Preliminary experiments for the fabrication of thermally actuated bimorph cantilever arrays on non-silicon wafers with vertical interconnects

This paper describes the first steps for the fabrication of low-cost cantilever arrays, developed at RAL, on non-silicon polymer substrates with vertical interconnects, produced at Profactor. The deflection and actuation of these cantilevers is based on the bimorph thermal actuation principle. The fabrication of the cantilever arrays requires many process steps which are presented in this article. The first step is the planarization between the via-holes interconnects with a uniform layer. This was achieved by spin coating of a thick (~58μm) SU-8 layer. In the subsequent step, two thin metal layers of Cr (500Å) and Au (1000Å) were thermally deposited and patterned, using UV lithography with a mask alignment process and wet etching. The following step was the coating of a 1μm structural Au layer, in which the deposited layer had a very poor adhesion. Alternative procedures were explored to overcome this problem in the future. Modifications of the photo masks design and the substrates will be carried out to make the RAL microcantilevers technology more compatible with Profactor substrates.Unión Europea MRTN-CT-2003- 50482

Skew-self-adjoint discrete and continuous Dirac type systems: inverse problems and Borg-Marchenko theorems

New formulas on the inverse problem for the continuous skew-self-adjoint Dirac type system are obtained. For the discrete skew-self-adjoint Dirac type system the solution of a general type inverse spectral problem is also derived in terms of the Weyl functions. The description of the Weyl functions on the interval is given. Borg-Marchenko type uniqueness theorems are derived for both discrete and continuous non-self-adjoint systems too

Multirectangular invariants for power Köthe spaces

Using some new linear topological invariants, isomorphisms and quasidiagonal isomorphisms are investigated on the class of first type power Köthe spaces [Proceedings of 7th Winter School in Drogobych, 1976, pp. 101–126; Turkish J. Math. 20 (1996) 237–289; Linear Topol. Spaces Complex Anal. 2 (1995) 35–44]. This is the smallest class of Köthe spaces containing all Cartesian and projective tensor products of power series spaces and closed with respect to taking of basic subspaces (closed linear hulls of subsets of the canonical basis). As an application, it is shown that isomorphic spaces from this class have, up to quasidiagonal isomorphisms, the same basic subspaces of finite (infinite) type

On Dragilev type power Köthe spaces

A complete isomorphic classification is obtained for Köthe spaces $X = K(exp[χ(p - κ (i)) - 1/p]a_i)$ such that $X qd_≃ X^2$; here χ is the characteristic function of the interval [0,∞), the function κ: ℕ → ℕ repeats its values infinitely many times, and $a_i → ∞$. Any of these spaces has the quasi-equivalence property

Equiconvergence of spectral decompositions of Hill operators

We study in various functional spaces the equiconvergence of spectral decompositions of the Hill operator L = -d (2)/dx (2) + v(x), x a L (1)([0, pi], with H (per) (-1) -potential and the free operator L (0) = -d (2)/dx (2), subject to periodic, antiperiodic or Dirichlet boundary conditions. In particular, we prove that parallel to S-N - S-N(0) : L-a -> L-b parallel to -> 0 if 1 < a <= b < infinity, 1/a - 1/b < 1/2, where S (N) and S (N) (0) are the N-th partial sums of the spectral decompositions of L and L (0). Moreover, if v a H (-alpha) with 1/2 < alpha < 1 and , then we obtain the uniform equiconvergence aEuro-S (N) -S (N) (0) : L (a) -> L (a)aEuro- -> 0 as N -> a

Remarks on bounded operators in Köthe spaces

We prove that if λ(A), λ(B) and λ(C) are Köthe spaces such that L(λ(A), λ(B)) and L(λ(C), λ(A)] consist of bounded operators then each operator acting on λ(A) that factors over λ(B)⊗̂πλ(C) is bounded

Compound invariants and embeddings of Cartesian products

New compound geometric invariants are constructed in order to characterize complemented embeddings of Cartesian products of power series spaces. Bessaga's conjecture is proved for the same class of spaces