Ordering events in Minkowski space

Let p₁,…,p_k be k points (events) in (n+1)-dimensional Minkowski space . Using the theory of hyperplane arrangements and chromatic polynomials, we obtain information on the number of different orders in which the events can occur in different reference frames if the events are sufficiently generic. We consider the question of what sets of orderings of the points are possible and show a connection with sphere orders and the allowable sequences of Goodman and Pollack.     

Transport in weighted networks: partition into superhighways and roads

Transport in weighted networks is dominated by the minimum spanning tree (MST), the tree connecting all nodes with the minimum total weight. We find that the MST can be partitioned into two distinct components, having significantly different transport properties, characterized by centrality--the number of times a node (or link) is used by transport paths. One component, superhighways, is the infinite incipient percolation cluster, for which we find that nodes (or links) with high centrality dominate. For the other component, roads, which includes the remaining nodes, low centrality nodes dominate. We find also that the distribution of the centrality for the infinite incipient percolation cluster satisfies a power law, with an exponent smaller than that for the entire MST. The significance of this finding is that one can improve significantly the global transport by improving a tiny fraction of the network, the superhighways.     

Bipolar pulse conductivity measurements applied to ion-selective electrodes

Bipolar pulse conductivity (BICON) measurements were evaluated as a means of using calciumion-selective electrodes with an upoised reference electrode. The study shows a change in total cell conductivity with Ca²⁺ concentration at low concentrations in the absence of other electrolytes but no change in conductivity with Ca²⁺ concentration in the presence of 0.1 M KCl. The computed voltage at zero current varied with Ca²⁺ concentration but electroactive species interfered with the measurements. For the conditions used, it is concluded that there is no change in conductivity of the ion-selective membrane with Ca²⁺ concentration and that reliable quantitation of Ca²⁺ is not feasible.     

Nonstandard Fock spaces

A theory of nonstandard inner product spaces is developed using methods of nonstandard analysis. Various results concerning nonstandard operators and their spectra are proved. The theory is applied to construct nonstandard Fock spaces which extend the standard Fock spaces. Moreover, a rigorous framework for the field operators of quantum field theory is presented. The results are illustrated for the case of Klein-Gordon fields.     

Isotope effects on the picosecond time-resolved emission spectroscopy of tris(2,2'-bipyridine)ruthenium (II)

The excited-state properties of the transition metal complexes tris(2,2'-bipyridine) ruthenium(II) and tris(4,7-diphenyl-1,10-phenanthroline) ruthenium(II) are examined using picosecond time-resolved luminescence spectroscopy. For both complexes, direct observation of a short-lived high-energy emission with a lifetime of less than 4 ps is reported. Upon deuteriation of the complexes the lifetime of the high-energy emission shows a marked increase with a biexponential decay (20 and approximately 300 ps components). Examination by time-resolved excited-state resonance Raman shows that for the perprotio complexes features attributable to the 3MLCT excited state are formed within 4 ps, while for the perdeuterio a rise time of approximately 20 ps is observed in the 3MLCT features. The results indicate that the emission in both cases may be 1MLCT in origin and are discussed with respect to heterogeneous electron transfer.     

Metal chelates of ligands containing the ONS donor grouping,Part II. Metal chelates of schiff bases derived from β-diketones and α-N-Methyl-S-methyldithiocarbazate

Summary The Schiff bases RC(OH)=CHC(R)=NNMeC(S)SMe (R = Ph,p-MeC₆H₄, R = Me; R = R = Ph) have been prepared by condensation of -diketones with -N-methyl-S-methyldithiocarbazate. By the loss of a proton they act as singly negatively charged tridentate ligands with oxygen, nitrogen and sulphur donor atoms (ONS). Iron forms the high-spin complexes [Fe^III(ONS)₂][Fe^IIICl₄]. Copper(II), palladium(II), and platinum(II) yield the square-planar 1 : 1 complexes, M(ONS)CI (M = Cu, Pd, Pt) and Cu(ONS)NO₃. Cobalt(II) and nickel(II) form high-spin, six-coordinate 1 : 2 complexes, M(ONS)₂. For M = Ni and R = R = Ph, the complex is high-spin and octahedral, but when R = Ph orp-MeC₆ H₄ and R = Me, the complexes are diamagnetic and square-planar with nitrogen and sulphur (NS) coordinatio of the Schiff base, indicating that a change in the Rgroup can bring about a change in spin-state and stereochemistry of nickel.Part I: see ref. 1.