Sentence examples for defined on the space from inspiring English sources

These equations, arising from a related class of probabilistic variational problems, are defined on the space of probability measures on Rd.

We derive a change of variable formula for non-anticipative functionals defined on the space of Rd-valued right-continuous paths with left limits.

We establish an unbounded version of Stinespring's Theorem and a lifting result for Stinespring representations of completely positive modular maps defined on the space of all compact operators.

We obtain a measure defined on the space of continuous sample paths, which describes a weakly self-avoiding Brownian motion in a 2-dimensional Euclidean space.

This paper presents a novel approach to the source seeking problem, where a group of mobile agents tries to locate the maximum of a scalar field defined on the space in which they are moving.

We establish the existence and uniqueness of the C1, 1 solution of an infinite-dimensional Hamilton-Jacobi equation defined on the space of probability measures on Rd, when the zeroth-order coefficient is sufficiently large.

Furthermore, they gave the conditions which characterize the classes of four-dimensional matrix transformations defined on the spaces (mathcal{CS}_{bp}), (mathcal{CS}_{p}) and (mathcal{CS}_{r}).

Equation (2.1) has the short form [ u, v ] = ( f, T v ), defined on the spaces W and H = L 2 ( R +, ρ ).

Finally, I characterize the classes of four-dimensional matrix mappings defined on the spaces (B(mathcal{M}_{u})), (B(mathcal{C}_{p})), (B(mathcal{C}_{bp})), (B(mathcal{C}_{r})) and (B(mathcal{L}_{q})) of double sequences.

In this section, we prove the existence theorem of a solution for a generalized equilibrium problem with a bifunction defined on the dual space of a Banach space.

To achieve this, usually, a template is registered to the subjects and then the anatomical parcellation map defined on the template space is warped to subjects' native spaces.