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961.
The nonlinear elliptic equation is investigated. It is supposed that u fulfils a mixed boundary value condition and that Ω ? IRn (n ≥ 3) has a piecewise smooth boundary. Ws,2 — regularity (s < 3/2) of u and Lp — properties of the first and the second derivatives of u are proven. 相似文献
962.
We study asymptotics as t → ∞ of solutions to a linear, parabolic system of equations with time‐dependent coefficients in Ω × (0, ∞), where Ω is a bounded domain. On ? Ω × (0, ∞) we prescribe the homogeneous Dirichlet boundary condition. For large values of t, the coefficients in the elliptic part are close to time‐independent coefficients in an integral sense which is described by a certain function κ (t). This includes in particular situations when the coefficients may take different values on different parts of Ω and the boundaries between them can move with t but stabilize as t → ∞. The main result is an asymptotic representation of solutions for large t. As a corollary, it is proved that if κ ∈ L1(0, ∞), then the solution behaves asymptotically as the solution to a parabolic system with time‐independent coefficients (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
963.
A classical theorem of Cauchy states that the eigenvalues of a principal submatrix A0 of a Hermitian matrix A interlace the eigenvalues of A. We consider the case of a matrix A which is Hermitian with respect to an indefinite inner product. 相似文献
964.
Julian Kund Jan-Hendrik Kruse Andreas Gruber Dr. Ivan Trentin Marcel Langer Dr. Clarissa Read Dr. Gregor Neusser Dominik Blaimer Dr. Ulrich Rupp Prof. Dr. Carsten Streb Prof. Dr. Kerstin Leopold Prof. Dr. Felix H. Schacher Prof. Dr. Christine Kranz 《Angewandte Chemie (International ed. in English)》2023,62(22):e202217196
Heterogeneous light-driven catalysis is a cornerstone of sustainable energy conversion. Most catalytic studies focus on bulk analyses of the hydrogen and oxygen evolved, which impede the correlation of matrix heterogeneities, molecular features, and bulk reactivity. Here, we report studies of a heterogenized catalyst/photosensitizer system using a polyoxometalate water oxidation catalyst and a model, molecular photosensitizer that were co-immobilized within a nanoporous block copolymer membrane. Via operando scanning electrochemical microscopy (SECM), light-induced oxygen evolution was determined using sodium peroxodisulfate (Na2S2O8) as sacrificial electron acceptor. Ex situ element analyses provided spatially resolved information on the local concentration and distribution of the molecular components. Infrared attenuated total reflection (IR-ATR) studies of the modified membranes showed no degradation of the water oxidation catalyst under the reported light-driven conditions. 相似文献
965.
Aequationes mathematicae - Investigating the future value F(K, s, t) of a capital K invested between dates s and t, the “natural” condition $$F(K,s,t)ge K$$ has lost... 相似文献
966.
967.
These notes develop aspects of perturbation theory of matrices related to so-called diagonalisation schemes. Primary focus is on constructive tools to derive asymptotic expansions for small/large parameters of eigenvalues and eigenprojections of families of matrices depending upon real/complex parameters. Applications of the schemes in different frameworks are also discussed and references to further applications given. 相似文献
968.
969.
970.
The Titchmarsh–Weyl function, which was introduced in Fulton (Math Nachr 281(10):1418–1475, 2008) for the Sturm-Liouville equation with a hydrogen-like potential on (0, ∞), is shown to belong to a generalized Nevanlinna class Nk{bf N_kappa}. As a consequence, also in the case of two singular endpoints for the Fourier transformation defined by means of Frobenius solutions there exists a scalar spectral function. This spectral function is given explicitly for potentials of the form dfracq0x2+dfracq1x, -dfrac 14 £ q0 < ¥{dfrac{q_0}{x^2}+dfrac{q_1}{x},,-dfrac 14le q_0 < infty}. 相似文献