Extreme value distribution for normalized sums from stationary Gaussian sequences

Let {X_i, i?0} be a sequence of independent identically distributed random variables with finite absolute third moment. Then Darling and Erdös have shown that

for -∞<t<∞ where and $\text{X}{}_{\mathrm{n}}\text{= (2 ln ln n)}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$. The result is extended to dependent sequences but assuming that {X_i} is a standard stationary Gaussian sequence with covariance function {r_i}. When {X_i} is moderately dependent (e.g. when $\text{v(∑}{}^{\mathrm{n}}{}_{\mathrm{i=1}}\text{X}{}_{\mathrm{i}}\text{) ? n}{}_{\mathrm{a}}\text{, 0 < a < 2)}$ we get

where H_a is a constant. In the strongly dependent case (e.g. when $\text{v(∑}{}^{\mathrm{n}}{}_{\mathrm{i=1}}\text{X}{}_{\mathrm{i}}\text{) ? n}{}^2\text{r(n))}$ we get

for-∞<t<∞.     

Elektrometrische Untersuchungen von Uranylarseniten

Zusammenfassung Mit Hilfe der pH- und konduktometrischen Titrationen wurde die Stöchiometrie der Verbindungen untersucht, die bei der Reaktion von Uranylnitrat mit Alkali-Ortho-, Pyro- und Metaarseniten entstehen. Der Verlauf der Titrationskurven zeigt klar die Bildung der Verbindungen 3 UO₂O · As₂O₃, 2 UO₂O · As₂O₃ und UO₂O · As₂O₃ in den pH-Bereichen 7,0–9,9 bzw. 6,0–7,5 bzw. 5,0–6,8. Der Anteil von Uranyl in den Alkaliarseniten wächst mit wachsender Konzentration von Na₂O. Die Bildung der Uranylarsenite ist also eine Funktion der H⁺-Ionenkonzentration. Wir fanden, daß die Ausfällung dieser Verbindungen fast quantitativ ist.

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The stoichiometry of the compounds formed by the interaction of uranyl nitrate and different alkali arsenites (ortho-, pyro-, and meta-) have been investigated by means of pH and conductometric titrations. The breaks and inflections in titration curves provide cogent evidence for the formation of 3 UO₂O · As₂O₃, 2 UO₂O · As₂O₃ and UO₂O · As₂O₃ in pH ranges 7.0–9.9, 6.0–7.5 and 5.0–6.8 respectively. The proportion of uranyl increases with the increase in the concentration of Na₂O molecules in alkali arsenites. The formation of uranyl arsenites is thus a function of H⁺ ion concentration. The precipitation of these compounds has been found to be almost quantitative.

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Mit 4 Abbildungen     

Reactions of hydroxyl radical (·OH) and oxide radical anion (O·−) with 2-aminopurine in aqueous medium

Pulse radiolysis has been used to investigate the reaction of hydroxyl radical (^·OH) and oxide radical anion (O^·−) with 2-aminopurine (2AP), a fluorescent analogue of adenine, in aqueous medium. The second-order rate constant for the reaction of ^·OH with 2AP was determined to be 3 × 10⁹ dm³ mol⁻¹s⁻¹ and for the reaction of O^·− it was 7.1 × 10⁸ dm³ mol⁻¹s⁻¹. The transient absorption spectrum obtained in the reaction of ^·OH at pH 7 has absorption maxima at 370 and 470 nm. The spectrum undergoes a time-dependent transformation at higher time-scale. The intermediate species was found to react with N,N,N′,N′-tetramethyl-p-phenylenediamine (TMPD). The yield of TMPD^·+ was calculated in terms of G(TMPD^·+) to be 3.3 × 10⁻⁷ mol J⁻¹ at pH 7. The ^·OH reactions were also carried out at pH 10 and the transient absorption spectra have λ _max at 400 and 480 nm. The transient spectra obtained in the reaction of O^·− at pH ≈14 have maxima at 400 and 480 nm. The transient intermediate species at pH 7 are assigned to the formation of 2AP-4-OH^· (54%), 2AP-5-OH^· (7%) and 2AP-8-OH^· (39%) based on the spectral evidence and TMPD^·+ build-up. Both 2AP-4-OH^· and 2AP-5-OH^· undergo OH⁻ elimination to form a radical cation. At higher pH (pH 10), the dehydration reaction of these OH-adducts leads to a N-centered radical (2AP-N(9)^·, 71%). Formation of 2AP-8-OH^· (29%) is also proposed at this pH. In the reaction of O^·− with 2AP, it is proposed that a similar nitrogen centered 2AP-N(9)^· radical is formed by an electron-transfer reaction at N(9).     

