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Theory of linear magnetoelastic effects

Physical Review B, 1985
A theory for the elastic properties of magnetostrictive materials is presented. The complete elastic constant tensor is obtained from simple linear magnetoelastic approximations as a function of the magnetoelastic coupling coefficients and the susceptibility. It is also shown that, by using the proper dynamic susceptibility tensor, most of the observed
, Rinaldi, , Turilli
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Effectively Well-Conditioned Linear Systems

SIAM Journal on Scientific and Statistical Computing, 1988
The authors discuss effective well-conditioning of the linear system \(Ax=b\). The condition number \(K(A)=\| A\| \| A^{-1}\|\) is often an overly conservative measure of the sensitivity of x under perturbations of \(\Delta\) A and \(\Delta\) b to A and b respectively. Two practical cases in which the sensitivity of x may be significantly less than the
Chan, Tony F., Foulser, David E.
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Linear Mixed Effects Models

2007
Statistical models provide a framework in which to describe the biological process giving rise to the data of interest. The construction of this model requires balancing adequate representation of the process with simplicity. Experiments involving multiple (correlated) observations per subject do not satisfy the assumption of independence required for ...
Ann L, Oberg, Douglas W, Mahoney
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Linear Transformations of Linear Mixed-Effects Models

The American Statistician, 1997
Abstract A number of articles have discussed the way lower order polynomial and interaction terms should be handled in linear regression models. Only if all lower order terms are included in the model will the regression model be invariant with respect to coding transformations of the variables.
Christopher H. Morrell   +2 more
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