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We expect the limit to satisfy the equation in a distributional sense as well as an optimal energy-dissipation relation. Similarly, we construct weak solutions to the Cahn-Hilliard equation with degenerate mobility and elastic misfits. Finally, we aim to prove that the sharp interface limit is a...
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This expression vanishes in homogeneous matter, and we recover the in-medium Schrödinger equation for α clusters in matter without external potential. Then, the eigenvalue F(R) of Eq. (9) represents the bound state energy of the α particle which is shifted in dense matter because of ...
FM represents a regression algorithm that models interactions between pairs of variables ‘X’ and the target ‘Y’ by using factors. FMs are suitable for the massive sparse problem such as recommendation. It accurately models the interaction of contextual variables/features during context-aware ...
We derived the FE equation as follows98: $${y}_{it}={\beta }_{1}{x}_{it}\ldots +{a}_{i}+{\delta }_{t}+{u}_{it,}t=1,2$$ (1) for each plot (i), we averaged the equation over time (t), yielding: $${\bar{y}}_{i}={\beta }_{1}{\bar{x}}_{i}\ldots...
The evolution of normalized local magnetization m in a ferromagnetic (FM) system and m(s) (s = 1,2) in two magnetic sublattices of an antiferromagnetic (AFM) system are governed by the LLG equation. The LLG equation for the FM system is expressed as, $$\begin{array}{*{20}{c}...
9. The value of the contact angle (θ) can be determined between 0° and 180° and is wholly derived due to the intermolecular force balance, as expressed by Young's equation (7):(7)where θ is the contact angle derived due to the intermolecular force balance, γ is the IFT force ...
It confuses the income and expenditure sides of the equation. Logically, you might as well say fee loans wouldn’t be an issue, given a high enough level of grant, because people could work to pay their fees. Unless you accept the second of these arguments, you can’t use the first. ...
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