Explore the vast range of titles available.

Systems of interacting species, such as biological environments or chemical reactions, are often described mathematically by sets of coupled ordinary differential equations. While a large number β of species may be involved in the coupled dynamics, often only α<β species are of interest or of consequence. In this paper, we explored how to construct models that include only those given α species, but still recreate the dynamics of the original β-species model. Under some conditions detailed here, this reduction can be completed exactly, such that the information in the reduced model is exactly the same as the original one, but over fewer equations. Moreover, this reduction process suggests a promising type of approximate model—no longer exact, but computationally quite simple.

The study gives a brief overview of publications on exact solutions for functional PDEs with delays of various types and on methods for constructing such solutions. For the first time, second-order wave-type PDEs with a nonlinear source term containing the unknown function with proportional time delay, proportional space delay, or both time and space delays are considered. In addition to nonlinear wave-type PDEs with constant speed, equations with variable speed are also studied. New one-dimensional reductions and exact solutions of such PDEs with proportional delay are obtained using solutions of simpler PDEs without delay and methods of separation of variables for nonlinear PDEs. Self-similar solutions, additive and multiplicative separable solutions, generalized separable solutions, and some other solutions are presented. More complex nonlinear functional PDEs with a variable time or space delay of general form are also investigated. Overall, more than thirty wave-type equations with delays that admit exact solutions are described. The study results can be used to test numerical methods and investigate the properties of the considered and related PDEs with proportional or more complex variable delays.

In this paper, a new notion of eigenvalue trim or co-trim for n-D Roesser (state-space) model is first introduced, which reveals the internal connection between the eigenvalues of the system matrix and the reducibility of the considered Roesser model. Then, new reducibility conditions and the corresponding order reduction algorithms based on eigenvalue trim or co-trim are proposed for exact order reduction of a given n-D Roesser model, and it will be shown that this eigenvalue trim approach can be applied even to those systems for which the existing approaches cannot do any further order reduction. Furthermore, a new transformation for n-D Roesser models, by swapping certain rows and columns and interchanging certain entries that belong to different blocks corresponding to different variables, will be established, which can transform an n-D Roesser model whose order cannot be reduced any more by the proposed approach to another equivalent Roesser model with the same order so that this transformed Roesser model can still be reduced further. Examples are given to illustrate the details as well as the effectiveness of the proposed approach.

The preparation, characterization, and catalytic activity of supported metal phosphides are reviewed. Reduction of metal compounds together with phosphate is a convenient method to prepare metal phosphides, but requires high temperature. Reduction with phosphite, hypophosphite, or phosphine and the plasma reduction of phosphate can be carried out at lower temperatures, which leads to smaller metal phosphide particles and more active catalysts. Organometallic routes allow the separate synthesis of metal phosphide nanoparticles, which have to be added to the support in a second step. LEED, STM, XPS, and DFT studies have shown that the surfaces of Ni 2 P reconstruct to P-rich surfaces. The investigation of metal phosphides as catalysts for hydrotreating reactions continues to be a topic of considerable research with recent advances realized in using bimetallic and noble metal phosphides to achieve high activities and tailored selectivities. Finally, hydrodeoxygenation catalysis over metal phosphides is a growing area of research given the need to develop catalysts for upgrading biomass to transportation fuels. Graphical Abstract

The composition of sulfur isotopes in sedimentary sulfides and sulfates traces the sulfur cycle throughout Earth's history. In particular, depletions of sulfur-34 ( 34 S) in sulfide relative to sulfate exceeding 47 per mil (‰) often serve as a proxy for the disproportionation of intermediate sulfur species in addition to sulfate reduction. Here, we demonstrate that a pure, actively growing culture of a marine sulfate-reducing bacterium can deplete 34 S by up to 66‰ during sulfate reduction alone and in the absence of an extracellular oxidative sulfur cycle. Therefore, similar magnitudes of sulfur isotope fractionation in sedimentary rocks do not unambiguously record the presence of other sulfur-based metabolisms or the stepwise oxygenation of Earth's surface environment during the Proterozoic.

Electrochemical conversion of carbon dioxide (CO₂) to carbon monoxide (CO) is a potentially useful step in the desirable transformation of the greenhouse gas to fuels and commodity chemicals. We have found that modification of iron tetraphenylporphyrin through the introduction of phenolic groups in all ortho and ortho' positions of the phenyl groups considerably speeds up catalysis of this reaction by the electrogenerated iron(0) complex. The catalyst which uses one of the most earth-abundant metals, manifests a CO faradaic yield above 90% through 50 million turnovers over 4 hours of electrolysis at low overpotential (0.465 volt), with no observed degradation. The basis for the enhanced activity appears to be the high local concentration of protons associated with the phenolic hydroxyl substituents.

