Furthermore, we give the probabilistic representation of the solutions for a class of stochastic partial differential equations by virtue of mean-field BDSDEs, which can be viewed as the stochastic Feynman-Kac formula for SPDEs of mean-field type.
It has the virtue that all partial answers \(g\) in \(D(B \) are comparable with each other: \(g\) is better than \(g'\) if and only if the value of (3) is larger for \(g\) than for \(g'\).
It will be recalled that a polar molecule has an electric dipole moment by virtue of the existence of partial charges on its atoms.
For example, it may be true that the Protestant Reformation is a partial cause of World War II, in virtue of some causal chain leading from the former to the latter.
The partial shear connection in this paper is by virtue of the effective flexural rigidity as AISC 1993 [American Institute of Steel Construction AISCC). Load and resistance factor design specifications. 2nd ed., Chicago; 1993].
A positive answer to this question emerges from considerations on truth values as structured entities which, by virtue of their internal structure, give rise to natural partial orderings on the set of values.
In case you have been in hibernation these last six months: Mr. Bush has proposed with great fanfare a partial privatization of Social Security, an idea that has its virtues (and its vices, but never mind that right now).
I have to admit, I'm partial to the recycling center, which feels like an island of enviromental virtue in a sea of suburban excess.
By virtue of mechanism method and TS fuzzy modeling technique, a partial linear structured mechanism model is firstly obtained, which contains a parametric linear part with unknown coefficients and a non-parametric part with unknown functional expression.
These political circles are partial to drawing sweeping distinctions between East and West, applauding the virtues of the former while berating the vices of the latter.
