On the Stable Morse number of a Closed Manifold

This paper provides examples of closed manifolds having a Morsenumber different from the stable Morse number. 2000 MathematicsSubject Classification 57Q10, 20F05.     

Catalytic determination of Pb(II) in the presence of Cu(II)

A kinetic method is presented to determine micro-molar amounts of Pb(II) from various river and wastewater samples, in the presence of trace copper. The procedure is based on the catalytic effect of both species on the oxidation of mercaptosuccinic acid by chromate in acidic media. The extent of the reaction is followed spectrophotometrically at 420 nm and pseudo-first-order rate coefficients of the rate-determining step are determined as a function of catalyst concentrations. The optimum operating conditions (ionic strength, temperature, and concentration of reagents) regarding sensitivity towards lead were established. Interference by several ionic species has been studied. The effect of Fe(III), the only severe interferent, is suppressed by complexation with 1,10-phenantroline. The bi-component calibration model employs an artificial neural network to compute the Pb(II) concentration from a k(obsd) value and the a priori-known Cu(II) concentration of the sample. Working concentration ranges are 20-2160 micro g L(-1) for Pb(II) and 80-650 micro g L(-1) for Cu(II), respectively. Detection limits are 20 micro g L(-1) Pb(II) and 80 micro g L(-1) Cu(II), respectively. The relative standard deviations (3 measurements) for four different testing points are lower than 2.5%. The method was applied to samples of river and wastewater of the mining region of Baia-Mare, Northern Romania. The results were compared to those obtained by an officially standardized AAS method. Good agreement was achieved. The method is inexpensive, fairly rapid, and sensitive. Its working range covers the exact range of concentrations usually encountered in the mentioned geographic area.     

Kinetic catalytic determination of trace Cu(II) in water samples with the thioglycolic/thiolactic acid–chromate reaction

The use of two novel similar indicator reactions as applied to the kinetic determination of Cu(II) in water is investigated. The methods rely on the catalytic effect of the analyte on the oxidation of thioglycolic (TGA) and thiolactic (TLA) acids by chromate in acidic media. The extent of the reactions was followed spectrophotometrically at 345 nm. Pseudo-first-order rate coefficients, k_obsd, were determined as a function of catalyst concentration. Interference of Fe(III) and Pb(II) was suppressed by complexation with pyrophosphate. For the reaction of TGA, a linear regression for k_obsd versus [Cu(II)] was obtained for the entire concentration range considered. Although the plot corresponding to TLA oxidation exhibits a sharp change of slope at approximately 1.8×10^–5 M Cu(II), it can still be described effectively by two linear regressions with different slopes. The reaction of TGA is more sensitive than that of TLA at low Cu(II) concentration. The opposite is true for higher catalyst contents. The detection limits were 65 gL^–1 for TGA and of 80 gL^–1 for TLA oxidation, respectively. The relative standard deviations, of 0.4% for TGA and 1.1% for TLA oxidation, respectively, were obtained for five replicate runs at 1000 g L^–1. Samples of river and wastewater from the mining region of Baia-Mare, Northern Romania were analyzed using the more sensitive reaction of thioglycolic acid. Results were compared to those obtained by the officially standardized methods. Good agreement was obtained, even for an untreated sample. Measurements did not require prior separation of interfering species.     

Electrochemistry and electrogenerated chemiluminescence of a thin solid film of a hydrophobic tris(bipyridine) Ru(II) derivative in contact with an aqueous solution

The present study shows the electrochemistry, electrogenerated chemiluminescence and solid-state electroluminescence of [Ru(bpy)₂(4,4-(CH₃(CH₂)₁₂COO)bpy)](ClO₄)₂ as thin film deposited onto ITO. Cyclic voltammetry in aqueous solution of the Ru-LC film shows two reversible waves with peak potentials at about 1.27 V and –0.97 V. The apparent diffusion coefficient of the slowest species was found to be 4–6×10^–10 cm²/s, with a concentration of active sites of about 0.4–0.5 M.Relatively strong ECL was observed during both oxidation and reduction, in both potential scans and potential step experiments. The reduced species appears to be much less stable than the oxidized one, as already known for other tris(bipyridine) Ru(II) derivatives in aqueous media.Two-electrode solid-state devices prepared by Ga-In printing on the tops of Ru-LC films are similar to the Ru(bpy)₃ ones. The currents that flow through these devices are however about three orders of magnitude smaller than those for Ru(bpy)₃ devices as a result of their low electron and hole mobilities.Dedicated to Zbigniew Galus on the occasion of his 70th birthday.     

Non-negative hereditary polynomials in a free *−algebra

We prove a non-negative-stellensatz and a null-stellensatz for a class of polynomials called hereditary polynomials in a free *-algebra.Partially supported by NSF, DARPA and Ford Motor Co.Partially supported by NSF grant DMS-0140112Partially supported by NSF grant DMS-0100367     

Lamb waves propagation in elastic plane layers with a joint strip

The Lamb waves are used for the ultrasonic characterization of welds because of their relative long-range propagation. In this paper, a simplified model of a weld-strip between two identical semi-infinite elastic layers is investigated. The reflected and transmitted ultrasonic fields are expressed by modal series whose coefficients are obtained by application of orthogonality relation. Comparisons with solutions obtained by finite elements wave propagation simulations are made. The energy balance between the incident and the scattered waves is also used to verify the accuracy of the obtained modal amplitudes.     

Microcavity confinement based on an anomalous zero group-velocity waveguide mode

We propose and demonstrate a mechanism for small-modal-volume high-Q cavities based on an anomalous uniform waveguide mode that has zero group velocity at a nonzero wave vector. In a short piece of a uniform waveguide with a specially designed cross section, light is confined longitudinally by small group-velocity propagation and transversely by a reflective cladding. The quality factor Q is greatly enhanced by the small group velocity for a set of cavity lengths that are separated by approximately pi/k0, where k0 is the longitudinal wave vector for which the group velocity is zero.     

Surface-plasmon-assisted guiding of broadband slow and subwavelength light in air

A class of axially uniform waveguides is introduced, employing a new mechanism to guide light inside a low-index dielectric material without the use of photonic band gap, and simultaneously exhibiting subwavelength modal size and very slow group velocity over an unusually large frequency bandwidth. Their basis is the presence of plasmonic modes on the interfaces between dielectric regions and the flat unpatterned surface of a bulk metallic substrate. These novel waveguides allow for easy broadband coupling and exhibit absorption losses limited only by the intrinsic loss of the metal.     

On the rate of convergence of sequential quadratic programming with nondifferentiable exact penalty function in the presence of constraint degeneracy

We analyze the convergence of a sequential quadratic programming (SQP) method for nonlinear programming for the case in which the Jacobian of the active constraints is rank deficient at the solution and/or strict complementarity does not hold for some or any feasible Lagrange multipliers. We use a nondifferentiable exact penalty function, and we prove that the sequence generated by an SQP using a line search is locally R-linearly convergent if the matrix of the quadratic program is positive definite and constant over iterations, provided that the Mangasarian-Fromovitz constraint qualification and some second-order sufficiency conditions hold. Received: April 28, 1998 / Accepted: June 28, 2001?Published online April 12, 2002