In the sequel, the main task is to prove the asymptotic compactness of v and the exponential decay
of w in [Q.sub.N][H.sup.1] for large N.
The theory of the Christiansen experiment is concluded from optical interference , and it states that the transmittance oftransparent media undergoes exponential decay
. Particularly within transparent soil, incident light is scattered and refracted consecutively on multiple solid-liquid interfaces while transmitted light is attenuated.
These values are substantially higher than estimates from the traditional exponential decay
formula, which ignores the background contribution (7.09, 1.57, and 0ng/mL, respectively).
Raffoul, Inequalities and exponential decay
in time varying delay differential equations.
Third region is characterized by an exponential decay
of the switched polarization with the increase of the frequency.
From an implementation point of view, the reference current [bar.y] is computed from the bus current by using a linear differentiator to compute [DELTA][I.sub.bus] with exponential decay
[theta]; that is, by using the linear filter with transfer function
On the other hand, the author of  only studied the switched positive systems with the homogeneity of a degree of one, in which the common exponential decay
rate for all subsystems independent of initial conditions can be easily found for all subsystems.
A single exponential decay
function is fit to the extinction data to describe the oxidation process and the half-life of the decay is used as a measure of the oxidation rate.
The sinusoidal exponential decay
in ACF associated with an oscillating PACF suggested that the model should contain a non-seasonal AR and MA components.
According to (13), the PSWF eigenvalues have more than exponential decay
. Consequently, (33) is dominated by the PSWF eigenvalue of order N, and as such has more than exponential decay
) Suppose that the conditions of Theorem 1 hold.
The exponential decay
of the oscillation observed prior to the appearance of the developed charge indicates that the charges are uniformly distributed over the specimen, allowing us to put [nabla]([nabla] x v) = 0 on the right-hand side of Eq.