Next, we will show that (F(a) ) (F is defined as in (1.4)) blows up in finite time assuming that (a_{x}(0,t) ) stays finite.
The paper focuses on the deterministic complexity of factoring polynomials over finite fields assuming the extended Riemann hypothesis (ERH).
A thermo-elastic problem of uniform heating is studied for a single hollow spherical inclusion embedded in a finite matrix assuming power-law variation of the thermo-elastic properties.
For each loading path, the effect of the anisotropic damage evolution on the plastic anisotropy and vice-versa is carefully studied in the context of finite plasticity assuming small elastic strains.
Bayesian analysis was also used for upscaling estimates for a larger finite population, assuming that it is similar to the study population.
To test the accuracy of the product rule theoretically, Laurie and Weir (2003) provided a method to compute the equilibrium MPs in an ideal finite population, assuming an infinite alleles model of mutation.
Theorem 2.14 (Characterization of the smallest finite eigenvalue) Assume (1.1).
Restrict attention to finite universes, assume ISOM throughout, and consider first type <1> quantifiers, or type <1,1> quantifiers that are relativizations (Section 7) of these; we'll see in Section 12 that these types are highly relevant in natural language contexts.
Let K be a h -finite submodule of M having only finite heights in M. If N is a finitely generated submodule of M then N + K is also h -finite assuming finite heights only.
The population size was assumed to be infinitely large (the model assuming finite populations is described in Additional file 1 under 'Effect of finite populations').
Nonetheless, for finite dimensional systems, assuming a uniform prior can be better justified and very useful; see, e.g., [46].
