(I) If L is a rational function, then A ≡ C, L is a constant and B = L D. (II) If L is a transcendental function, then one of the following cases holds: If, in addition, L has finite order in case (ii), then A, B, C, D are polynomials and so is A 1. (i) B ≡ D ≡ 0 and v, w have no zeros.
There is a formal possibility that V itself is finite, in which case there would be a last natural number {V}; one usually assumes an Axiom of Infinity to rule out such possibilities.
Lemma 3.4 For all x, y ∈ D ( ( H 0 J ∗ ) or D ( ( H a, 0 J ∗ ), lim t → a − 1 ( x, y ) ( t ) exists and is finite in the case of a = − ∞, and for all x, y ∈ D ( ( H 0 J ∗ ) or D ( ( H b, 0 J ∗ ), lim t → b ( x, y ) ( t ) exists and is finite in the case of b = + ∞.
As Schaffer points out, while (iv) and (vi) seem true, (v) seems false the fact that S has three members rather than two makes no difference to whether S is finite or not, for it would be finite in either case.
As a result of finite element simulations, in case of external heat flow, the temperature distribution in this central region becomes inhomogeneous and hence the object feels the flow of heat indeed.
Thus, if { d ( T j n x, T j n y ) } is non-decreasing, it cannot have a strictly increasing subsequence so that it is bounded and has a finite limit as in Case A. Case C: { d ( T j n x, T j n y ) } has an oscillating subsequence.
A full-order state estimator is constructed to estimate the neuron state, in presence of the uncertain and jumping parameters, such that the resulting error dynamics of the state estimation is (i) finite-time stable in the disturbance-free case; and (ii) finite-time bounded in case of exogenous disturbances on the measurements.
And then a stochastic Fubini theorem is established for the compensated Poisson random measure whose intensity measure is σ-finite compared to a finite case in [10].
