Sentence examples for by a suitable function from inspiring English sources

The Rayleigh random variable is transformed, by a suitable function, to produce the Rice fading.

The commutators generated by a suitable function b and the operator (I_{alpha }) are formally defined by [b,I_{alpha }]f=I_{alpha }(bf -bI_{alpha }(f), respectively.

The best-worked-out version of this view is the usual mathematical description of change of position by a suitable function of time; and then motion as velocity, that is rate of change of position, is given by the first derivative, which is a relation to nearby intervals.

For (0by a suitable function b and (I_{alpha}) is defined by begin{aligned} [b,I_{alpha}]f(x &:=b(x cdot I_{alpha}f(x -I_{alpha}(bf) (x -I_{alpha}{gamma(alpha)} int_{mathbf {R}^{n}}frac{[b(x)-b(y)]cdot f(y)}{|x-y|^{n-alpha}},dy. end{aligned}.

There have been many generalizations and extensions of the Banach fixed point theorem, and the approaches used in these generalizations and extensions include (a) replacing the contraction constant L by a suitable function ϕ : R + ∪ { 0 } ⟶ R of d ( x, y ) to obtain contractive maps [1, 2]; (b) modifying d ( x, y ) on the R H S with displacements of the forms d ( x, T x ) and d ( y, T x ) [3 6].

It is possible to obtain various summability methods by choosing a suitable function Φ.

Next, we will show that the constant 1 is a sharp bound by constructing a suitable function.

The second step in general involves calculating the new set of parameters by maximizing a suitable function given the expected value of the hidden variables.

Then (4) holds at each point of the interior of D. Furthermore, if (u_{x_{1}x_{2}}ne0) and (u_{x_{2}x_{2}}ne0) in D, then we may define the function A as in (2), and then A is given by (3) for a suitable function Φ.

When one discusses the existence of weak solutions for fractional BVPs by critical point theory, a suitable function space is necessary.

To get a lower solution for (1.1), we will proceed with a limit process in, where is a classical solution of problem (1.10) (given by Theorem 1.6) with, is a suitable function and for and is such that in.