Rigorous solution of linear programming problems with uncertain data

This note gives a synopsis of new methods for solving linear systems and linear programming problems with uncertain data. All input data can vary between given lower and upper bounds. The methods calculate very sharp and guaranteed error bounds for the solution set of those problems and permit a rigorous sensitivity analysis. For problems with exact input data in general the calculated bounds differ only in the last bit in the mantissa, i.e. they are of maximum accuracy. This is a written account of an invited lecture delivered by the second author on occasion of the 14. Symposium über Operations Research, Ulm, 6.–8.9.1989.     

Varifocal liquid-filled microlens operated by an electroactive polymer actuator

We designed, fabricated, and characterized varifocal microlenses, whose focal length varies along with the deformation of a transparent elastomer membrane under hydraulic pressure tailored by electroactive polymer actuators. The microfluidic channel of the microlens was designed to be embedded between silicon and glass so that transient fluctuation of the optical fluid and elastomer membrane is effectively suppressed, and thus the microlens is optically stabilized in a reduced time. Multilayered poly(vinylidene fluoride-trifluoroethylene-clorotrifluoroethylene) actuators were also developed and integrated onto the microfluidic chambers. We demonstrated that the developed microlenses are suitable for use in microimaging systems to make their foci tunable.     

Enrichment of N-terminal sulfonated peptides by a water-soluble fullerene derivative and its applications to highly efficient proteomics

Recent studies have shown that N-terminal sulfonation of tryptic peptides by various sulfonating molecules greatly improves their post-source decay processes (e.g., in matrix-assisted laser desorption ionization) or the gas phase fragmentation processes (e.g., in tandem mass spectrometer), enhancing the ability to identify their sequences de novo. In the present work, we have demonstrated that incorporation of water-soluble C₆₀-N,N-dimethylpyrrolidinium iodide selectively precipitates the 4-sulfophenyl isothiocyanate-modified peptide (SPITC-GGYR, SPITC-ASHLGLAR) by forming a noncovalent ion pair to the SO₃⁻ group of the SPITC, and thereby the C₆₀ derivative can be utilized to enrich the modified peptide. Electrospray ionization (ESI) mass analyses show that the cationic SPITC-GGYR and SPITC-ASHLGLAR species are well separated from unmodified peptides and the modified peptides are subsequently detached from the C₆₀ derivative upon using an acidic solution.     

Verified error bounds for multiple roots of systems of nonlinear equations

It is well known that it is an ill-posed problem to decide whether a function has a multiple root. Even for a univariate polynomial an arbitrary small perturbation of a polynomial coefficient may change the answer from yes to no. Let a system of nonlinear equations be given. In this paper we describe an algorithm for computing verified and narrow error bounds with the property that a slightly perturbed system is proved to have a double root within the computed bounds. For a univariate nonlinear function f we give a similar method also for a multiple root. A narrow error bound for the perturbation is computed as well. Computational results for systems with up to 1000 unknowns demonstrate the performance of the methods.