Extensions to the continuous ordered median problem

Classical location models fix an objective function and then attempt to find optimal points to this objective. In the last years a flexible approach, the ordered median problem, has been introduced. It handles a wide class of objectives, such as the median, the center and the centdian function. In this paper we present new properties of the ordered median problem such as solvability for the situation of attractive and repulsive locations. We also develop a new solution method that even yields local optimal points for non-convex objective functions. Furthermore, we discuss separability of ordered median problems without repulsion and derive a sufficient criterion. Finally, we introduce a useful model extension, the facility class model, which allows to deal with a wider range of real world problems in the ordered median setting.     

Electron exchange chemiluminescence from a sterically stabilized cyclobutadiene-1,2-dioxetane

The rather stable 1,2-dioxetanes ($\text{2}$) and ($\text{3}$), derived from the sterically stabilized cyclobutadiene ($\text{1}$), exhibit distinct enhanced chemiluminescence behavior, namely energy transfer chemiluminescence (ETC) for ($\text{2}$) and electron exchange chemiluminescence (EEC) for ($\text{3}$).     

Untersuchungen über S?H …︁ S-Wasserstoffbrücken Die Kristallstruktur der Diphenyldithiophosphinsäure bei 140 und 293 K

Die Kristallstruktur der Diphenyldithiophosphinsäure (C₆H₅)₂P(S)SH wurde röntgenographisch bei tiefer Temperatur und Normaltemperatur aus Einkristalldiffraktometerdaten bestimmt und bis zu R-Werten von 0,037 (140 K, (sin Θ)/λ < 0,81 Å^?1) und 0,035 (293 K, (sin Θ)/λ < 0,64 Å^?1) verfeinert. Die Verbindung kristallisiert in der monoklinen Raumgruppe P2₁/c mit den bei 140 K (in Klammern: 293 K) gemessenen Gitterkonstanten a = 9,824(3) (9,887), b = 10,061(3) (10,175), c = 14,342(4) (14,433) Å, β = 122,08(3) (121,73)° und V = 1201,1 (1234,9) ų, Z - 4. Im Kristall sind individuelle Moleküle über fast lineare S? H…?S-Wasserstoffbrückenbindungen zu schraubenförmig gewundenen Ketten verknüpft. Bei 140 K beträgt der S…?S-Abstand innerhalb der Brücke 3,790(1) Å; die weiteren geometrischen Daten der Wasserstoffbrücke sind: d(S? H): 1,25(2), d(S…?H): 2,56(2), d(P? S): 2,077(1), d(P?S): 1,954(1) Å, ? (S? H…?S): 169,5(14), ? (P? S…?S): 98,87(2), ? (P?S…?S): 96,65(2)°. Investigations on Compounds Containing S? H…?S Hydrogen Bonds. Crystal Structure of Diphenyldithiophosphinic Acid at 140 and 293 K The crystal structure of diphenyldithiophosphinic acid (C₆H₅)₂P(S)SH was determined from X-ray diffraction data collected at 140 and 293 K and was refined to R factors of 0.037 (140 K, (sin Θ)/λ < 0.81 Å^?1) and 0.035 (293 K, (sin Θ)/λ < 0.64 Å^?1) respectively. The compound crystallizes in the monoclinic space group P2₁/c with unit cell parameters at 140 K (in parentheses: at 293 K): a = 9.824(3) (9.887), b = 10.061(3) (10.175), c = 14.342(4) (14.433) Å, β = 122.08(3) (121.73)° and V = 1201.1 (1234.9) ų, Z = 4. In the crystalline state individual molecules are linked together by nearly linear S? H…?S hydrogen bonds so that endless helical chains are formed. At 140 K the S…?S distance within the hydrogen bond is 3.790(1) Å; the other distances and angles associated with the bridge are: d(S? H): 1,25(2), d(S…?H): 2,56(2), d(P? S): 2,077(1), d(P?S): 1.954(1) Å, ? (S? H…?S): 169.5(14), ? (P? S…?S): 98.87(2), ? (P? S…?S): 96.65(2)°.