Optimizing a linear function over an efficient set

The problem (P) of optimizing a linear functiond ^T x over the efficient set for a multiple-objective linear program (M) is difficult because the efficient set is typically nonconvex. Given the objective function directiond and the set of domination directionsD, ifd ^T 0 for all nonzero D, then a technique for finding an optimal solution of (P) is presented in Section 2. Otherwise, given a current efficient point , if there is no adjacent efficient edge yielding an increase ind ^T x, then a cutting plane is used to obtain a multiple-objective linear program ( ) with a reduced feasible set and an efficient set . To find a better efficient point, we solve the problem (I_i) of maximizingc _i ^T x over the reduced feasible set in ( ) sequentially fori. If there is a that is an optimal solution of (I_i) for somei and , then we can choosex ⁱ as a current efficient point. Pivoting on the reduced feasible set allows us to find a better efficient point or to show that the current efficient point is optimal for (P). Two algorithms for solving (P) in a finite sequence of pivots are presented along with a numerical example.The authors would like to thank an anonymous referee, H. P. Benson, and P. L. Yu for numerous helpful comments on this paper.     

The standard model at low energies

The hadronic sector of the standard model at low energies is described by a nondecoupling effective field theory, chiral perturbation theory. An introduction is given to the construction of effective chiral Lagrangians, both in the purely mesonic sector and with inclusion of baryons. The connection between the relativistic formulation and the heavy baryon approach to chiral perturbation theory with baryons is reviewed.Lecture presented at the Indian-Summer School on Interaction in Hadronic Systems, Praha (The Czech Republic), 25–31 August 1993.Work supported in part by FWF, Project No. P09505-PHY (EURODANE Collaboration).I want to thank Jürg Gasser and Helmut Neufeld for helpful comments.     

Double-helical ultrastructure of polycationic dendronized polymers determined by single-particle Cryo-TEM

The ultrastructure of cationic dendronized polymers (denpols) of third and fourth generations (PG3 and PG4) in water was determined by using single-particle cryo-transmission electron microscopy (cryo-TEM). At concentrations in the region of 50 mg L(-1), networks of double-stranded fibers were revealed that exhibit well-defined diameters of 5.9 nm+/-0.4 nm for PG3 and 7.4 nm+/-0.4 nm for PG4. The structure varies with progression along the fibers, and includes a double helix with a pitch of 7.0+/-0.4 nm for PG3 and 9.0+/-0.4 nm for PG4. The formation of the double strands is attributed to the hydrophobic effect and limited crowding in the dendron shell of the third and fourth generation denpols investigated. From solutions of lower concentrations (around 10 mg L(-1)), isolated molecular fibers were adsorbed onto high-energy surfaces and examined by performing scanning force microscopy (SFM) on mica, and after staining, TEM on glow-discharged carbon films. In both cases, characteristic undulations of single strands were observed, which are attributed largely to the adsorption process.     

Levcromakalim Revisited: NMR Spectroscopic and Theoretical Investigations

 The conformative behaviour of the potassium channel opener levcromakalim ((−)-cromakalim) was thoroughly investigated applying NMR spectroscopy in different solvents as well as ab initio and DFT calculations. One predominant conformation was found to prevail in solution. Chemical shift values (¹H, ¹³C) obtained by the GIAO method employing high basis sets (B3LYP/6-311++G^**) proved to be sensitive to conformational changes. Those correlating best with the measured data correspond to the structure as determined by 2D NMR spectroscopy.