Transition metal chemistry of oxime containing ligands,VII

Complexes of pyridine-2-aldoxime (Hpox) with iron(II) and chromium(III) of type, [Fe(Hpox)₂ X ₂] (X=Cl, Br, I or NCS); [Cr(Hpox)₃]Cl₃·3 H₂O; [Cr(Hpox)₂ X ₂]ClO₄ (X=F, Cl or Br) and [Cr(Hpox)₂(H₂O)₂]Br₃·H₂O were prepared and characterized by analytical X-ray powder diffraction, magnetism, vibrational (conventional and far-infrared) and electronic spectroscopy techniques. X-ray and electronic spectral data indicate that all the complexes except [Cr(Hpox)₃]Cl₃·3 H₂O havetrans-pseudo-octahedral microsymmetry around the metal ion. Infrared spectral data indicate that the ligand, Hpox, behaves like a neutral ligand and coordinates to the metal ion through pyridine nitrogen atom and oxime nitrogen atom in all these complexes. The magnetic susceptibilities of chromium(III) complexes, measured over a temperature range 300–78 K, are independent of temperature whereas the magnetic moments of iron(II) complexes over a temperature range 300–20 K are dependent of temperature. The observed temperature dependence of magnetic moments of iron(II) complexes was used to evaluate the magnitude of orbital reduction factor,k, the low-symmetry distortion parameter, , and the extent of reduction in spin-orbital coupling, . In all these iron(II) complexes the magnetic results indicate the presence of an orbitally non-degenerate,⁵B_2g, ground state. Magnetically unperturbed and perturbedMössbauer spectra of iron(II) complexes at various temperatures have also been reported. Magnetically perturbedMössbauer spectra of iron(II) complexes at 4.2 K in an axial field of 60kGauss indicate that the principal component of electric field gradient tensor is positive and consistent with⁵B_2g ground electronic state in a tetragonal (D _4h) local site symmetry.

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Übergangsmetallkomplexe mit Oxim-enthaltenden Liganden, VII. Elektronische und strukturelle Eigenschaften vonFe(II)-undCr(III)-Komplexen mit Pyridin-2-aldoxim

Zusammenfassung Es wurden Komplexe von Pyridin-2-aldoxim (Hpox) mit Fe(II) und Cr(III) vom Typ [Fe(Hpox)₂ X ₂] (X=Cl, Br, I, NCS), [Cr(Hpox)₃]Cl₃·3 H₂O, [Cr(Hpox)₂ X ₂]ClO₄ (X=F, Cl, Br) und [Cr(Hpox)₂(H₂O)₂]Br₃·H₂O hergestellt. Charakterisierung und Diskussion von Geometrie und Bindungsverhalten in den Komplexen erfolgte auf Grund von analytischen Daten, Röntgen-Pulveraufnahmen, Elektronenanregungsspektroskopie, Infrarotspektroskopie, magnetischen Messungen undMössbauer-Spektroskopie.

     

PVC-based dicyclohexano-18-crown-6 sensor for La(III) ions

A new ion-selective electrode (ISE) based on dicyclohexano-18-crown-6 (DC18C6) as a neutral carrier is developed for lanthanum(III) ions. The electrode comprises of dicyclohexano-18-crown-6 (6%), PVC (33%), and ortho-nitrophenyl octyl ether (o-NPOE) (61%). The electrode shows a linear dynamic response in the concentration range of 10⁻⁶ to 10⁻¹ M with a Nernstian slope of 19 mV per decade and a detection limit as 5×10⁻⁷ M. It has a response time of <30 s and can be used for at least 5 months without any significant divergence in potentials. The selectivity coefficients for mono-, di-, and trivalent cations indicate good selectivity for La(III) ions over a large number of interfering cations. The sensor has been used as an indicator electrode in the potentiometric titrations of La(III) with EDTA. The membrane is successfully applied in partially non-aqueous medium. It can be used in the pH range 4-9.     

