Decaying exponent

We solve the integro-differential equation (6.2.21) by fitting the memory kernels to a function consisting of a sum of decaying exponents... 

Decaying exponents were chosen because in this representation the memory kernels (6.2.22) separate and the integro-difFerential equation (6.2.21) can be reduced to a set of ordinary coupled first order differential equations. This is achieved by introducing the functions ... 

Lai, Y.-C., Ding, M., Grebogi, C. and Bliimel, R. (1992a). Algebraic decay and fluctuations of the decay exponent in Hamiltonian systems, Phys. Rev. A46, 4661 669. 

R Dose rate or actual value of decay exponent N/A State dose rate in cGyph. See sample NBC4 for terms associated with this line. 

The difference between the two rate values at a cross-over from the two experiments is solely due to decay, since both rates are measured at the same conversion (X) and temperature (Te). According to the above logarithmic relationship the two points therefore belong on a straight line with slope N and rate-axis intercept of r(0)(x,T>. The same is true for each pair of rates at all the cross-over points. This in turn means that all such pairs should lie on parallel lines in the ln(r(t)(x,T)) vs. ln(l+G gt) plane, since the slope defined by the decay exponent, N, is the same for all pairs. 

We collect in the next proposition a number of soft results on f(-, ) and hc -), which is a function from [0,00) to R. Note in particular that formula (5.3) does not depend on a, the decay exponent of K -). 

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