Second-order optimality conditions for nondominated solutions of multiobjective programming with C 1,1 data

We examine new second-order necessary conditions and sufficient conditions which characterize nondominated solutions of a generalized constrained multiobjective programming problem. The vector-valued criterion function as well as constraint functions are supposed to be from the class C ^1,1. Second-order optimality conditions for local Pareto solutions are derived as a special case.     

Synthesis and characterization of micrometer‐sized particles of narrow size distribution with chloromethyl functionality on the basis of single‐step swelling of uniform polystyrene template microspheres

Polystyrene template microspheres of 1.4 ± 0.1 μm were prepared by dispersion polymerization of styrene in a mixture of ethanol and 2‐methoxy ethanol. These template particles were then swelled at room temperature in a single step with emulsion that was prepared in sodium dodecyl sulfate aqueous solution from a swelling solvent (dibutyl phthalate) containing the initiator (benzoyl peroxide) and monomer(s) (chlormethylstyrene, divinylbenzene, or ethylene dimethacrylate). Composite uniform particles composed of the template polystyrene and noncrosslinked or crosslinked polychloromethylstyrene were prepared by polymerizing the monomer(s) within the swelled particles at 73 °C. Crosslinked uniform polychloromethylstyrene particles of higher surface area were formed by dissolving the template polystyrene polymer of the composite particles. The influence of various reaction parameters, such as dibuthyl phthalate concentration, chloromethylstyrene concentration, crosslinker type and concentration, and so forth on the molecular weight, size, size distribution, shape, morphology, surface area, and decomposition temperature of the particles was investigated. © 2002 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 40: 1342–1352, 2002     

Elimination versus ring opening: a convergent route to alkylidene-cyclobutanes

Functionalized alkylidene-cyclobutanes have been prepared from 2-fluoropyridinyl-6-oxy precursors derived from vinyl cyclobutanols by a radical addition-elimination process. A wide range of functional groups is tolerated, and the alkylidene-cyclobutanes can be further elaborated into cyclopentanones. The limitation of this approach resides in the competition with opening of the cyclobutane ring.     

Omega limit sets and distributional chaos on graphs

We give a full topological characterization of omega limit sets of continuous maps on graphs and we show that basic sets have similar properties as in the case of the compact interval. We also prove that the presence of distributional chaos, the existence of basic sets, and positive topological entropy (among other properties) are mutually equivalent for continuous graph maps.     

There Is No Face-to-Face Partition of R5 into Acute Simplices

We prove that a point in the Euclidean space R⁵ cannot be surrounded by a finite number of acute simplices. This fact implies that there does not exist a face-to-face partition of R⁵ into acute simplices. The existence of an acute simplicial partition of R^d for d > 5 is excluded by induction, but for d = 4 this is an open problem. Dedicated to Prof. Miroslav Fiedler on the occasion of his 80th birthday     

Dirubidium fluoro­trioxophosphate,Rb2PO3F,at 290 and 130 K,and dicaesium fluoro­trioxophosphate,Cs2PO3F,at 240 and 100 K

The structure of Rb₂PO₃F was determined at 290 and 130 K, while that of Cs₂PO₃F was determined at 240 and 100 K. Both compounds belong to the β‐K₂SO₄ family. The structure analysis did not reveal signs of a phase transition in either compound. Crystal chemical considerations do not favour the presence of a phase transition in either Rb₂PO₃F or Cs₂PO₃F. However, glass‐like phase transitions were observed by differential scanning calorimetry in slightly humid samples at 175 and 177 K for Rb₂PO₃F and Cs₂PO₃F, respectively, but were not observed in well dried samples. The bond distances are normal and Cs₂PO₃F is twinned.     

Differential invariants of generic hyperbolic Monge-Ampère equations

In this paper basic differential invariants of generic hyperbolic Monge-Ampère equations with respect to contact transformations are constructed and the equivalence problem for these equations is solved.