Sentence examples for cases of functions from inspiring English sources
For instance, (i audio signal (amplitude in time): " ", (ii)spectrum (amplitude in frequency): " ". "Vector" types, notated " ", are special cases of functions used to specify the types for homogeneous sets of values.
However, for special cases of functions (1.1) can be given in a more specific form e.g. by giving lower estimates of the so-called 'Jensen gap' J ( varphi,mu,f ) = int_{Omega}varphi bigl( f ( s ) bigr),dmu ( s ) -varphi biggl( int_{Omega }f ( s ),dmu ( s ) biggr), thus obtaining refined versions of (1.1).
The two contrasting (but practical) cases of function of utility, that is characteristic of a decision maker with an aversion to risk, and decision maker with a predilection to risk, are then analysed in detail.
This is unfortunately not true in the case of functions.
For the sake of notational simplicity, these generalizations are described in the case of functions of two variables.
In this paper we prove this conjecture in the case of functions with one singularity.
This was established in the case of functions of positive integers by Church and Kleene (Church 1936a, Kleene 1936).
In the case of functions derived from natural selection, he views a "virtuous" consequence as an adaptive consequence.
We already have the result of Hölder continuity for functions by Morrey lemma in the case of functions.
From Example 3.1, even in its simple case of functions, SOCBLP is a nonconvex and nondifferentiable optimization problem.
end{aligned}The following result proved in [47] plays the same role as fundamental inequality (1.4.2) in the case of functions of one self-adjoint operator.
