Wavelet-based Preconditioners for Dense Matrices with Non-Smooth Local Features

We present algorithms for the detection of local non-smooth features within a dense matrix and show how, by isolating such features, we are able to use wavelet compression to design preconditioners for the corresponding dense linear system. We illustrate our approach with examples from the solution of elastohydrodynamic lubrication problems and boundary integral equations.This revised version was published online in October 2005 with corrections to the Cover Date.     

Search for lepton flavor violation in the decay tau+/- --> mu+ gamma

A search for the nonconservation of lepton flavor number in the decay tau(+/-) --> mu(+/-) has been performed using 2.07 x 10(8) e(+ )e(-) tau(+) tau(-) events produced at a center-of-mass energy near 10.58 GeV with the BABAR detector at the PEP-II storage ring. We find no evidence for a signal and set an upper limit on the branching ratio of Beta(tau(+/-) --> mu(+/-) gamma) < 6.8 x 10(-8) at 90% confidence level.     

Six-coordinate nitrato complexes of iron(III) porphyrins

The interaction of tetrahydrofuran (THF) with thin films of the nitrato complexes Fe(III)(Por)(eta(2)-O(2)NO) [Por = meso-tetraphenylporphyrinato (TPP) and meso-tetratolylporphyrinato (TTP) dianion] at low temperature leads to the formation of the six-coordinate nitrato complex Fe(Por)(THF)(NO(3)), which was characterized by IR and UV-visible spectroscopies. Formation of the THF adduct was accompanied by nitrate linkage isomerization from bidentate to monodentate coordination. The iron(III) center remains in a high spin state in contrast with the previously observed low-spin nitratonitrosyl complex Fe(TPP)(NO)(eta(10-ONO(2)). Upon warming, THF dissociates to restore the initial five-coordinate bidentate nitrato complex.     

Genetic engineering to enhance the selectivity of protein separations

The ability to recover and purify natural and recombinant proteins, and the costs of doing so remain a major task in introducing the potential products of biotechnology. The bases for separation range from specific binding onto tailored reagents to solubility and partitioning behavior governed by a mixed bag of size, charge, and hydrophobicity. In most cases, a combination of methods is used in sequence, and improvements in the selectivity at an early stage can enhance the effectiveness of subsequent (and usually more costly) steps. Genetic engineering provides a means of improving the selectivity within the context of existing separation methods. By this strategy, improvements in selectivity are sought by bestowing a distinctive property on the protein of interest. The primary sequence of amino acids is altered, such that the protein can be selectively removed from other components of the multicomponent mixture in which such products are commonly found. In this article, the range of these “distinctive properties” and their pairing with various separation methods will be reviewed. Specific examples from our work, in which a distinctive charge is provided via a polypeptide “purification” fusion tail, will be discussed. Separation methods we have used with these fusion proteins are precipitation, two-phase aqueous extraction, reversed micellar extraction, and ion exchange using both resins and membranes.     

Synthesis and characterization of uniform alumina-mesoporous silica hybrid membranes

The synthesis and characterization of alumina-mesoporous silica (alumina-MS) hybrid membranes are reported. The hybrids are formed using a variation of the evaporative-induced self-assembly (EISA) process reported by Hayward et al. (Langmuir 2004, 20, 5998) based on dip coating of an Anopore 200 nm membrane with a Brij-56/TEOS/HCl/H2O solution. Numerous analytical methods are used to probe both the hybrid material and the silica phase after dissolution of the Anopore substrate. Most importantly, He/N2 permeation measurements show that the effective pore size of the membrane can be tuned from 20 to 5 nm based on the number of dip-coating cycles used. The observed He/N2 permselectivity of 2.7 +/- 0.11 is nearly identical to the theoretical value obtained (2.65) assuming Knudsen diffusion dominates. The selectivity of these membranes is higher than that of most commercial "5 nm" membranes (2.29), which is ascribed to the lack of pinhole defects in the materials reported here. The hybrid membranes as well as the silica obtained after dissolution of the Anopore substrate have been characterized using scanning and transmission electron microscopy and X-ray diffraction. Those results indicate that the silica deposited in the Anopore membrane possesses uniform pores approximately 5 nm in size, consistent with the permeation studies. The current work presents an alternative approach to materials that possess many of the properties of mesoporous silica thin films (i.e., pores of controlled size and topology) without the difficulty of growing mesoporous silica thin films on porous supports.     

Multi-step nonlinear conjugate gradient methods for unconstrained minimization

Conjugate gradient methods are appealing for large scale nonlinear optimization problems, because they avoid the storage of matrices. Recently, seeking fast convergence of these methods, Dai and Liao (Appl. Math. Optim. 43:87–101, 2001) proposed a conjugate gradient method based on the secant condition of quasi-Newton methods, and later Yabe and Takano (Comput. Optim. Appl. 28:203–225, 2004) proposed another conjugate gradient method based on the modified secant condition. In this paper, we make use of a multi-step secant condition given by Ford and Moghrabi (Optim. Methods Softw. 2:357–370, 1993; J. Comput. Appl. Math. 50:305–323, 1994) and propose two new conjugate gradient methods based on this condition. The methods are shown to be globally convergent under certain assumptions. Numerical results are reported.