Determination of the spacetime from local time measurements

We consider an inverse problem for a Lorentzian spacetime (M, g), and show that time measurements, that is, the knowledge of the Lorentzian time separation function on a submanifold \(\Sigma \subset M\) determine the \(C^\infty \)-jet of the metric in the Fermi coordinates associated to \(\Sigma \). We use this result to study the global determination of the spacetime (M, g) when it has a real-analytic structure or is stationary and satisfies the Einstein-scalar field equations. In addition to this, we require that (M, g) is geodesically complete modulo scalar curvature singularities. The results are Lorentzian counterparts of extensively studied inverse problems in Riemannian geometry—the determination of the jet of the metric and the boundary rigidity problem. We give also counterexamples in cases when the assumptions are not valid, and discuss inverse problems in general relativity.     

Coating of open tubular capillaries with discoidal and spherical high-density lipoprotein particles in electrochromatography

A new method was developed for the coating of fused-silica capillaries with human high-density lipoproteins (HDLs) for use in electrochromatography. The HDL particles used for the coating differed in particle shape and composition. Both discoidal and spherical particles formed a monolayer on the inner silica wall as confirmed by atomic force microscopy. The effect of coating conditions, such as HDL concentration and coating time, was investigated with spherical HDL particles. Examination of the influence of pH on the coating stability also allowed the determination of pI values for the HDL particles attached to the capillary wall. The pI values for spherical and discoidal HDL particles were close to 5.0. The repeatabilities of the EOF mobility and the retention factors of the uncharged steroid hormones used as model compounds were exploited in the evaluation of the coating stability. The optimal coating was achieved with 0.1 mg/mL HDL protein and 50 min flushing with coating solution followed by 15 min standing time. Electrochromatography with HDL-coated open tubular capillaries offers a new tool for the study of HDL particle structure and transformations.     

Pt(II)-mediated nitrile-tetramethylguanidine coupling as a key step for a novel synthesis of 1,6-dihydro-1,3,5-dihydrotriazines

The coupling between tetramethylguanidine, HN=C(NMe2)2, and coordinated organonitriles in the platinum(II) complexes cis/trans-[PtCl2(RCN)2] (R = Me, Et, Ph) proceeds rapidly under mild conditions to afford the diimino compounds containing two N-bound monodentate 1,3-diaza-1,3-diene ligands [PtCl2{NH=C(R)N=C(NMe2)2}2] (R = Et, trans-1; R = Ph, trans-2; R = Me, cis-3; R = Et, cis-4), and this reaction is the first observation of metal-mediated nucleophilic addition of a guanidine to ligated nitrile. Complexes 1-4 were characterized by elemental analyses (C, H, N), X-ray diffraction, FAB mass spectrometry, IR, and 1H and 13C{1H} NMR spectroscopies; assignment of signals from E/Z-forms of 1,3-diaza-1,3-diene ligands and verification of routes for their Z right harpoon over left harpoon E isomerization in solution were performed using 2D 1H,1H-COSY, 1H,13C-HETCOR, and 1D NOE NMR experiments. The newly formed and previously unknown 1,3-diaza-1,3-dienes NH=C(R)N=C(NMe2)2 were liberated from the platinum(II) complexes [PtCl2{NH=C(R)N=C(NMe2)2}2] (1-3) by substitution with 2 equiv of 1,2-bis-(diphenylphosphino)ethane (dppe) to give the uncomplexed HN=C(R)N=C(NMe2)2 species (5-7) in solution and the solid [Pt(dppe)2](Cl)2. The former were utilized in situ, after filtration of the latter, in the reaction with 1,3-di-p-tolylcarbodiimide, (p-tol)N=C=N(tol-p), in CDCl3 to generate (6E)-N,N-dimethyl-1-(4-methylphenyl)-6-[(4-methylphenyl)imino]-1,6-dihydro-1,3,5-triazin-2-amines) (8-10) due to the [4 + 2]-cycloaddition accompanying elimination of HNMe2. The formulation of 8-10 is based on ESI-MS, 1H, 13C{1H} NMR, and X-ray crystal structures determined for 9 and 10. The reaction of 1,3-diaza-1,3-dienes with 1,3-di-p-tolylcarbodiimide, described in this article, constitutes a novel synthetic approach to a useful class of heterocyclic species like 1,6-dihydro-1,3,5-triazines.     

Exploiting the Chiral Ligands of Bis(imidazolinyl)- and Bis(oxazolinyl)thiophenes—Synthesis and Application in Cu-Catalyzed Friedel–Crafts Asymmetric Alkylation

Five new C₂-symmetric chiral ligands of 2,5-bis(imidazolinyl)thiophene (L1–L3) and 2,5-bis(oxazolinyl)thiophene (L4 and L5) were synthesized from thiophene-2,5-dicarboxylic acid (1) with enantiopure amino alcohols (4a–c) in excellent optical purity and chemical yield. The utility of these new chiral ligands for Friedel–Crafts asymmetric alkylation was explored. Subsequently, the optimized tridentate ligand L5 and Cu(OTf)₂ catalyst (15 mol%) in toluene for 48 h promoted Friedel–Crafts asymmetric alkylation in moderate to good yields (up to 76%) and with good enantioselectivity (up to 81% ee). The bis(oxazolinyl)thiophene ligands were more potent than bis(imidazolinyl)thiophene analogues for the asymmetric induction of the Friedel–Crafts asymmetric alkylation.     

