For simple functions such as quadratic functions, you may already be familiar with the "quadratic formula," which gives the two roots of exactly.
However, when the boundary conditions are time-varying, such as a time-varying energy source as in our case, these solutions exist only for simple functions such as steps, ramps, or simple deterministic variations.
Interpreting the syntactic derivation for 'Everyone loves someone', the semantic types no longer match for simple function application: the verb expects two e type arguments, but instead finds two arguments of type (e → t) → t.
We write M ( R loc ) for the space of measurable real functions on ( Ω, R loc ) and S ( R ) for the space of simple functions with support in ℛ (or ℛ-simple functions).
The optimum longitudinal field variation for the generation of the lowest emittance has been calculated numerically – and analytically for different classes of simple functions: exponential-, power-, hyperbolic- and step-function.
We conclude this paper by mentioning that, by suitably specializing the parameters involved, our main results (Theorem 1 to Theorem 5) would yield a number of (known or new) results for much simpler function classes, which were investigated in several earlier works by employing many special cases of the new generalized Srivastava-Attiya operator.
There is a search for simpler psychological functions that can account for age-related changes in higher-level, more complex cognitive functions.
On the contrary, Gaver Stehfest and Piessens methods furnish results not very reliable for almost all classes of transformed functions and they seem good only for "simple" transformed functions.
