Derivation of O(3) Electrodynamics from the Einstein–Sachs Theory of General Relativity

General relativity is reduced to O(3) electrodynamics by consideration of the irreducible representations of the Einstein group and through a particular choice of basis. The photon is shown always to possess a scalar curvature R, and so the origin of quantization is found in general relativity.     

Knoevenagel kondensationen mit TiCl4/base-IV : Umsetzungen von aldehyden und ketonen mit phosphonoessigester und methylendiphosphonsäureestern

In the presence of titanium tetrachloride and an organic base in tetrahydrofurane, triethyl phosphonoacetic acid undergoes condensation with aliphatic and aromatic aldehydes and aromatic ketones to yield the corresponding triethyl alkylidene and arylidene phosphonoacetic acids respectively. Tetraalkyl methylenediphosphonates and aromatic or aliphatic α-branched aldehydes react under identical conditions in the same way. The largely unknown triethyl alkylidene and arylidene phosphonoacetic acids and the new tetraalkyl alkylidene and arylidene methanediphosphonic acids are easily hydrogenated either catalytically or by sodium borohydride in ethanol to give the corresponding saturated compounds in nearly quantitative yields.     

Establishing a chromium-reactor design for measuring δ2H values of solid polyhalogenated compounds using direct elemental analysis and stable isotope ratio mass spectrometry

²H/¹H isotope ratios of polyhalogenated compounds were determined by elemental analysis and isotope ratio mass spectrometry (EA-IRMS). Initial measurements with standard EA-IRMS equipment, which used high-temperature pyrolysis to convert the organic compounds into hydrogen, did not achieve significant signals for polychlorinated pesticides and related compounds, presumably due to the formation of HCl instead of hydrogen. To reverse this problematic reaction, a chromium reactor was incorporated into the element analyzer system, which scavenged Cl, forming chromium chloride and releasing hydrogen again in the form of H₂. The optimized system therefore allowed the δ²H values of polyhalogenated compounds to be determined. A quality assurance program was developed based on several parameters. (i) Each compound was analyzed using a sequence of five injections, where the first measurement was discarded. (ii) Recovery of H (when calculated relative to acetanilide) had to be >90% for all replicates in a sequence. (iii) All δ-values within a sequence had to vary by less than 10‰. (iv) Results had to be reproducible on another day with a different sample scheme. Once this reproducibility had been established, variabilities in the δ²H values of organohalogen standards were investigated using the technique. The highest δ²H value of +75‰ was found for o,p′-DDD, whereas the strongest depletion in deuterium was found for Melipax (–181‰). The most important results for comparable compounds were as follows. DDT-related compounds gave δ²H values of between +59 and +75‰ (technical DDT, o,p′- and p,p′-DDD) or in the range of approximately −1‰, indicative of the different sources/methods of producing this compound. Four HCH isomers from the same supplier showed relatively similar hydrogen isotope distributions, whereas two lindane (γ–HCH) standards from other sources had 39‰ less deuterium. This difference is likely due to different purification steps during the isolation of pure lindane from the technical HCH mixture. An even greater difference was observed between the δ²H values of Toxaphene (US product dating from 1978) and Melipax (product from the former East Germany, dating from 1979), which gave δ²H values of –101‰ and –181‰, respectively, meaning that both products were easily distinguished via δ²H-IRMS. Fractioning of hydrogen isotopes in the atmospheric water cycle was suggested as one reason for the different values. In this theory, the water (which had different δ²H values depending on where it was taken from) was incorporated during the biosynthesis of camphene, which is the natural product used to produce both products. These results indicate that hydrogen isotope-specific analysis can be a valuable tool for tracing the origins of a compound in certain cases.     

Detailed assignment of the magnetic circular dichroism and UV-vis spectra of five-coordinate high-spin ferric [Fe(TPP)(Cl)

High-spin (hs) ferric heme centers occur in the catalytic or redox cycles of many metalloproteins and exhibit very complicated magnetic circular dichroism (MCD) and UV-vis absorption spectra. Therefore, detailed assignments of the MCD spectra of these species are missing. In this study, the electronic spectra (MCD and UV-vis) of the five-coordinate hs ferric model complex [Fe(TPP)(Cl)] are analyzed and assigned for the first time. A correlated fit of the absorption and low-temperature MCD spectra of [Fe(TPP)(Cl)] lead to the identification of at least 20 different electronic transitions. The assignments of these spectra are based on the following: (a) variable temperature and variable field saturation data, (b) time-dependent density functional theory calculations, (c) MCD pseudo A-terms, and (d) correlation to resonance Raman (rRaman) data to validate the assignments. From these results, a number of puzzling questions about the electronic spectra of [Fe(TPP)(Cl)] are answered. The Soret band in [Fe(TPP)(Cl)] is split into three components because one of its components is mixed with the porphyrin A2u72-->Eg82/83 (pi-->pi*) transition. The broad, intense absorption feature at higher energy from the Soret band is due to one of the Soret components and a mixed sigma and pi chloro to iron CT transition. The high-temperature MCD data allow for the identification of the Q v band at 20 202 cm(-1), which corresponds to the C-term feature at 20 150 cm(-1). Q is not observed but can be localized by correlation to rRaman data published before. Finally, the low energy absorption band around 650 nm is assigned to two P-->Fe charge transfer transitions, one being the long sought after A1u(HOMO)-->d pi transition.     

Skewness Term-Structure Tests

In this paper, we conduct skewness term-structure tests to check whether the temporal structure of risk-neutral skewness is consistent with rational expectations. Because risk-neutral skewness is substantially mean reverting, skewness shocks should decay quickly and risk-neutral skewness of more distant option should display the rationally expected smoothing behaviour. Using an equilibrium asset and option-pricing model in a production economy under jump diffusion with stochastic jump intensity, we derive this elasticity analytically. In an empirical application of the model using more than 20 years of data on S&P500 index options, we find that this elasticity turns out to be different than suggested under rational expectations – smaller on the short end (underreaction) and larger on the long end (overreaction) of the ‘skewness curve’.     

FeIII(tmdta)]--twist-boat/half-chair conformer ratio reliably deduced from DFT-calculated Raman spectra

The equilibrium between the twist-boat (tb) and half-chair (hc) conformers of the central diamine chelate ring of [Fe(III)(tmdta)]- in solids and aqueous solution has been studied by Raman spectroscopy, supported by calculated Raman spectra using Density Functional Theory.     

A General Theory of Non-Abelian Electrodynamics

The general theory of gauge fields is used to develop a theory of electrodynamics in which the fundamental structure is non-Abelian and in which the internal gauge field symmetry is O(3), based on the existence of circular polarization and the third Stokes parameter. The theory is used to provide an explanation for the Sagnac effect with platform at rest and in motion. The Sagnac formula is obtained by considering the platform in motion to be a gauge transformation. The topological phases can be described straightforwardly with non Abelian electrodynamics, which produces a novel magnetic field component for all types of radiation, a component which is proportional to the third Stokes parameter. The theory provides a natural explanation for the inverse Faraday effect without phenomenology.     

In situ detection and surface coverage measurements of CO during CO oxidation on polycrystalline platinum using sum frequency generation

Received: 20 September 1998 / Revised version: 9 December 1998