On the Distribution of the Extremes of Unequally Correlated Normal Variables with Applications to Antedependent Cluster Data

Based on a small correlations approach, this paper deals with the probability distributions of the order statistics under a general Gaussian model with unequal (positive or negative) correlations. Illustrations are given for the cluster data those follow suitable antedependence models.     

Solutions for a Cosmic String

For a conformally flat metric ds² = a²(η)(dη² – dx² – y² – dz²) Vilenkin obtained the equation $$\frac{\partial }{{\partial _{\eta } }}\left[ {\frac{{a^2 \left( {\eta } \right)\dot y}}{{\sqrt {1 + y'^2 - \dot y^2 } }}} \right] = \frac{\partial }{{\partial _x }}\left[ {\frac{{a^2 \left( {\eta } \right)\dot y'}}{{\sqrt {1 + y'^2 - \dot y^2 } }}} \right]$$ for a cosmic string and gave some particular solutionsboth for a = const and a const. The present workcompletely solves the equation for a = const and extendthe work of Vilenkin for a ≠ const.     

Observation of 3MC emission in a mixed 1,10-phenanthroline complex of ruthenium(II) having a RuIIN6 core at room temperature in solution

[Ru(1,10-phenanthroline)(2)(4,4,4',4'-tetramethyl-2,2'-bisoxazoline)](PF(6))(2).H(2)O (1) shows a (3)MC emission in CH(3)CN and CH(3)OH at room temperature around 590 nm with radiative lifetimes of 1.22 x 10(-4) and 1.40 x 10(-4) s, respectively. The X-ray crystal structure of 1 has been determined.     

A new coordination mode of the photometric reagent glyoxalbis(2-hydroxyanil) (H2gbha): bis-bidentate bridging by gbha2- in the redox series [(mu-gbha)[Ru(acac)2]2]n (n = -2, -1, 0, +1, +2), including a radical-bridged diruthenium(III) and a Ru(III)/Ru(IV) intermediate

The bis-bidentate bridging function of gbha2- with N,O-/N,O- coordination was observed for the first time in the complex (mu-gbha)[Ru(III)(acac)2]2 (1). Density functional theory calculations of 1 yield a triplet ground state with a large (deltaE > 6000 cm(-1)) singlet-triplet gap. Intermolecular antiferromagnetic coupling was observed (J approximately -5.3 cm(-1)) for the solid. Complex 1 undergoes two one-electron reduction and two one-electron oxidation steps; the five redox forms [(mu-gbha)[Ru(acac)2]2]n (n = -2, -1, 0, +1, +2) were characterized by UV-vis-NIR spectroelectrochemistry (NIR = near infrared). The paramagnetic intermediates were also investigated by electron paramagnetic resonance (EPR) spectroscopy. The monoanion with a comproportionation constant K(c) of 2.7 x 10(8) does not exhibit an NIR band for a Ru(III)/Ru(II) mixed-valent situation; it is best described as a 1,4-diazabutadiene radical anion containing ligand gbha*3-, which binds two ruthenium(III) centers. A Ru(III)-type EPR spectrum with g1 = 2.27, g2 = 2.21, and g3 = 1.73 is observed as a result of antiferromagnetic coupling between one Ru(III) and the ligand radical. The EPR-active monocation (K(c) = 1.7 x 10(6)) exhibits a broad (deltanu(1/2) = 2600 cm(-1)) intervalence charge-transfer band at 1800 nm, indicating a valence-averaged (Ru3.5)2 formulation (class III) with a tendency toward class II (borderline situation).     

Spreading and recoil of a surfactant-containing water drop on glass-supported alcohol films

In this paper we report the experimental observation of spreading and recoil of surfactant-containing water drops on various alcohol films supported on glass slides. The time evolution of spreading and recoil behavior was recorded by placing a web camera above the drop. We observed that the drop spread the fastest on CH3OH, followed by C2H5OH, and the slowest on i-PrOH. On the other hand, the recoil behavior was just the opposite. The drop recoiled the slowest on CH3OH and fastest on i-PrOH, while it recoiled in an intermediate time on C2H5OH. In addition, concentration of surfactant in the drop played a prominent role in the spreading and recoil time of the drop, with higher surfactant concentration making the drop spread and recoil faster. The time evolution of spreading velocity of the drop on different alcohol films at various surfactant concentrations occurred with a Gaussian distribution and the peak velocity was reached earliest on CH3OH followed by C2H5OH, while on i-PrOH it took the longest time. The recoil behavior was similar. The variation of velocity as a function of radius exhibited oscillatory behavior, indicating the existence of an interfacial phenomenon. We also report the observation that spreading of the drop occurred without observable fingering instability. Further, we observed by Fourier transform infrared (FTIR) spectroscopic measurements that the drop had mixed with the alcohol films as it spread. Miscibility of the alcohol in the film with the drop, alcohol evaporation cooling-induced temperature gradient, and Marangoni effect probably play important roles in the spreading and recoil behavior of the drop.     

Identification of butyryl derivatives of cyclic nucleotides by positive ion fast atom bombardment mass spectrometry and mass-analysed ion kinetic energy spectrometry

The syntheses of the dibutyryl derivatives of the 3′,5′-cyclic monophosphates of adenosine, guanosine and cytidine are described. The fast atom bombardment mass spectra of these compounds are discussed, together with the mass-analysed ion kinetic energy spectra of their protonated molecular ions and of diagnostic fragments. A protocol for the identification of the derivatives is reported which includes criteria for confirming retention of the cyclic phosphodiester moiety, substitution of both heterocyclic base and ribose ring, and butyrylation of the 2′-O-position. The origins of significant fragments in the spectra are discussed.     

Position and contextuality in Bohm''s causal completion of quantum mechanics

We argue that, in Bohm's formulation, the assumption stipulating the position probability density to be ψ² is both necessary and sufficient for satisfying the requirement of “noncontextuality” (absence of any dependence on the specifics of the measurement procedure) of the observable probabilities at the ensemble level. The reasons as to why position needs to have a special status in a causal completion of quantum mechanics are also discussed.     

Precise frequency measurements of atomic transitions by use of a Rb-stabilized resonator

We demonstrate a technique for frequency measurements of atomic transitions with a precision of 30 kHz. The frequency is measured with a ring-cavity resonator whose length is calibrated against a reference laser locked to the D2 line of 87Rb, the frequency of which is known with 10-kHz accuracy. We have used this method to measure the hyperfine structure in the 5P(3/2) state of 85Rb. We obtain precise values for the hyperfine constants, A = 25.041(6) MHz and B = 26.013(25) MHz, and a value of 77.992(20) MHz for the isotope shift in the D2 line.