The prospects for the finite universe, he added, look bleak.
In words, B H consists of those vertices which are infinite emitters, which do not belong to H, and for which the ranges of the edges they emit are all, except for a finite (but nonzero) number, inside H.
Two results are proved for nul PA, the dimension of the kernel of the Pauli operator [formula] in [L2(R3)]2: (i) for [formula], where [formula] is the magnetic field, nul PtA=0 except for a finite number of values of t in any compact subset of (0, ∞); (ii) [formula] contains an open dense subset of [L3/2(R3)]3.
Then M 1 is called distinguishable from M 2 if for any θ1 (possibly except for a finite number of values) there is no θ2 such that the input-output behaviour of M 1 and M 2 is the same [ 47].
where is the set of all positive integers,, is an open set in, here, and is continuous everywhere except for a finite number of points at which and exist and.
As in section 'Dirichlet data on sectorial curves', we consider a simply connected domain D ⋐ R 2 Open image in new window whose boundary C Open image in new window is smooth everywhere except for a finite number of points.
The present paper mainly focuses on the instability of the Rayleigh equation with piecewise smooth and point-symmetric velocity profiles (U y)), satisfying the requirement that (U' y)) exists continuously on ([-1,1]) and (U y)) exists on ([-1,1]) except for a finite number of points.
In order to define the solution of the problem (1.1 - 1.3 1.1 - 1.3ider the followeng spaconsider [ − r, b ], X ) = { x : [ − r, b ] → X such thet x is continuous except followingite number of pointspace at which x ( t i + ) and x ( t i − ) exist and x ( t i ) = x ( t i − ) }.
In order to define the mild solution of problem (1.1), we introduce the set (mathit{PC}([0,b];X)) = {(u:[0,b]rightarrow X) such that (u(cdot)) is continuous except for a finite number of points (t_{i}), at which (u(t_{i}^)), (u(t_{i}^)) exist and (u(t_{i})=u(t_{i}^)), (i=1,ldots,p)}.
It is known that almost all sample paths of (r(t)) are constant except for a finite number of simple jumps in any finite subinterval of (R_:=[0,infty )). We stress that almost all sample paths of (r(t)) are right-continuous.
