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In fact, if ( g v) = alpha v + b), V splits according to the eigenspaces of the linear map (alpha ), which has order exactly m, and we can write ( V = V_1 oplus V_2), where (V_1 = ker ( alpha - Id)).
Under tensile loading, such a singularity is characterized by a generalized stress intensity factor which is analogous to the mode I stress intensity factor used in fracture mechanics, but which has order less than one-half.
This analysis shows that while some τ-leap methods may have higher order moments (for instance, the midpoint τ-leap has order two moments for linear systems), their covariance is invariably of unit order, unless this is specially taken into consideration (as with the TTTL method, which has order two moments and covariance).
Similar(57)
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