Assume that there exists a change of coordinates K in a neighborhood Ω satisfying (6).
Correspondingly, there exists a change of rubber particles from roughly spherical shape to highly elongated and oriented shape at D B transition.
Theorem 4.4 If b 2 = − a 1, b 1 = − a 2 holds, there exists a change of coordinates which transforms system (3) into u ˙ = 3 u, v ˙ = − q v, namely, u = x ( 3 q − 3 a 1 y + q a 2 x ) − 1, v = y ( 3 q − 3 a 1 y + q a 2 x ) − 1 ; thus system (3) is linearizable.
Moreover,there exists a change of variables (v-overline{v}rightarrow V) such that J Biggl(sum_{i=1}^{p} alpha_{i}delta_{(a_{i}, lambda_{i})}+alpha_{0}(w+h)+v Biggr)=J Biggl(sum_{i=1}^{p} alpha_{i} delta_{(a_{i}, lambda_{i})}+alpha_{0}(w+h)+overline {v} Biggr)+Vert V Vert ^{2}.
Moreover, there exists a change of variables (v-overline{v}rightarrow V) such that J Biggl(sum_{i=1}^{p} alpha_{i}delta_{(a_{i},lambda_{i})}+v Biggr)=J Biggl(sum _{i=1}^{p} alpha_{i}delta_{(a_{i},lambda_{i})}+ overline{v} Biggr)+| V |^{2}.
Moreover, there exists a change of variables v − v ¯ → V such that J ( ∑ i = 1 p α i δ ˜ ( a i, λ i ) + α 0 ( w + h ) + v ) = J ( ∑ i = 1 p α i δ ˜ ( a i, λ i ) + α 0 ( w + h ) + v ¯ ) + ∥ V ∥ 2. We notice that in the V variable we define a pseudo-gradient by setting ∂ V ∂ s = − μ V, where μ is a very large constant.
If a strong association between flowering time and local conditions exists, a change in these conditions will directly impact on reproductive isolation [ 41].
We apply Bayesian hierarchical models to formulate the change point where there exists a step change, a linear trend and a known multiple number of changes in the Poisson rate.
Assareh et al. (2013) applied Bayesian hierarchical models to estimate change point where there exists a step change, a linear trend and a known multiple number of changes in the Poisson quality characteristic.
(In Apple's defense, its help documentation for iOS 6 also pointed the way to itunes.com/passbookapps, but really, who even knew that an online manual existed?) A subtle change in the new iOS 6.1 software, released last month, makes things easier.
