Vector-valued Lg-splines I. Interpolating splines

The theory of Lg-splines developed by Jerome and Schumaker is extended to the vector-valued (multivariate) case. The extension is described in the frame-work of a reproducing-kernel Hilbert space which among other things allows the establishment of a congruent least-squares estimation problem for a vectorvalued lumped random process. The results include a dynamic recursive algorithm for vector-valued Lg-splines with EHB data and a useful structural characterization theorem for such splines. Some results on computable approximation error bounds are also included.     

Investigation of the quantitative properties of the quadrupole orthogonal acceleration time-of-flight mass spectrometer with electrospray ionisation using 3,4-methylenedioxymethamphetamine

This paper describes the investigation of the potential of a quadrupole orthogonal acceleration time-of-flight mass spectrometer (Q-TOF) equipped with an atmospheric pressure ionisation interface for quantitative measurements of small molecules separated by reversed phase liquid chromatography. To this end, the detection limits and linear dynamic range in particular were studied in an LC/MS/MS experiment using 3,4-methylenedioxymethamphetamine standards and 3,4-methylenedioxyethylamphetamine for internal standardisation. In a second phase, the experiment was repeated with real biological extracts (whole blood, serum, and vitreous humour). A calibration for 3,4-methylenedioxymethamphetamine and its metabolite 3,4-methylenedioxyamphetamine was prepared in each of these matrices again using 3,4-methylenedioxyethylamphetamine as internal standard. The resulting quantitative data were compared with those obtained by liquid chromatography with fluorescence detection for the same extracts. The Q-TOF results revealed excellent sensitivity and a linear dynamic range of nearly four decades (2-10 000 pg on-column, r(2) = 0.9998, 1/x weighting). Furthermore, all the calibration curves prepared in biological material were superimposable, LC/MS/MS and LC-fluorescence, and the quantitative results for actual samples compared very favourably. It was concluded that the Q-TOF achieves a linear dynamic range for quantitative LC/MS/MS work exceeding that of fluorescence detection and at much better absolute sensitivity. Copyright 1999 John Wiley & Sons, Ltd.     

Dynamically stabilized growth of polar oxides: the case of MgO(111)

By using MgO(111) as a model system for polar oxide film growth, we show by first-principles calculations that H acts as a surfactant, i.e., the H changes its position and bonding during the growth process, remaining in the surface region. Continuous presence of H during the growth of MgO(111) film efficiently removes the microscopic dipole moment, thus enabling the growth of perfect fcc-ordered MgO(111) films. These theoretical predictions are confirmed experimentally by molecular beam epitaxy single crystal growth of MgO(111) on SiC(0001).     

Optical fluid and biomolecule transport with thermal fields

A long standing goal is the direct optical control of biomolecules and water for applications ranging from microfluidics over biomolecule detection to non-equilibrium biophysics. Thermal forces originating from optically applied, dynamic microscale temperature gradients have shown to possess great potential to reach this goal. It was demonstrated that laser heating by a few Kelvin can generate and guide water flow on the micrometre scale in bulk fluid, gel matrices or ice without requiring any lithographic structuring. Biomolecules on the other hand can be transported by thermal gradients, a mechanism termed thermophoresis, thermal diffusion or Soret effect. This molecule transport is the subject of current research, however it can be used to both characterize biomolecules and to record binding curves of important biological binding reactions, even in their native matrix of blood serum. Interestingly, thermophoresis can be easily combined with the optothermal fluid control. As a result, molecule traps can be created in a variety of geometries, enabling the trapping of small biomolecules, like for example very short DNA molecules. The combination with DNA replication from thermal convection allows us to approach molecular evolution with concurrent replication and selection processes inside a single chamber: replication is driven by thermal convection and selection by the concurrent accumulation of the DNA molecules. From the short but intense history of applying thermal fields to control fluid flow and biological molecules, we infer that many unexpected and highly synergistic effects and applications are likely to be explored in the future.     

Modulating the frontier orbitals of L(X)Ga-substituted diphosphenes [L(X)GaP]2 (X = Cl,Br) and their facile oxidation to radical cations

Modulating the electronic structures of main group element compounds is crucial to control their chemical reactivity. Herein we report on the synthesis, frontier orbital modulation, and one-electron oxidation of two L(X)Ga-substituted diphosphenes [L(X)GaP]₂ (X = Cl 2a, Br 2b; L = HC[C(Me)N(Ar)]₂, Ar = 2,6-i-Pr₂C₆H₃). Photolysis of L(Cl)GaPCO 1 gave [L(Cl)GaP]₂2a, which reacted with Me₃SiBr with halide exchange to [L(Br)GaP]₂2b. Reactions with ^MeNHC (^MeNHC = 1,3,4,5-tetramethylimidazol-2-ylidene) gave the corresponding carbene-coordinated complexes L(X)GaPP(^MeNHC)Ga(X)L (X = Cl 3a, Br 3b). DFT calculations revealed that the carbene coordination modulates the frontier orbitals (i.e. HOMO/LUMO) of diphosphenes 2a and 2b, thereby affecting the reactivity of 3a and 3b. In marked contrast to diphosphenes 2a and 2b, the cyclic voltammograms (CVs) of the carbene-coordinated complexes each show one reversible redox event at E_1/2 = −0.65 V (3a) and −0.36 V (3b), indicating their one-electron oxidation to the corresponding radical cations as was confirmed by reactions of 3a and 3b with the [FeCp₂][B(C₆F₅)₄], yielding the radical cations [L(X)GaPP(^MeNHC)Ga(X)L]B(C₆F₅)₄ (X = Cl 4a, Br 4b). The unpaired spin in 4a (79%) and 4b (80%) is mainly located at the carbene-uncoordinated phosphorus atoms as was revealed by DFT calculations and furthermore experimentally proven in reactions with ⁿBu₃SnH, yielding the diphosphane cations [L(X)GaPHP(^MeNHC)Ga(X)L]B(C₆F₅)₄ (X = Cl 5a, Br 5b). Compounds 2–5 were fully characterized by NMR and IR spectroscopy as well as by single crystal X-ray diffraction (sc-XRD), and compounds 4a and 4b were further studied by EPR spectroscopy, while their bonding nature was investigated by DFT calculations.

Carbene-coordination allowed for one-electron oxidation of diphosphenes [LGa(X)P]₂ to P-centered radicals cations 4a (X = Cl) and 4b (X = Br), in which the unpaired spin mainly reside at the carbene uncoordinated P-atoms.     

ChemInform Abstract: Glass Formation in the System BaS-Ga2S3-GeS2 and the Structure of Ba2. 7Ga5.4Ge3.6S18.

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