Invex multifunctions and duality

For optimization problems with multifunction objective and constraints, duality theorems are proved for analogs of the Wolfe and Mond–Weir dual problems, assuming that the multifunctions satisfy a generalization of the invex property for functions. Several characterizations of generalized invexity are obtained.     

Correction to: Two-Dimensional Culture Systems to Enable Mechanics-Based Assays for Stem Cell-Derived Cardiomyocytes

Experimental Mechanics - The authors would like to correct the sentence “The mass ratio……” in the subsection on Engineered Substrate System in MATERIALS AND METHODS, to read:     

Symmetric dual fractional programming

A pair of symmetric dual fractional programming problems is formulated and appropriate duality theorems are established.

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Zusammenfassung Es wird ein symmetrisches Paar primaler und dualer Quotientenprogramme eingeführt, für das Dualitätsbeziehungen hergeleitet werden.

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Research by this author was carried out while he was a visiting research fellow at the University of Melbourne.     

Enhanced ligand affinity for receptors in which components of the binding site are independently mobile

Using calmodulin antagonism as a model, it is demonstrated that, under circumstances in which binding sites are motionally independent, it is possible to create bifunctional ligands that bind with significant affinity enhancement over their monofunctional counterparts. Suitable head groups were identified by using a semiquantitative screen of monofunctional tryptophan analogs. Two bifunctional ligands, which contained two copies of the highest-affinity head group tethered by rigid linkers, were synthesized. The bifunctional ligands bound to calmodulin with a stoichiometry of 1:1 and with an affinity enhancement over their monofunctional counterparts; the latter bound with a stoichiometry of 2:1 ligand:protein. A lower limit to the effective concentrations of the domains of calmodulin relative to each other (0.2-2 mM) was determined. A comparable effective concentration was achieved for bifunctional ligands based on higher-affinity naphthalene sulphonamide derivatives.     

Permanently oriented antibody immobilization for digoxin determination with a flow-through fluoroimmunosensor

This paper reports a new flow-through fluoroimmunosensor, the function of which is based on antibodies immobilized on an inmunoreactor of controlled-pore glass (CPG), for determination of digoxin, used in the treatment of congestive heart failure and artery disease. The immunosensor has a detection limit of 1.20 microg L(-1) and provides high reproducibility (RSD=4.5% for a concentration of 0.0025 mg L(-1), and RSD=6.7% for 0.01 mg L(-1)). The optimum working concentration range was found to be 1.2 x 10(-3)-4.0 x 10(-2) mg L(-1). The lifetime of the immunosensor was about 50 immunoassays; if stored unused its lifetime can be extended to three months. A sample speed of about 10-12 samples per hour can be attained. Possible interference from substances with structures similar to digoxin (morphine, heroin, tebaine, codeine, pentazocine and narcotine) was investigated. No cross-reactivity was seen at the highest digoxin: interferent ratio studied (1:100). The proposed fluoroimmunosensor was successfully used to determine digoxin concentrations in human serum samples.     

Implicit function theorems and lagrange multipliers

Several implicit function theorems are proved, for systems of inequalities as well as equalities, assuming weaker differentiability than continuous Fréchet. These results give sufficient hypotheses for the Kuhn-Tucker conditions to hold, in a constrained minimization problem, with cone constraints and in any dimension. A condition is given for an inequality constraint system to be equivalently replaced by another, for which the function involved has surjective derivative. This allows some known implicit function theorems to be applied to inequality systems.     

Eisen und Stab

Ohne Zusammenfassung     

The mechanism of copolymerization of maleic anhydride with styrene and with vinyl acetate

A nonaqueous potentiometric direct titration method was used to determine the composition diagrams for the copolymerization of maleic anhydride with styrene and with vinyl acetate in methyl ethyl ketone at 50°C. The data were analyzed using nonlinear least-squares minimization routines to fit composition equations for the terminal, penultimate, and complex models directly. The applicability of each model to both systems were evaluated statistically. The penultimate model was found to best describe both systems, although in the case of the maleic anhydride/vinyl acetate system this was only a small improvement over the terminal model. Although significant comonomer complexation occurs in both systems, the complex model did not provide statistically significant improvement in fit to the data compared with the terminal model.