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.     

Metrization of Weighted Graphs

We find a set of necessary and sufficient conditions under which the weight ${w: E \rightarrow \mathbb{R}^{+}}$ on the graph G = (V, E) can be extended to a pseudometric ${d : V \times V \rightarrow \mathbb{R}^{+}}$ . We describe the structure of graphs G for which the set ${\mathfrak{M}_{w}}$ of all such extensions contains a metric whenever w is strictly positive. Ordering ${\mathfrak{M}_{w}}$ by the pointwise order, we have found that the posets $({\mathfrak{M}_{w}, \leqslant)}$ contain the least elements ρ _0,w if and only if G is a complete k-partite graph with ${k \, \geqslant \, 2}$ . In this case the symmetric functions ${f : V \times V \rightarrow \mathbb{R}^{+}}$ , lying between ρ _0,w and the shortest-path pseudometric, belong to ${\mathfrak{M}_{w}}$ for every metrizable w if and only if the cardinality of all parts in the partition of V is at most two.     

Convergence of FFT‐based homogenization for strongly heterogeneous media

The FFT‐based homogenization method of Moulinec–Suquet has recently attracted attention because of its wide range of applicability and short computational time. In this article, we deduce an optimal a priori error estimate for the homogenization method of Moulinec–Suquet, which can be interpreted as a spectral collocation method. Such methods are well‐known to converge for sufficiently smooth coefficients. We extend this result to rough coefficients. More precisely, we prove convergence of the fields involved for Riemann‐integrable coercive coefficients without the need for an a priori regularization. We show that our L² estimates are optimal and extend to mildly nonlinear situations and L^p estimates for p in the vicinity of 2. The results carry over to the case of scalar elliptic and curl ? curl‐type equations, encountered, for instance, in stationary electromagnetism. Copyright © 2014 John Wiley & Sons, Ltd.     

A Unique Tryptophan C‐Prenyltransferase from the Kawaguchipeptin Biosynthetic Pathway

Cyanobactins are a rapidly growing family of linear and cyclic peptides produced by cyanobacteria. Kawaguchipeptins A and B, two macrocyclic undecapeptides reported earlier from Microcystis aeruginosa NIES‐88, are shown to be products of the cyanobactin biosynthetic pathway. The 9 kb kawaguchipeptin (kgp) gene cluster was identified in a 5.26 Mb draft genome of Microcystis aeruginosa NIES‐88. We verified that this gene cluster is responsible for the production of the kawaguchipeptins through heterologous expression of the kgp gene cluster in Escherichia coli. The KgpF prenyltransferase was overexpressed and was shown to prenylate C‐3 of Trp residues in both linear and cyclic peptides in vitro. Our findings serve to further enhance the structural diversity of cyanobactins to include tryptophan‐prenylated cyclic peptides.     

An Experimental Study of the Kinetics of the Reactions of Isopropyl,sec‐Butyl,and tert‐Butyl Radicals with Molecular Chlorine at Low Pressures (0.5–7.0 Torr) in the Temperature Range 190–480 K

In this work, we have measured the rate coefficients of the reactions of isopropyl (propan‐2‐yl), sec‐butyl (butan‐2‐yl), and tert‐butyl (2‐methylpropan‐2‐yl) radicals with molecular chlorine as a function of temperature (190–480 K). The experiments were done in a tubular laminar flow reactor coupled to a photoionization quadrupole mass spectrometer employing a gas‐discharge lamp for ionization. The radicals were homogeneously produced in the reactor by photolyzing suitable precursor molecules with 193‐nm pulsed exciplex laser radiation. The bimolecular rate coefficients were obtained by monitoring the radical decay signals in real time under pseudo–first‐order conditions. The rate coefficients of all three reactions showed negative temperature dependence. The bath gas used in the experiments was helium, and the rate coefficients appeared to be independent of the helium concentrations employed ([2.4–14] × 10¹⁶ cm^?3) for all three reactions. The rate coefficients of the reactions can be approximated in the studied temperature range by the following parameterizations: We estimate that the overall uncertainties of the measured rate coefficients are ±20%. We were able to observe 2‐chloropropane (i‐C₃H₇Cl) product for the i‐C₃H₇^● + Cl₂ reaction. No products were observed for the other two reactions, and the reasons for this are briefly discussed in the text.     

Synthesis of Inorganic Structural Isomers By Diffusion‐Constrained Self‐Assembly of Designed Precursors: A Novel Type of Isomerism

The structure of precursors is used to control the formation of six possible structural isomers that contain four structural units of PbSe and four structural units of NbSe₂: [(PbSe)_1.14]₄[NbSe₂]₄, [(PbSe)_1.14]₃[NbSe₂]₃[(PbSe)_1.14]₁[NbSe₂]₁, [(PbSe)_1.14]₃[NbSe₂]₂[(PbSe)_1.14]₁[NbSe₂]₂, [(PbSe)_1.14]₂[NbSe₂]₃[(PbSe)_1.14]₂[NbSe₂]₁, [(PbSe)_1.14]₂[NbSe₂]₂[(PbSe)_1.14]₁[NbSe₂]₁[(PbSe)_1.14]₁[NbSe₂]₁, [(PbSe)_1.14]₂[NbSe₂]₁[(PbSe)_1.14]₁[NbSe₂]₂[(PbSe)_1.14]₁[NbSe₂]₁. The electrical properties of these compounds vary with the nanoarchitecture. For each pair of constituents, over 20 000 new compounds, each with a specific nanoarchitecture, are possible with the number of structural units equal to 10 or less. This provides opportunities to systematically correlate structure with properties and hence optimize performance.     

