A note on comprehensive backward biorthogonalization

We present a backward biorthogonalization technique for giving an orthogonal projection of a biorthogonal expansion onto a smaller subspace, reducing the dimension of the initial space by droppingdbasis functions. We also determine which basis functions should be dropped to minimize theL2distance between a given function and its projection. This generalizes some results in [3].

Transient Heat Conduction in Laminated Composites

The layers are stacked parallel to the x axis. On the half-space x ⩾ 0 there is applied, at x = 0, a boundary temperature of y-periodicity conforming to the periodicity of the layered composite. The response is determined in the form of a normal mode expansion. A complex eigenvalue problem must be solved first, then the Fourier coefficients are determined from a biorthogonal expansion formula. The series converges to both the real and the imaginary parts of the prescribed input simultaneously. It is found that at low frequencies and not too small distances the static equivalent thermal constants kav, (ρc)av are applicable also in the non-static problem. This ceases to be true at high frequencies.