Catalysis of the reduction of nitrogen to ammonia under mild conditions by a tris(phosphine)borane-supported iron complex indicates that a single iron site may be capable of stabilizing the various N x H y intermediates generated during catalytic ammonia formation. In search of an easy fix for nitrogen Industrial nitrogen fixation is performed on a vast scale by the Haber–Bosch process, which uses a solid-state iron catalyst at very high temperatures and pressures. Synthetic chemists have searched for decades for small metal-containing complexes to catalyse the transformation of nitrogen into ammonia in less extreme conditions, taking their lead from the nitrogenases found in plants and bacteria. To that end Jonas Peters and colleagues describe a tris(phosphine)borane-supported iron complex that catalyses the reduction of nitrogen into ammonia under mild conditions with reasonable efficiency. This suggests that a single iron site is sufficient for mediating nitrogen fixation, in line with recent biochemical and spectroscopic data that point to iron rather than the molybdenum also present in the FeMo cofactor or nitrogenase as the site of nitrogen binding and activation. The reduction of nitrogen (N 2 ) to ammonia (NH 3 ) is a requisite transformation for life 1 . Although it is widely appreciated that the iron-rich cofactors of nitrogenase enzymes facilitate this transformation 2 , 3 , 4 , 5 , how they do so remains poorly understood. A central element of debate has been the exact site or sites of N 2 coordination and reduction 6 , 7 . In synthetic inorganic chemistry, an early emphasis was placed on molybdenum 8 because it was thought to be an essential element of nitrogenases 3 and because it had been established that well-defined molybdenum model complexes could mediate the stoichiometric conversion of N 2 to NH 3 (ref. 9 ). This chemical transformation can be performed in a catalytic fashion by two well-defined molecular systems that feature molybdenum centres 10 , 11 . However, it is now thought that iron is the only transition metal essential to all nitrogenases 3 , and recent biochemical and spectroscopic data have implicated iron instead of molybdenum as the site of N 2 binding in the FeMo-cofactor 12 . Here we describe a tris(phosphine)borane-supported iron complex that catalyses the reduction of N 2 to NH 3 under mild conditions, and in which more than 40 per cent of the proton and reducing equivalents are delivered to N 2 . Our results indicate that a single iron site may be capable of stabilizing the various N x H y intermediates generated during catalytic NH 3 formation. Geometric tunability at iron imparted by a flexible iron–boron interaction in our model system seems to be important for efficient catalysis 13 , 14 , 15 . We propose that the interstitial carbon atom recently assigned in the nitrogenase cofactor may have a similar role 16 , 17 , perhaps by enabling a single iron site to mediate the enzymatic catalysis through a flexible iron–carbon interaction 18 .

ABSTRACT With the unprecedented photometric precision of the Kepler spacecraft, significant systematic and stochastic errors on transit signal levels are observable in the Kepler photometric data. These errors, which include discontinuities, outliers, systematic trends, and other instrumental signatures, obscure astrophysical signals. The presearch data conditioning (PDC) module of the Kepler data analysis pipeline tries to remove these errors while preserving planet transits and other astrophysically interesting signals. The completely new noise and stellar variability regime observed in Kepler data poses a significant problem to standard cotrending methods. Variable stars are often of particular astrophysical interest, so the preservation of their signals is of significant importance to the astrophysical community. We present a Bayesian maximum a posteriori (MAP) approach, where a subset of highly correlated and quiet stars is used to generate a cotrending basis vector set, which is in turn used to establish a range of \"reasonable\" robust fit parameters. These robust fit parameters are then used to generate a Bayesian prior and a Bayesian posterior probability distribution function (PDF) which, when maximized, finds the best fit that simultaneously removes systematic effects while reducing the signal distortion and noise injection that commonly afflicts simple least-squares (LS) fitting. A numerical and empirical approach is taken where the Bayesian prior PDFs are generated from fits to the light-curve distributions themselves.

A new empirical algorithm is proposed to estimate surface chlorophyll a (Chl) concentrations in the global ocean for Chl ≤ 0.25 mg m −3 (∼78% of the global ocean area). The algorithm is based on a color index (CI), defined as the difference between remote‐sensing reflectance ( R rs , sr −1 ) in the green and a reference formed linearly between R rs in the blue and red. For low‐Chl waters, in situ data showed a tighter (and therefore better) relationship between CI and Chl than between traditional band ratios and Chl, which was further validated using global data collected concurrently by ship‐borne and Sea‐viewing Wide Field‐of‐view Sensor (SeaWiFS) and Moderate Resolution Imaging Spectroradiometer (MODIS)/Aqua instruments. Model simulations showed that for low‐Chl waters, compared with the band‐ratio algorithm, the CI‐based algorithm (CIA) was more tolerant to changes in chlorophyll‐specific backscattering coefficient and performed similarly for different relative contributions of nonphytoplankton absorption. Simulations using existing atmospheric correction approaches further demonstrated that the CIA was much less sensitive than band‐ratio algorithms to various errors induced by instrument noise and imperfect atmospheric correction (including sun glint and whitecap corrections). Image and time series analyses of SeaWiFS and MODIS/Aqua data also showed improved performance in terms of reduced image noise, more coherent spatial and temporal patterns, and better consistency between the two sensors. The reduction in noise and other errors is particularly useful to improve the detection of various ocean features such as eddies. Preliminary tests over Medium‐Resolution Imaging Spectrometer and Coastal Zone Color Scanner data indicate that the new approach should be generally applicable to all past, current, and future ocean color instruments. A completely novel algorithm and concept for remote sensing of ocean chlorophyll Significant improvement in ocean chlorophyll data quality Significant improvement in data consistency between SeaWiFS and MODIS

Several states and countries have adopted targets for deep reductions in greenhouse gas emissions by 2050, but there has been little physically realistic modeling of the energy and economic transformations required. We analyzed the infrastructure and technology path required to meet California's goal of an 80% reduction below 1990 levels, using detailed modeling of infrastructure stocks, resource constraints, and electricity system operability. We found that technically feasible levels of energy efficiency and decarbonized energy supply alone are not sufficient; widespread electrification of transportation and other sectors is required. Decarbonized electricity would become the dominant form of energy supply, posing challenges and opportunities for economic growth and climate policy. This transformation demands technologies that are not yet commercialized, as well as coordination of investment, technology development, and infrastructure deployment.