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We first define a new Laplacian spectrum based on Estrada index, namely, Laplacian Estrada-like invariant, LEEL, and two new Estrada index-like quantities, denoted by S and, respectively, that are generalized versions of the Estrada index.
However, our continuization method computes stress-like {〈σ〉c,〈S〉c,〈μ〉c} and strain-like quantities {〈ε〉c,〈εR〉c,〈∇ω〉c} independently and thus allows for an identification of material properties.
James, however, holds that just as God can make thing-like quantities to exist without a subject, so too must he be able to make a thing-like quality exist without the subject in which it inheres.
From the displacement gradients, strain-like quantities derive in analogy to Eqs. (9), (10) as begin{array}{*{20}l} langle boldsymbol{varepsilon} rangle_{mathrm{c}} &= frac{1}{2} left(langle boldsymbol{e} rangle_{mathrm{c}} + langle boldsymbol{e} rangle_{mathrm{c}}^{sf T} right), end{array} (17).
Several definitions of FST or FST-like quantities are now available, relying on a variety of different conceptual formulations but all measuring some aspect of population differentiation (e.g., Charlesworth 1998; Holsinger and Weir 2009).
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The strain-like quantity E characterizes the deformation of the fibre family and the operator 〈〉 stands for the Macauley bracket.
By considering the Estrada index defined in (1.1), the other Estrada index-like quantity can be defined as (3.2).
A time-like quantity is introduced that takes into account the varying transport effects, and provides a dimensionless time basis for analyzing crystal growth kinetics in this system.
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