Here a is the penetration depth of the ion along its trajectory, and β is the energy distribution width, assuming isotropy in the X and Y directions (i.e. a spherical distribution) to greatly simplify the terms, as utilized by Valbusa et al. (2002).
Flexibility itself depends on various factors and thus, we often had to simplify the terms "flexible" and "rigid" without considering factors like the succession of secondary structures (motifs) and interactions (H-bonds) between single motifs and domains.
To simplify the terms inside of the radicals, try to factor them to find at least one term that is a perfect square, such as 25 (5 x 5) or 9 (3 x 3).
Pudding is still consumed in many varieties across the Commonwealth, but people in the United States have simplified the term to mean a cold, custard-like dessert.
We simplify the exponent term in the right side of (14) by first approximating U ¯ n ( z ) over H N ( x ) by U ¯ n ( x ).
In addition, assuming that the sea bottom uplifts with a constantly increasing rate d χ /dt = α0 (> 0) during the source process time from 0 to T, and χ (t) = 0 when t > T, we further simplify the first term in the brackets in Eq. (27) as, which should be equal to 1 at t = T (i.e. α0 = 2/T2, and when t < T).
Initial fits of the model to our data revealed no saturation in the turning response, allowing us to simplify the first term.
In particular, Jensen's and Wirtinger based integral inequalities are employed to simplify the integral terms which appeared in the derivation of stabilization results.
In order to simplify the trigonometric terms in underactuated AUV motion functions, quaternion theory is applied to transform the function to develop a continuous time-varying controller.
To overcome this limitation, the Taylor series expansion is used to simplify the phase terms in (26), with a sufficient precision of approximation which has been verified in [39].
