is found through a logistic scoring function, (2) This choice is motivated by the initial exponential growth of the function followed by saturation.
Afterwards, assuming that and are monotone, we will give estimates on the growth of these functions in terms of the parameter to ensure solvability.
The number of poles is then estimated by estimating the growth of that function and using Jensen's inequality see the proof of Theorem 3 below.
With H=1, (frac {dF t)}{dt} = f(t)), which is the rate of growth of the increasing function and defined by the probability density function, a function of F and t.
Here (rho(g)) denotes the order of growth of the meromorphic function (g z)).