Towards a kinetic theory for fermions with quantum coherence

A new density matrix and corresponding quantum kinetic equations are introduced for fermions undergoing coherent evolution either in time (coherent particle production) or in space (quantum reflection). A central element in our derivation is finding new spectral solutions for the 2-point Green's functions written in the Wigner representation, that are carrying the information of the quantum coherence. Physically observable density matrix is then defined from the bare singular 2-point function by convoluting it with the extrenous information about the state of the system. The formalism is shown to reproduce familiar results from the Dirac equation approach, like Klein problem and nonlocal reflection from a mass wall. The notion of the particle number in the presence of quantum coherence is shown to be particularly transparent in the current picture. We extend the formalism to the case of mixing fields and show how the usual flavour mixing and oscillation of neutrinos emerges again from a singular shell structure. Finally, we show how the formalism can be extended to include decohering interactions.     

Comprehensive two-dimensional liquid chromatography-time-of-flight mass spectrometry in the analysis of acidic compounds in atmospheric aerosols

A novel method utilising comprehensive two-dimensional liquid chromatography interfaced to electrospray ionisation time-of-flight mass spectrometry was developed for the determination of organic acids in atmospheric aerosols. The system was applied to the analysis of methanolic extracts of filters from a high volume sampler. The enhanced separation power of two-dimensional separation was demonstrated in the analysis of both rural and urban samples. Quantification was performed for compounds for which standards were available. Limit of detection was 2-200ng/ml. Average reproducibility of retention times in each dimensions was 0.1%, and average reproducibility of peak areas was 8% (10mug/ml, n=3).     

Impact of reductive cleavage of an intramolecular disulfide bond containing cationic gemini surfactant in monolayers and bilayers

The properties of a novel disulfide-bond-containing gemini surfactant bis[N,N-dimethyl-N-hexadecyl-N-(2-mercaptoethyl)ammonium bromide] disulfide (DSP) were studied using a Langmuir balance, supported monolayers, differential scanning calorimetry, giant vesicles, and LUVs. In 150 mM NaCl the cmc for DSP was 7.5 microM whereas that of the monomer N,N-dimethyl-N-hexadecyl-N-(2-mercaptoethyl)ammonium bromide (MSP) was 12.1 microM. Both surfactants exhibited single endotherms upon DSC, with peak temperatures Tm at 21.7 and 20.1 degrees C for DSP and MSP, respectively. The endotherm for MSP was significantly broader indicating less cooperative melting. Both in monolayers and in vesicles reductive cleavage of the disulfide bond of DSP could be obtained by glutathione (GSH). For Langmuir films of DSP the addition of GSH into the subphase led to a decrease in surface pressure pi as well as surface dipole potential psi. Although the cleavage by GSH was significantly slower in the presence of a charge saturating concentration of DNA, it did not prevent the reaction. The resulting monomers detached from supported monolayers, leading to loss of affinity of the surface for DNA. Disruption of giant vesicles containing DSP within approximately 30 s following a local injection of GSH was observed, revealing membrane destabilization.     

Lasagna-type arrays with halide-nitromethane cluster filling. The first recognition of the Hal(-)···HCH2NO2 (Hal = Cl, Br, I) hydrogen bonding

The previously predicted ability of the methyl group of nitromethane to form hydrogen bonding with halides is now confirmed experimentally based on X-ray data of novel nitromethane solvates followed by theoretical ab initio calculations at the MP2 level of theory. The cationic (1,3,5-triazapentadiene)Pt(II) complexes [Pt{HN=C(NC(5)H(10))N(Ph)C(NH(2))=NPh}(2)](Cl)(2), [1](Hal)(2) (Hal = Cl, Br, I), and [Pt{HN=C(NC(4)H(8)O)N(Ph)C(NH(2))=NPh}(2)](Cl)(2), [2](Cl)(2), were crystallized from MeNO(2)-containing systems providing nitromethane solvates studied by X-ray diffraction. In the crystal structure of [1][(Hal)(2)(MeNO(2))(2)] (Hal = Cl, Br, I) and [2][(Cl)(2)(MeNO(2))(2)], the solvated MeNO(2) molecules occupy vacant spaces between lasagna-type layers and connect to the Hal(-) ion through a weak hydrogen bridge via the H atom of the methyl thus forming, by means of the Hal(-)···HCH(2)NO(2) contact, the halide-nitromethane cluster "filling". The quantum-chemical calculations demonstrated that the short distance between the Hal(-) anion and the hydrogen atom of nitromethane in clusters [1][(Hal)(2)(MeNO(2))(2)] and [2][(Cl)(2)(MeNO(2))(2)] is not just a consequence of the packing effect but a result of the moderately strong hydrogen bonding.     

Testing the neo-classical and the Newtonian theory of production

We search for regularities observed in the production of goods by studying Finnish data. Despite the heterogeneity of sectoral growth rates in Finland, unit root is observed in annual productions in all main sectors and all manufacturing industries. Thus a linear time trend exists in annual flows of production. This is inconsistent with the static neo-classical theory that assumes firms to produce at their equilibrium flow of production. A different framework is thus needed for modeling the behavior of firms. We test a Newtonian type of model for production against the neo-classical one, and our observation is that the former works better with annual data at every manufacturing industry in Finland.