Spectral,kinetics, and redox properties of the transients formed on one‐electron oxidation of 4,4′‐thiodiphenol: A pulse radiolysis study

The transient absorption bands (λ_max = 330, 525 nm, k_f = 5 × 10⁹ dm³ mol⁻¹ s⁻¹) obtained on pulse radiolysis of N₂O‐saturated neutral aqueous solution of 4,4′‐thiodiphenol (TDPH) are due to the reaction of TDPH with ^·OH radicals and are assigned to phenoxyl radical formed on fast deprotonation of the solute radical cation. The reaction of specific one‐electron oxidants (Cl₂^·−, Br₂^·−, N₃^·, TI²⁺, CCl₃OO^·) with TDPH also produced similar transient absorption bands. The phenoxyl radicals are also produced on pulse radiolysis of N₂‐saturated solution of TDPH in 1,2‐dichloroethane. The nature of transient absorption spectrum obtained on reaction of ^·OH radicals with TDPH is not affected in acidic solutions, showing that OH‐adduct is not formed in neutral solutions. The oxidation potential for the formation of phenoxyl radical is determined to be 0.98 V. © 1999 John Wiley & Sons, Inc. Int J Chem Kinet 31: 603–610, 1999     

Finite element study of vortex‐induced cross‐flow and in‐line oscillations of a circular cylinder at low Reynolds numbers

Vortex‐induced vibrations of a circular cylinder placed in a uniform flow at Reynolds number 325 are investigated using a stabilized space–time finite element formulation. The Navier–Stokes equations for incompressible fluid flow are solved for a two‐dimensional case along with the equations of motion of the cylinder that is mounted on lightly damped spring supports. The cylinder is allowed to vibrate, both in the in‐line and in the cross‐flow directions. Results of the computations are presented for various values of the structural frequency of the oscillator, including those that are sub and superharmonics of the vortex‐shedding frequency for a stationary cylinder. In most of the cases, the trajectory of the cylinder corresponds to a Lissajou figure of 8. Lock‐in is observed for a range of values of the structural frequency. Over a certain range of structural frequency (F_s), the vortex‐shedding frequency of the oscillating cylinder does not match F_s exactly; there is a slight detuning. This phenomenon is referred to as soft‐lock‐in. Computations show that this detuning disappears when the mass of the cylinder is significantly larger than the mass of the surrounding fluid it displaces. A self‐limiting nature of the oscillator with respect to cross‐flow vibration amplitude is observed. It is believed that the detuning of the vortex‐shedding frequency from the structural frequency is a mechanism of the oscillator to self‐limit its vibration amplitude. The dependence of the unsteady solution on the spatial resolution of the finite element mesh is also investigated. Copyright © 1999 John Wiley & Sons, Ltd.     

Unsteady incompressible flows past two cylinders in tandem and staggered arrangements

A stabilized finite element formulation is employed to study incompressible flows past a pair of cylinders at Reynolds numbers 100 and 1000 in tandem and staggered arrangements. Computations are carried out for three sets of cylinder arrangements. In the first two cases the cylinders are arranged in tandem and the distance between their centres is 2·5 and 5·5 diameters. The third case involves the two cylinders in staggered arrangement. The distance between their centres along the flow direction is 5·5 diameters, while it is 0·7 diameter in the transverse direction. The results are compared with flows past a single cylinder at corresponding Reynolds numbers and with experimental observations by other researchers. It is observed that the qualitative nature of the flow depends strongly on the arrangement of cylinders and the Reynolds number. In all cases, when the flow becomes unsteady, the downstream cylinder, which lies in the wake of the upstream one, experiences very large unsteady forces that may lead to wake-induced flutter. The Strouhal number, based on the dominant frequency in the time history of the lift coefficient, for both cylinders attains the same value. In some cases, even though the near wake of the two cylinders shows temporal periodicity, the far wake does not. © 1997 John Wiley & Sons, Ltd.     

Effect of blockage on free vibration of a circular cylinder at low Re

The effect of the blockage on vortex‐induced vibrations of a circular cylinder of low non‐dimensional mass (m^*=10) in the laminar flow regime is investigated in detail. A stabilized space–time finite element formulation is utilized to solve the incompressible flow equations in primitive variables form in two dimensions. The transverse response of the cylinder is found to be hysteretic at both ends of synchronization/lock‐in region for 5% blockage. However, for the 1% blockage hysteresis occurs only at the higher Re end of synchronization/lock‐in region. Computations are carried out at other blockages to understand its effect on the hysteretic behavior. The hysteresis loop at the lower Re end of the synchronization decreases with decrease in blockage and is completely eliminated for blockage of 2.5% and less. On the other hand, hysteresis persists for all values of blockage at the higher Re end of synchronization/lock‐in. Although the peak transverse oscillation amplitude is found to be same for all blockage (～0.6D), the peak value of the aerodynamic coefficients vary significantly with blockage. The r.m.s. values show lesser variation with blockage. The effect of streamwise extent of computational domain on hysteretic behavior is also studied. The phase between the lift force and transverse displacement shows a jump of almost 180° at, approximately, the middle of the synchronization region. This jump is not hysteretic and is independent of blockage. Copyright © 2008 John Wiley & Sons, Ltd.