Adaptation of the human skin by chronic solar-simulating UV irradiation prevents ultraviolet-B irradiation-induced rise in serum C-reactive protein levels

Exposure of the skin to UV radiation induces local inflammation. We hypothesized that inflammation induced by erythemal UV-B irradiation could elevate levels of serum C-reactive protein (CRP) and that suberythemal repeating doses of solar-simulating UV radiation (SSR) would produce photoadaptation to such inflammation. Separation-free high-sensitivity assays of CRP show an increase by 42% (P = 0.046) in CRP concentrations in healthy human subjects 24 h after a 3 minimal erythemal dose (MED) dose of UV-B delivered onto a 100 cm2 skin area. Preceding daily suberythemal doses of whole-body SSR for 10 or 30 consecutive days completely prevented the CRP increase. UV-B-induced skin erythema was partially attenuated by 30 preceding days of SSR only (P = 0.00066). After 10 daily SSR doses, the mean baseline CRP concentrations (0.24 +/- 0.21 mg/L) declined by 35% (P = 0.018). Using high-sensitivity analysis of serum CRP as the endpoint marker for cutaneous inflammation, we show that acute exposure of even a relatively small skin area to erythemal UV-B induces skin inflammation detectable also at the systemic level and that photoadaptation by preceding repeating suberythemal doses of SSR reduces signs of inflammation. Our data complement the view given by previous studies in that local photoadaptation also has systemic manifestations.     

Molecular recognition in a uradinyl-functionalized stable radical

Stable radical 2-(6-uradinyl)-4,4,5,5-tetramethyl-4,5-dihydro-1H-imidazole-1-oxyl (1) binds to hydrogen-bonding complement 2,6-di(propylamido)pyridine (DAP) in chloroform with Ka=220 M(-1) at 33 degrees C; ESI-MS shows not only 1:DAP complementary dyad formation, but also 1:(DAP)2 formation at higher concentrations of DAP.     

Towards new molecular photocatalysts for CO2 reduction: photo-induced electron transfer versus CO dissociation within [Os(NN)(CO)2Cl2] Complexes

Optical excitation in the visible region of trans-(Cl)-[Os(bpy)(CO)(2)Cl(2)] (bpy=2,2'-bipyridine; C1) and trans-(Cl)-[Os(dmbpy)(CO)(2)Cl(2)] (dmbpy=4,4'-dimethyl 2,2'-bipyridine; C2) is known to induce the common CO dissociation reaction. However, the quantum yield of the reactions is less than 0.15, although C1 and C2 display pronounced photoluminescence in the visible region at room temperature with a lifetime of few tens of nanoseconds. Taking into account the characteristics of their emitting state, we have investigated the capability of C1 and C2 to act as a photosensitiser in redox reactions in different solvents (MeCN, PrCN and DMF). The efficient oxidation and reduction of both complexes under continuous irradiation in the presence of a sacrificial electron acceptor or donor is reported here. The photo-induced transformations and the nature of the resulting compounds were analysed by UV/Vis and IR spectroscopies and cyclic voltammetry. Photo-induced oxidation of C1 and C2 leads to the corresponding monocarbonyl oxidised species, whereas photo-induced reduction under argon leads mainly to the formation of the corresponding Os-bonded molecular wires P1 and P2 after exchange of two electrons associated with the loss of two chloro ligands. The chemical yield of the latter reaction (around 65%) becomes quantitative by adding [Ru(bpy)(3)](2+) as an external redox photosensitiser. This behaviour has been used to photocatalyse the two electron, two proton conversion of CO(2) to CO. Turnover numbers (TON) of 11.5 and 19.5 have been obtained respectively for C1 and C2 after 4.5 h of irradiation under CO(2) in DMF with triethanolamine as the electron donor. TON can be slightly increased by adding [Ru(bpy)(3)](2+) to the solution.     

Noncovalent Axial I⋅⋅⋅Pt⋅⋅⋅I Interactions in Platinum(II) Complexes Strengthen in the Excited State

Coordination compounds of platinum(II) participate in various noncovalent axial interactions involving metal center. Weakly bound axial ligands can be electrophilic or nucleophilic; however, interactions with nucleophiles are compromised by electron density clashing. Consequently, simultaneous axial interaction of platinum(II) with two nucleophilic ligands is almost unprecedented. Herein, we report structural and computational study of a platinum(II) complex possessing such intramolecular noncovalent I⋅⋅⋅Pt⋅⋅⋅I interactions. Structural analysis indicates that the two iodine atoms approach the platinum(II) center in a “side-on” fashion and act as nucleophilic ligands. According to computational studies, the interactions are dispersive, weak and anti-cooperative in the ground electronic state, but strengthen substantially and become partially covalent and cooperative in the lowest excited state. Strengthening of I⋅⋅⋅Pt⋅⋅⋅I contacts in the excited state is also predicted for the sole previously reported complex with analogous axial interactions.