Lexicographic quasiconcave multiobjective programming

Summary Letf _i :A R ben real-valued objective functions on a convex setA -K ^m ,K:=R orC, n, mN. Letg: A R ⁿ be defined by , where for eachxA, (i ₁ (x), ..., i _n (x)) is a permutation of (1, ...,n) such that . In this paper we treat the problem of findingx ^*A such that , wherel-max denotes the lexicographic maximum. If the f_i's are strongly quasiconcave we can reduce the problem stepwise until finally it is in the form of a scalar programming problem. Further, we consider conditions for the existence and uniqueness of a solution and discuss the relationship of the problem to the vector maximum (i.e. Pareto) and maxmin (i.e. Chebychev) problems.

---

Zusammenfassung f _i :AR seienn reellwertige Zielfunktionen über einer konvexen MengeA-K ^m ,K:=R oderC, n, mN. g:AR ⁿ sei definiert durch , wobei für jedesxA (i ₁ (x), ... i _n (x)) eine Permutation von (1, ...,n) derart ist, daß Wir betrachten das Problem, einx ^*A so zu finden, daß , wobeil-max das lexikographische Maximum bedeute. Falls dief _i stark quasikonkav sind, läßt sich das Problem stufenweise reduzieren, bis es schließlich die Gestalt eines skalaren Optimierungsproblems annimmt. Wir geben Existenz- und Eindeutigkeitsbedingungen an und besprechen Zusammenhänge mit dem Vektormaximumproblem (d.h. Pareto-Optimierung) und dem Maxmin-Problem (d.h. Tschebyscheff-Optimierung).

     

Synthesis,characterization and antioxidant,antibacterial activity Zn2+, Cu2+, Ni2+ and Co2+, complexes of ligand [2-(thiophen-2-yl)-1-(thiophen-2-ylmethyl)-1H-benzo[d]imidazole]

New metal complexes of (Zn(II), Co(II), Ni(II) and Cu(II)) based on the ligand 2-(thiophen-2-yl)-1-(thiophen-2-ylmethyl)-1H-benzo[d]imidazole] were synthesized, whose structures were determined with the different spectroscopic techniques ¹H NMR,¹³C NMR, FT-IR, UV–Visible and by mass spectrometry. The thermal analysis was performed by TG-DTA. The antioxidant activity of the ligand and its complexes was evaluated by DPPH (2,2-diphenyl-1-picrylhydrazyl) method, in comparison with the synthetic antioxidant, ascorbic acid. The results obtained showed that the antioxidant activity of the ligand and its complexes is moderate and that the copper complex has a high activity that exceeds that of ascorbic acid. Antimicrobial activity of the ligand and its metal complexes was studied against two Gram-positive bacteria: Bacillus subtilis ILP1428B, Staphylococcus aureus CIP543154 and two Gram-negative bacteria: Pseudomonas aeruginosa ATCC27653, Escherichia coli CIP5412 (American Type Culture Collection)the activity data show that the metal complexes are more potent than the free ligand.     

A hybrid particle-continuum resolution method and its application to a homopolymer solution

We discuss in detail a recently proposed hybrid particle-continuum scheme for complex fluids and evaluate it at the example of a confined homopolymer solution in slit geometry. The hybrid scheme treats polymer chains near the impenetrable walls as particles keeping the configuration details, and chains in the bulk region as continuous density fields. Polymers can switch resolutions on the fly, controlled by an inhomogeneous tuning function. By properly choosing the tuning function, the representation of the system can be adjusted to reach an optimal balance between physical accuracy and computational efficiency. The hybrid simulation reproduces the results of a reference particle simulation and is significantly faster (about a factor of 3.5 in our application example).     

Introduction to the focus issue on granular materials

In a review paper [H. M. Jaeger, S. R. Nagel, and R. P. Behringer, "Granular solids, liquids and gases," Rev. Mod. Phys. 68, 1259-1273 (1996)] a few years ago, we wrote about granular material as a distinctive form of matter that exhibits behavior rather different from that of ordinary solids, liquids, or gases. We traced this distinction to three characteristic properties. First, the individual particles making up a granular material are typically large so that thermal energy is irrelevant compared to gravitational energy. Consequently, concepts from equilibrium statistical mechanics are often not applicable. Second, the interactions between particles are frictional and can be mobilized to different degrees depending on the preparation history, giving rise to memory effects, i.e., a static pile will remember how it was formed. Third, when particles collide they do so inelastically so that a "gas" of particles will slow down and come to rest in clumps. In the intervening years, the research on granular matter has progressed rapidly and this may be a good time to ask what we have learned since that article was written. In this spirit, the present special issue of the journal Chaos assembles a spectrum of papers discussing recent developments in the field. (c) 1999 American Institute of Physics.     

Measurement of atom and molecule number densities in hydrogen arcs by means of VUV spectroscopy

The number density of ground state atoms in the 2mm hydrogen arc (T≈20000 K) and the number density of molecules in the 5 mm hydrogen arc (T≈12000 K) have been measured by means of vuv spectroscopy. These species' are particularly likely to deviate from the equilibrium population and may therefore falsify the hydrogen transport coefficients measured in arc experiments. In the present investigation the optically thick line wings of Ly-α and the H₂ molecular spectrum around 1600 Å have been analyzed. The results demonstrate that the former assumptions of LTE and PLTE, respectively, are completely justified on and near the arc axis. However, in the outer zones of these arcs a considerable overpopulation of the molecules must be expected as a consequence of radial diffusion.     

Substrate interactions, effects of symmetry breaking, and convection in a 2D horizontally shaken granular system

We describe experiments on a horizontally shaken [x = Asin(omegat)] single layer of hard spheres rolling on a nearly horizontal surface. We identify a novel substrate-mediated convective flow which occurs when the system is tilted slightly so that the weak gravitational force, g-->(eff), acting on the particles is not parallel to the driving direction. As the shaking amplitude is increased, the system progresses through four regimes: solid-flat, solid-inclined, convective, and disordered. The control parameter is the driving velocity, Aomega, rather than the usual Aomega(2) of vertically shaken 3D systems. At the onset of convection, the critical velocity is V(c) approximately sqrt[2g(eff)d].