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Dr. Christian Hering‐Junghans Max Thomas Dr. Alexander Villinger Prof. Dr. Axel Schulz 《Chemistry (Weinheim an der Bergstrasse, Germany)》2015,21(18):6713-6717
This work describes the synthesis and full characterization of elusive chloropnictenium ion salts of the type [RAr*N(SiMe)ECl][A] (RAr*=2,6‐(CHPh2)‐4‐R‐C6H2, R=Me, tBu; E=Sb, Bi; A?=GaCl4, Al(OCH(CF3)2)4). In these species the cation is significantly stabilized by weak arene interactions to flanking phenyl groups of the RAr* moiety. In this context the bonding situation has been studied by computational means and the reactivity towards the Lewis base 4‐dimethylaminopyridine (dmap) was investigated. 相似文献
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Britta Schmitt Boris N. Khoromskij Venera Khoromskaia Volker Schulz 《Numerical Linear Algebra with Applications》2022,29(1):e2404
We introduce the tensor numerical method for solving optimal control problems that are constrained by fractional two- (2D) and three-dimensional (3D) elliptic operators with variable coefficients. We solve the governing equation for the control function which includes a sum of the fractional operator and its inverse, both discretized over large 3D spacial grids. Using the diagonalization of the arising matrix-valued functions in the eigenbasis of the one-dimensional Sturm–Liouville operators, we construct the rank-structured tensor approximation with controllable precision for the discretized fractional elliptic operators and the respective preconditioner. The right-hand side in the constraining equation (the optimal design function) is supposed to be represented in a form of a low-rank canonical tensor. Then the equation for the control function is solved in a tensor structured format by using preconditioned CG iteration with the adaptive rank truncation procedure that also ensures the accuracy of calculations, given an -threshold. This method reduces the numerical cost for solving the control problem to (plus the quadratic term with a small weight), which outperforms traditional approaches with complexity in the 3D case. The storage for the representation of all 3D nonlocal operators and functions involved is also estimated by . This essentially outperforms the traditional methods operating with fully populated matrices and vectors in . Numerical tests for 2D/3D control problems indicate the almost linear complexity scaling of the rank truncated preconditioned conjugate gradient iteration in the univariate grid size n. 相似文献
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René Schulz 《偏微分方程通讯》2017,42(5):703-730
We prove that Hörmander’s global wave front set and Nakamura’s homogeneous wave front set of a tempered distribution coincide. In addition, we construct a tempered distribution with a given wave front set, and we develop a pseudodifferential calculus adapted to Nakamura’s homogeneous wave front set. 相似文献
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Prof. Dr. Tunga Salthammer Friederike Monegel Nicole Schulz Dr. Erik Uhde Prof. Dr. Stefan Grimme Jakob Seibert Prof. Dr. Uwe Hohm Dr. Wolf-Ulrich Palm 《Chemistry (Weinheim an der Bergstrasse, Germany)》2021,27(3):1046-1056
The chemical background of olfactory perception has been subject of intensive research, but no available model can fully explain the sense of smell. There are also inconsistent results on the role of the isotopology of molecules. In experiments with human subjects it was found that the isotope effect is weak with acetone and D6-acetone. In contrast, clear differences were observed in the perception of octanoic acid and D15-octanoic acid. Furthermore, a trained sniffer dog was initially able to distinguish between these isotopologues of octanoic acid. In chromatographic measurements, the respective deuterated molecule showed weaker interaction with a non-polar liquid phase. Quantum chemical calculations give evidence that deuterated octanoic acid binds more strongly to a model receptor than non-deuterated. In contrast, the binding of the non-deuterated molecule is stronger with acetone. The isotope effect is calculated in the framework of statistical mechanics. It results from a complicated interplay between various thermostatistical contributions to the non-covalent free binding energies and it turns out to be very molecule-specific. The vibrational terms including non-classical zero-point energies play about the same role as rotational/translational contributions and are larger than bond length effects for the differential isotope perception of odor for which general rules cannot be derived. 相似文献