The domain of definition of the differential equation is divided into two subintervals.
A social choice function may or may not satisfy a desirable property depending on its domain of definition.
So, see, the problem with that vector field here is precisely that its domain of definition is not simply connected because there is a hole, namely the origin.
OK, so for this guy, domain of definition, which is plane minus the origin with the origin removed is not simply connected.
The "continuation functions" arising from a function f converge super-algebraically to f in its domain of definition as discretizations are refined.
But this one is somehow better and closer to what exactly is needed if curl F is zero and the domain of definition where F is defined is simply connected -- -- then F is conservative.
The methods are based on spatial discretization using the method of weighted residuals with spatially global basis functions (i.e., functions that cover the entire domain of definition of the process and satisfy the boundary conditions).
Because their domain of definition is infinite, the convergence properties of the Chebyshev rational functions allow handling the boundary conditions with higher accuracy than with the previously studied Fourier transform method.
The problem is traced to the large order behavior of Bessel's function and is rectified by defining a set of subdomain basis functions with suitably normalized Bessel functions that are well behaved over their domain of definition.
A map of the form I−f with a strictly condensing operator f is 0-epi if and only if it has nonzero degree on a component of its domain of definition.
Unlike most of existing methods which require the contractivity of their domain of definition, the proposed control Lyapunov functions are defined over a so-called N-step controllable set, which is known not to be contractive.
