Stabilized wavelet approximations of the Stokes problem

We propose a new consistent, residual-based stabilization of the Stokes problem. The stabilizing term involves a pseudo-differential operator, defined via a wavelet expansion of the test pressures. This yields control on the full -norm of the resulting approximate pressure independently of any discretization parameter. The method is particularly well suited for being applied within an adaptive discretization strategy. We detail the realization of the stabilizing term through biorthogonal spline wavelets, and we provide some numerical results.

     

Possibilities of study of the human plasma cholinesterase variants by affinity electrophoresis

Affinity electrophoresis has been applied to the study of the multiple molecular forms of three human plasma cholinesterase phenotypes (usual enzyme U, atypical enzyme A and intermediate UA). Electrophoreses were carried out in polyacrylamide gels containing a water-soluble macromolecular derivative of m-amino-(substituted)-phenyltrimethylammonium immobilized within the gel network. Apparent dissociation constants (KD app) were estimated from the mobilities of the enzymes versus ligand concentration. The ratio of KD app values of the molecular forms of phenotypes A and U which is approximately 2 is consistent with the hypothesis that the anionic site is altered in atypical enzyme.     

Essential self-adjointness for highly singular potentials

The essential self-adjointness of the Hamiltonian operator associated with non-spherically symmetric potentials which are highly singular and repulsive at the origin is proved.     

Migration brownienne de cristallites sur une surface et relation avec l'épitaxie: II. Partie théorique

The thermal migration of small crystal buildings on a crystalline substrate is considered from two points of views. In the first the surface self diffusion of the atoms on the crystallites is supposed to be able to move the crystallites. In the second, special atomic configurations located in the interface crystallites-substrate are rendered responsible of these motions. Both hypotheses are formulated and compared with some experiments given in the fore going paper. The second theory is in qualitative accordance with these experiments so that the formation of an epitaxy is now better understood.     

On the self-adjointness of the (g(x)φ4)2 Hamiltonian

An alternate proof to that provided by Glimm and Jaffe of the essential self-adjointness of the HamiltonianH for a relativistic scalar quantum field in two dimensional space-time with a space cut-off quartic interactionH _I (g) is given. The proof depends mainly on the estimateH _I ² (g)const. (N+I)⁴ and on the semiboundedness ofH=H ₀+H _I (g).Supported in part by the National Research Council of Canada.     

Nondestructive monitoring of the photochromic state of dithienylethene monolayers by surface plasmon resonance

The use of surface plasmon resonance (SPR) as a nondestructive, nonerasing readout of the isomerization state of a photochromic dithienylethene covalently linked to a chemically modified gold surface was investigated. Four different binding layers were examined: 11-mercaptoundecanol (MUO), an amine-modified 11-mercaptoundecanol (MUO-NH2), dextran, and an amine-modified dextran. The binding of dithienylethene to the modified gold surface and photoisomerization of the photochrome in the bound state were established by FTIR. Solvent effects were measured for every layer tested using ethanol and hexanes. In general, large, easily measurable SPR signal changes could be detected under conditions where photoisomerization of the dithienylethene photochrome was not quenched by the gold plasmon, establishing SPR as a viable form of readout for potential dithienylethene-based optical data storage or processing devices. Dextran-bound photochrome in ethanol exhibited the largest SPR response upon photoisomerization, but is more prone to time-dependent fluctuations resulting from swelling of the dextran layer (caused by slow diffusion of the solvent) than the other layers. Large responses are also provided by MUO-NH2 and MUO, and the signal is much more stable than that for dextran.     

Monitoring of recombinant survival motor neuron protein using fiber-optic surface plasmon resonance

Spinal muscular atrophy (SMA) is the leading genetic cause of infant mortality. SMA is caused by the homozygous loss of the survival motor neuron 1 (SMN1) gene. A nearly identical copy gene exists known as SMN2, however, due to an aberrant splicing event, the SMN2 gene fails to produce sufficient full-length protein to protect against disease development in the absence of SMN1. While a number of compounds have recently been identified that can stimulate full-length survival motor neuron (SMN) expression from the nearly identical copy SMN2, one of the difficulties has been the lack of a highly reproducible and quantitative means to measure the levels of SMN protein. To develop a technique that allows the rapid and highly sensitive measurement of SMN protein, a Surface Plasmon Resonance (SPR) application has been developed. The ability to quantify unassociated SMN protein and monitor the binding of SMN with other proteins in solution using a SPR sensor in less than 15 min and at low ng mL(-1) levels in HEPES Buffer Saline (HBS) has been achieved. The detection limit for the specific binding of SMN in HBS pH 7.4 solution is 0.99 ng mL(-1) with non-specific binding accounting for approximately 30% of the signal. Quantification of SMN is based on an immunoassay performed on the gold surface of the SPR sensor. 16-mercaptohexadecanoic acid (MHA) was reacted with dicyclohexylcarbodiimide (DCC) and N-hydroxysuccinimide (NHS) to form a pre-activated thiol (MHA-NHS). Antibodies for SMN were then coupled to the sensor with the pre-activated thiol. Sensor specificity was examined with mixtures of myoglobin (MG) and SMN. SMN sensor response decreases by more than 60% when MG was added to SMN. The decrease in sensor response can be attributed to non-specific binding of SMN to MG, verified with a sensor for MG.