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Jan Zelenka Dr. Aleksandr Pereverzev Dr. Ullrich Jahn Prof. Dr. Jana Roithová 《Chemistry (Weinheim an der Bergstrasse, Germany)》2022,28(28):e202104493
Photocatalytic generation of nitrenes and radicals can be used to tune or even control their reactivity. Photocatalytic activation of sulfonyl azides leads to the elimination of N2 and the resulting reactive species initiate C−H activations and amide formation reactions. Here, we present reactive radicals that are generated from sulfonyl azides: sulfonyl nitrene radical anion, sulfonyl nitrene and sulfonyl amidyl radical, and test their gas phase reactivity in C−H activation reactions. The sulfonyl nitrene radical anion is the least reactive and its reactivity is governed by the proton coupled electron transfer mechanism. In contrast, sulfonyl nitrene and sulfonyl amidyl radicals react via hydrogen atom transfer pathways. These reactivities and detailed characterization of the radicals with vibrational spectroscopy and with DFT calculations provide information necessary for taking control over the reactivity of these intermediates. 相似文献
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In this paper, we discuss the classical ill-posed problem of numerical differentiation, assuming that the smoothness of the function to be differentiated is unknown. Using recent results on adaptive regularization of general ill-posed problems, we propose new rules for the choice of the stepsize in the finite-difference methods, and for the regularization parameter choice in numerical differentiation regularized by the iterated Tikhonov method. These methods are shown to be effective for the differentiation of noisy functions, and the order-optimal convergence results for them are proved.
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Helmut?HarbrechtEmail author Sergei?Pereverzev Reinhold?Schneider 《Numerische Mathematik》2003,95(1):123-143
It is well known, that pseudodifferential equations of negative order considered in Sobolev spaces with small smoothness indices are ill–posed. On the other hand, it is known that efficient discretization schemes with properly chosen discretization parameters allow to obtain a regularization effect for such equations. The main accomplishment of the present paper is the principle for the adaptive choice of the discretization parameters directly from noisy discrete data. We argue that the combination of this principle with wavelet–based matrix compression techniques leads to algorithms which are order–optimal in the sense of complexity. 相似文献
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We consider a new version of the projection-iterative method for the solution of operator equations of the first kind. We show that it is more economical in the sense of amount of used discrete information. 相似文献
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For linear statistical ill-posed problems in Hilbert spaces we introduce an adaptive procedure to recover the unknown solution from indirect discrete and noisy data. This procedure is shown to be order optimal for a large class of problems. Smoothness of the solution is measured in terms of general source conditions. The concept of operator monotone functions turns out to be an important tool for the analysis.
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We present a model for conductivity and energy diffusion in a linear chain described by a quadratic Hamiltonian with Gaussian noise. We show that when the correlation matrix is diagonal, the noise-averaged Liouville-von Neumann equation governing the time evolution of the system reduces to the [Lindblad, Commun. Math. Phys. 48, 119 (1976)] equation with Hermitian Lindblad operators. We show that the noise-averaged density matrix for the system expectation values of the energy density and the number density satisfies discrete versions of the heat and diffusion equations. Transport coefficients are given in terms of model Hamiltonian parameters. We discuss conditions on the Hamiltonian under which the noise-averaged expectation value of the total energy remains constant. For chains placed between two heat reservoirs, the gradient of the energy density along the chain is linear. 相似文献
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In this paper we consider a collocation method for solving Fredholm integral equations of the first kind, which is known to be an ill-posed problem. An “unregularized” use of this method can give reliable results in the case when the rate at which smallest singular values of the collocation matrices decrease is known a priori. In this case the number of collocation points plays the role of a regularization parameter. If the a priori information mentioned above is not available, then a combination of collocation with Tikhonov regularization can be the method of choice. We analyze such regularized collocation in a rather general setting, when a solution smoothness is given as a source condition with an operator monotone index function. This setting covers all types of smoothness studied so far in the theory of Tikhonov regularization. One more issue discussed in this paper is an a posteriori choice of the regularization parameter, which allows us to reach an optimal order of accuracy for deterministic noise model without any knowledge of solution smoothness. 相似文献