504 research outputs found
Nanostructured Molybdenum Oxide Catalysts for the Selective Oxidation of C3 Hydrocarbons
Convergence bounds for local least squares approximation
We consider the problem of approximating a function in a general nonlinear
subset of , when only a weighted Monte Carlo estimate of the -norm
can be computed. Of particular interest in this setting is the concept of
sample complexity, the number of sample points that are necessary to achieve a
prescribed error with high probability. Reasonable worst-case bounds for this
quantity exist only for particular model classes, like linear spaces or sets of
sparse vectors. For more general sets, like tensor networks or neural networks,
the currently existing bounds are very pessimistic. By restricting the model
class to a neighbourhood of the best approximation, we can derive improved
worst-case bounds for the sample complexity. When the considered neighbourhood
is a manifold with positive local reach, its sample complexity can be estimated
by means of the sample complexities of the tangent and normal spaces and the
manifold's curvature.Comment: 17 pages, 4 figures, text overlap with arXiv:2108.0523
Prospects and challenges for autonomous catalyst discovery viewed from an experimental perspective
The urgency with which fundamental questions of energy conversion and the sustainable use of raw materials must be solved today requires new approaches in catalysis research. One way is to couple high-throughput experiments with machine learning methods in autonomous catalyst development. The fact that the active form of a catalyst is only created under working conditions and that the catalytic function is always in a very complex relationship with a number of physical and chemical properties of the material makes it essential to integrate operando experiments into systems of autonomous catalyst development. The analysis of the current state of the art and knowledge revealed a lack of integration of the numerous, technically very different unit operations in catalyst discovery and a great need for new developments in online and in situ analytics, especially in catalyst synthesis. To pave the way for autonomous processing of work packages by robots, it is proposed to advance the automation of single unit operations currently performed by human researchers by introducing standard operating procedures described in handbooks. The work according to rigorous protocols produces, on the one hand, reliable data that can be evaluated using artificial intelligence and facilitates on the other hand the automation. Special attention should be paid to the acquisition and real-time evaluation of analytical data in in situ and operando experiments as well as the automatic storage of data and metadata in databases
Single-Site Vanadyl Species Isolated within Molybdenum Oxide Monolayers in Propane Oxidation
The cooperation of metal oxide subunits in complex mixed metal oxide catalysts for selective oxidation of alkanes still needs deeper understanding to allow for a rational tuning of catalyst performance. Herein we analyze the interaction between vanadium and molybdenum oxide species in a monolayer supported on mesoporous silica SBA-15. Catalysts with variable Mo/V ratio between 10 and 1 were studied in the oxidation of propane and characterized by FTIR, Raman, and EPR spectroscopies, temperature-programmed reduction, UV/vis spectroscopy in combination with DFT calculations, and time-resolved experiments to analyze the redox properties of the catalysts. Molybdenum oxide (sub)monolayers on silica contain mainly dioxo (SiâOâ)2Mo(âO)2 species. Dilution of silica-supported vanadium oxide species by (SiâOâ)2Mo(âO)2 prevents the formation of VâOâV bonds, which are abundant in the pure vanadium oxide catalyst that predominantly contains two-dimensional vanadium oxide oligomers. Existing single vanadyl (SiâOâ)3V(âO) sites and neighboring (SiâOâ)2Mo(âO)2 sites do not strongly interact. The rates of reduction in propane and of oxidation in oxygen are lower for single metal oxide sites compared to those for oligomers. The rate of propane oxidation correlates with the overall redox rates of the catalysts but not linearly with the chemical composition. Retarded redox behavior facilitates selectivity toward acrolein on single-site catalysts. The abundance of MâOâM bonds is more important in terms of activity and selectivity compared to the nature of the central atom (molybdenum versus vanadium)
HPA as freighter to introduce RuO<sub>x</sub> into MOX host catalysts further work based on this concept
Synthesis and reactivity of molybdenum-based transition metal carbides in the dehydrogenation of propane
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Convergence bounds for empirical nonlinear least-squares
We consider best approximation problems in a nonlinear subset of a Banach space of functions. The norm is assumed to be a generalization of the L2 norm for which only a weighted Monte Carlo estimate can be computed. The objective is to obtain an approximation of an unknown target function by minimizing the empirical norm. In the case of linear subspaces it is well-known that such least squares approximations can become inaccurate and unstable when the number of samples is too close to the number of parameters. We review this statement for general nonlinear subsets and establish error bounds for the empirical best approximation error. Our results are based on a restricted isometry property (RIP) which holds in probability and we show sufficient conditions for the RIP to be satisfied with high probability. Several model classes are examined where analytical statements can be made about the RIP. Numerical experiments illustrate some of the obtained stability bounds
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