Isometric Equivalence of Integration Operators

We are interested in the isometric equivalence problem for the Cesàro operator C(f) (z) = \frac1z ò₀^zf(x) \frac11-xd x{C(f) (z) =\frac{1}{z} \int_{0}^{z}f(\xi) \frac{1}{1-\xi}d \xi} and an operator T_g(f)(z)=\frac1zò₀^zf(x) g^￠(x) d x{T_{g}(f)(z)=\frac{1}{z}\int_{0}^{z}f(\xi) g^{\prime}(\xi) d \xi}, where g is an analytic function on the disc, on the Hardy and Bergman spaces. Then we generalize this to the isometric equivalence problem of two operators T_g1{T_{g_{1}}} and T_g2{T_{g_{2}}} on the Hardy space and Bergman space. We show that the operators T_g1{T_{g_{1}}} and T_g2{T_{g_{2}}} satisfy T_g1U₁=U₂T_g2{T_{g_{1}}U_{1}=U_{2}T_{g_{2}}} on H ^p , 1 ≤ p < ∞, p ≠ 2 if and only if g₂(z) = lg₁(e^iqz){g_{2}(z) =\lambda g_{1}(e^{i\theta}z) }, where λ is a modulus one constant and U _i , i = 1, 2 are surjective isometries of the Hardy Space. This is analogous to the Campbell-Wright result on isometrically equivalence of composition operators on the Hardy space.     

Simultaneous determination of tetrathiomolybdates and molybdates in spiked blood plasma by differential pulse voltammetry and their speciation

A selective, sensitive and reliable voltam- metric method for the simultaneous determination of MoS^2-₄ and MoO^2-₄ has been developed. The reduction of HgMoS₄ at –0.43 V and the reduction of Mo as complex of MoO₂-oxine₂ at –0.63 V in acetate buffer at pH 4.9 are utilized for the simultaneous determination by differential pulse cathodic stripping voltametry (DPCSV). Cadmium and lead form complexes with MoS^2-₄, but do not interfere with the determination. The limit of detection is 0.59 g/l Mo for MoS^2-₄ and 1.8 g/l Mo for MoO^2-₄. The R.S.D at a concentration level of 20 g/l is 4.7% for MoO^2-₄ and 3.6% for MoS^2-₄. The method is applied to spiked blood plasma samples for the determination of free tetrathiomolybdates and molybdates. Additionally, labile tetrathiomolybdates and molybdates can be determined in spiked blood plasma after treatment of the sample with 0.15 mol/lKCN and ultrafiltration.     

Simultaneous voltammetric determination of molybdenum and copper in biological samples

 A selective, sensitive and reliable voltammetric method for the simultaneous determination of Cu and Mo is developed. Both metals form complexes with 8-hydroxyquinoline (oxine). Mo gives two reduction peaks with oxine in acidic chloride media at −0.52 V and −0.58 V, while copper exhibits only one at −0.14 V. Common heavy metals do not interfere at all. The limit of detection is 0.29 ng/ml for Mo and 0.14 ng/ml for Cu after preconcentration on the hanging mercury drop electrode for 30 s at −0.2 V. The R.S.D. at a concentration level of 10 ng/ml is 3.8% for Cu and 5.3% for Mo. The method is applied to different biological samples. Received: 15 January 1996/Revised: 11 April 1996/Accepted: 16 April 1996     

Semigroups of Composition Operators on the Dirichlet Space

We show that semigroups of composition operators are strongly continuous on the Dirichlet space. The infinitesimal generator is identified and we give some spectral properties.     

Atomic absorption spectroscopic determination of molybdenum in aqueous tetrathiomolybdate solutions

The flame atomic absorption spectroscopic determination of molybdenum, in aqueous solutions of tetrathiomolybdate (MoS ₄ ^2– , TTM) and paramolybdate species (Mo₇O ₂₄ ^2– , PM) has been investigated. A serious signal decrease occurred, if molybdenum has been present as tetrathiomolybdate species, and the sensitivity loss has been 85%. To improve the sensitivity, the solutions of TTM have been digested by wet-acid treatment, and made 0.14 mol·l^–1 ammonia. Finally, Mo has been determined by AAS using a nitrous oxide-acetylene flame. The range of the calibration was 0–100 mg·l^–1 and the relative standard deviation of the slope was less than 1%.Dedicated to Professor Dr. Dieter Klockow on the occasion of his 60th birthday     

Enhancement of color purity in blue light emitting poly(fluorene)s and poly(p‐phenylene)s with 2,6‐distyrylpyridine kinked segments along the backbone

2,6‐bis(4‐Distyrylpyridine) ( 1 ) was synthesized by the condensation of 2,6‐dimethylpyridine with 4‐bromobenzaldehyde. Two new series of soluble random or alternating polyfluorenes ( PF‐Py ) and poly‐p‐phenylenes ( PP‐Py ) with various compositions were prepared by Suzuki coupling utilizing 1 as a comonomer. These polymers showed optical band gaps of 3.00–3.07 eV and photoluminescence (PL) quantum yields in solution of 0.37–0.91 for PF‐Py and 0.29–0.38 for PP‐Py . Polymers PF‐Py emitted blue light with PL maximum at 410–424 nm in solution and 406–428 nm in thin films that was red shifted with increasing distyrylpyridine content. Polymers PP‐Py behaved as blue emitters both in solution and in solid state, with PL maximum at 416–436 nm. The optical properties of these polymers could be tuned by the reversible protonation–deprotonation process of the pyridine ring. The emitted color of the polymers in solution and thin film could be changed continuously between blue and green (PL maximum up to about 520 nm) by exposing the polymers to the acid or base environment. Thin films of PF‐Py displayed excellent color stability with a small red shift of 10 nm but without additional emission band in the long wave region of the spectrum, even after being annealed at high temperature for a long time. © 2005 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 43: 4486–4495, 2005