Quantum Instruments and Related Transformation Valued Functions

The notion of an instrument in the quantum theory of measurement is studied in the context of transformation valued linear maps on von Neumann algebras and their ^*-subalgebras. An extension theorem is proved which yields among other things characterizations of the Fourier transforms of instruments and their noncommutative analogues. As an application, an ergodic type theorem for a general class of transformation valued functions on a locally compact group is obtained.     

Ligand entrapment in twofold interpenetrating PtS matrixes by metallo-organic frameworks

Single-crystal X-ray crystallography was used to determine the structures of four metallo-organic frameworks (MOFs). A dendritic tetradentate ligand (tetrakis(isonicotinoxymethyl)methane, TINM) was used with first-row transition-metal elements copper, nickel, and cobalt to synthesize MOFs with a PtS interpenetration, due to both planar and tetrahedral junctions being present in the framework. Two different polymeric complexes, 1 and 2, were obtained from similar starting materials, TINM and Cu(NO(3))(2).3H(2)O, but different solvents. The use of dichloromethane in addition to methanol and water promoted the coordination of nitrate ions to the copper. With only methanol and water used as solvent, the copper atom was coordinated to water molecules instead. Compound 1 has pores going through the structure in two dimensions, along crystallographic axes a and c with diameters of the pores (the diameters correspond to the minimum distances between van der Waals surfaces of opposing walls defined by projection along channel axis) approximately 1.0 x 3.1 and 2.5 x 3.7 A, respectively. Compound 2 has channels along all crystallographic axes. The dimensions of the channels are 3.2 x 3.7, 3.7 x 5.0, and 2.8 x 4.1 A, respectively. The structures of 3 and 4 entrap a large guest ligand molecule in the framework. The guest ligand is uncoordinated, although the pattern that the entrapped guests form brings the two arms of any two guests within close range. The lack of 3-fold penetration is due to only two arms being close to each other and also the fact that there is no space for an additional set of metal centers.     

Two geometric character formulas for reductive Lie groups

In this paper we prove two formulas for the characters of representations of reductive groups. Both express the character of a representation in terms of the same geometric data attached to . When specialized to the case of a compact Lie group, one of them reduces to Kirillov's character formula in the compact case, and the other, to an application of the Atiyah-Bott fixed point formula to the Borel-Weil realization of the representation .

     

RETENTION AND PHOTOTOXICITY OF TETRA(4-SULFONATOPHENYL)PORPHINE IN CULTIVATED HUMAN CELLS. THE EFFECT OF FRACTIONATION OF LIGHT

Human cervix carcinoma cells of the line NHIK 3025 were incubated for 18 h with tetra(4-sulfonatophenyl)porphine (TPPS4) and further incubated for 1-29 h in sensitizer free medium before exposure to light. After 1 h in sensitizer free medium only a 20% further loss of TPPS4 was observed within the next 28 h. During the time in sensitizer free medium, each TPPS4 molecule became more efficient in sensitizing single cells to photoinactivation. This enhanced photosensitizing efficiency of TPPS4 correlated well with the enhanced fluorescence yield of TPPS4. In some experiments the cells were exposed to a light dose inactivating 10% of the cells after incubation for 1 h in sensitizer free medium and a second graded light dose given 4-28 h later. Exposure of the cells to the first light dose led to loss of 60% of TPPS4 from the cells. Despite the significant loss of sensitizer from the cells the fluorescence yield of TPPS4 from each cell was found to increase (e.g. by 100% 4 h after light exposure). The enhanced fluorescence yield of cell bound TPPS4 was followed by a 1.6-2.5-fold increase in sensitivity of each cell to second light dose. Thus, a small light dose increased the photosensitivity of TPPS4-loaded NHIK 3025 cells for several hours after the first light exposure. The advantageous effect of light fractionation was reduced by a significantly enhanced loss of sensitizer induced by the first light exposure. The optimal time between the two fractions of light seems to be 30-90 min.     

Resorcarenes in the boat conformation as building blocks for hydrogen-bonded assemblies including two ammonium cations

Crystal structures are reported for various co-crystals of rccc-resorcarenes with triethylammonium chloride. Usually, two molecules of a C2v-symmetric tetraester 2 in the boat conformation are linked through four hydrogen-bonded chloride anions to give dimeric assemblies. Two of the chloride anions may be replaced by four hydrogen-bonded ethanol molecules in an otherwise similar structure. These assemblies, which consist of six or eight components, posses voluminous, negatively charged chambers in which two triethylammionium cations, 3+, are included as guests by strong electrostatic and hydrogen-bonding interactions. The host-guest N-H...Cl hydrogen bonds were clearly detected at 173 K. These are the first examples of hydrogen-bonded, solid-state capsules trapping two ions of the same charge in close proximity. In the 1:2 complex with 3+ Cl-, the molecule of the parent resorcarene 1 also adopts a boat conformation whose cavity is considerably extended by four hydrogen-bonded chloride anions. The pocket formed in this way again includes two 3+ ions as a result of electrostatic and hydrogen bonding host-guest interactions. All these structures show that the boat conformers of resorcarenes can be used as a novel motif for the construction of hydrogen-bonded assemblies capable of molecular inclusion and encapsulation.     

The effect of pretreatment of calcite dispersions with anionic sodium polyacrylate on their flocculation behavior induced by cationic starch

The flocculation performance of cationic starches on calcite pretreated with anionic sodium polyacrylate (NaPA) was investigated by measuring the mean particle size and the dynamic mobility of the calcite dispersions. Cationic starches of different molecular weight and degree of substitution were used. By varying the amount of anionic sodium polyacrylate, which has a strong affinity to the calcium carbonate surface, one is able to anionically modify the particles and reverse the charge character of the originally cationic calcium carbonate. By such modification of the charge character of the calcium carbonate dispersion, it is possible to approach the mechanisms of flocculation caused by cationic macromolecules like starch. The importance of different mechanisms of flocculation, such as bridging, charge neutralization, and flocculation induced by polyelectrolyte complexes (PEC), was further investigated in this work. It was found that when the NaPA is completely absorbed at the calcite surfaces the mechanism of the flocculation induced by the starch is mainly bridging flocculation. Excess NaPA in the calcium carbonate dispersion will result in polyelectrolyte complexes formed between the non-absorbed NaPA and the oppositely charged starch polymers. These complexes will in most cases strongly enhance the flocculation due to mainly charge neutralization. Depending on the ratio of non-absorbed NaPA and the starch in the aqueous phase, the calcite dispersion is either re-stabilized or more strongly flocculated due to the formed polyelectrolyte complexes. Both the mobility and the particle size measurements support the mechanisms described. It was further demonstrated that the molecular weight and degree of substitution of the starches might be adjusted to control the flocculation behavior.