Sentence examples for functional interval from inspiring English sources
end{aligned} The function θ is quadratic, vanishes at (x=c) and (x=d), and is negative in (]c,d[). Given two functions (phileqpsi) in ([c,d]), let us denote by ([phi,psi]) the functional interval [phi,psi]=bigl{ V in W^{2,1}bigl [c,d]bigr) : phi(x) le V x) le psi(x) mbox{ for all }x in[c,d]bigr}.
Following [ 18] we term this region as a functional interval (window) for GATA-3 deeming the statistical over-representation as functionally related.
The interface has a two-level architecture: functional interval arithmetic at low-level, which is only a specification to be implemented by specific libraries, and a set of operations required by solvers, such as relational interval arithmetic or bisection primitives.
The solution u of problem (19) belongs to the functional interval ([alpha,beta]).
Then problem (27) has a solution belonging to the functional interval ([alpha, beta]).
If (k >0) satisfies (13), then problem (11) has extremal (W^{2,1} -solutions in the functional interval ([alpha _{k},beta]).
The ISMISIP model can simultaneously quantify coefficients expressed as probability distribution functions, intervals and functional intervals without generating more complicated intermediate models during the solving process.
The ISMISIP model can simultaneously tackle a waste management problem with coefficients expressed as probability distribution functions (capacities of the landfill, WTE and composting facilities), intervals and functional intervals, without requiring more complicated intermediate models.
The IFJMP-EPS model cannot only deal with uncertainties expressed as joint probabilities, crisp interval values and functional intervals, but also examine the risk of violating joint-probabilistic constraints.
He et al. ([2008a]) developed an interval full-infinite programming (IFIP) method through introduction of functional intervals into an optimization framework and applied it to waste management planning with infinite objectives and constraints under uncertainty.
The model integrated mixed-integer linear programming, interval-parameter programming, semi-infinite programming and fuzzy-chance-constrained programming within a general framework, which can tackle multiple uncertainties expressed as intervals, functional intervals (dual uncertainties), random variables, fuzzy sets, and their combinations (fuzzy-interval admissible probability).
