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This is a mathematical convenience, not a biological observation.
For mathematical convenience, the problem is investigated under mode III-a simple case in fracture mechanics.
Pi reminds us that the universe is what it is, that it doesn't subscribe to our ideas of mathematical convenience.
Based on mathematical convenience, the volumetric part is usually assumed to be a finite polynomial in the volume change.
Second, to include physically important effects often left out of models for such systems as a mathematical convenience.
In practice, it is important to quantitatively establish that the prior is not too informative, particularly when the particular form of the prior is chosen for mathematical convenience rather than because of a considered subjective belief.
Although Planck did propose the basic hypothesis that the energy of a quantum of radiation is proportional to its frequency of vibration, it is not clear whether he used this hypothesis merely for mathematical convenience or intended it to have a broader physical significance.
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We cannot observe the a, i or r, while t and λ(t) are unknown and, as we shall see, only mathematical conveniences that are supplanted by θ in our calculations.
Therefore, in this section, we briefly review some theory and existing methods on Riemannian manifolds that are closely related to the proposed method, for the sake of mathematical and conceptual convenience in subsequent sections.
For mathematical and conceptual convenience we illustrate this mechanism as a change in threshold in Fig. 1C.
For the convenience of mathematical research, we assume that the exposed and infected individuals have the same infection rate.
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