Sentence examples for characterizes the solutions from inspiring English sources

Then, a fixed-point proximity-gradient iterative scheme is developed based on the fixed-point equation which characterizes the solutions.

To derive the correspondence between the Lagrangian equivalent system and the original system, we have to consider the space D, which characterizes the solutions in the original system: D = { ( z, μ ) | z ∈ H 1 ( R ) × [ L 2 ( R ) × L ∞ ( R ) ]  and  μ ac = ( u 2 + u x 2 + v 2 ) d x }, where z = ( u, v ) and μ is a positive finite Radon measure with μ ac as its absolute continuous part.

The following proposition characterizes the solution to (10).

Leveraging the control framework of viability theory, we characterize the solutions to the Hamilton-Jacobi equation by a Lax-Hopf formula, and show that the solution satisfies an inf-morphism property.

These solutions can be accurately computed with an overhead that is substantially independent of the smallness of the scale length characterizing the solutions.

We first characterize the solutions of the optimization problem as fixed-points of a mapping defined in terms of the gradient of the differentiable function and the proximity operators of the other two functions.

Furthermore, we shall characterize the solutions to the Cauchy type problem by the interval-valued integral equation under certain conditions.

To explain the three parameters, we have chosen to characterize the solutions and why they suit this problem, it is helpful to have a look at the lower left part of Fig. 5, in which an example solution is displayed.

In particular, we need to characterize the solutions of (x'=-nabla F x)) (or (x'in -partial F x))) by only using metric quantities (in particular, avoiding derivatives, gradients, and more generally vectors).

We characterize the solution for a fault-diagnosis context in cyber-physical systems, and for an opinion-classification/community-discovery setup in social networks.

We show that knowledge of the first moment does not guarantee strictly positive revenue for the seller, characterize the solution for the cases of two moments and derive some characteristics of the solution for the general case.