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Kleer  Pieter  Schäfer  Guido 《Mathematical Programming》2021,190(1-2):523-560
Mathematical Programming - We study the computation and efficiency of pure Nash equilibria in combinatorial congestion games, where the strategies of each player i are given by the binary vectors...  相似文献   
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Incorporation of small amounts of α-tocopherol (vitamin E) in blends with the cellobiose–triazole-linked atactic poly(4-methyl-1-pentene) (CB-aPMP) sugar–polyolefin conjugate can be used to exert external control over thermotropic phase behavior and provide access to non-canonical soft matter Frank–Kasper A15 and σ phases. These results establish a paradigm that can be used for the further design and development of scalable quantities of soft matter FK phases of increased structural complexity and functional capability.  相似文献   
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A novel thiophene-bridged donor–acceptor system was synthesized with a carbazole as donor and a borole as acceptor unit. The borole group was successfully installed via the tin–boron exchange reaction of 1,1-dimethyl-2,3,4,5-tetraphenylstannole with 9-(5-(dibromoboryl)thiophen-2-yl)carbazole. The effect of the borole on the optoelectronic properties of the donor–acceptor system was explored by spectroscopic (UV/Vis and fluorescence spectroscopy), electrochemical (cyclic voltammetry) and theoretical (TD-DFT) methods as well as by modifying its structure. The corresponding donor–acceptor compound bearing the widely employed dimesitylboryl acceptor group was also synthesized for comparison.  相似文献   
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In this article we introduce a natural extension of the well-studied equation for harmonic maps between Riemannian manifolds by assuming that the target manifold is equipped with a connection that is metric but has non-vanishing torsion. Such connections have already been classified in the work of Cartan(1924).The maps under consideration do not arise as critical points of an energy functional leading to interesting mathematical challenges. We will perform a first mathematical analysis of these maps which we will call harmonic maps with torsion.  相似文献   
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In organic photovoltaics, porphyrins (PPs) are among the most promising compounds owing to their large absorption cross-section, wide spectral range, and stability. Nevertheless, a precise adjustment of absorption band positions to reach a full coverage of the so-called green gap has not been achieved yet. We demonstrate that a tuning of the PP Q- and Soret bands can be carried out by using a computational approach for which substitution patterns are optimized in silico. The most promising candidate structures were then synthesized. The experimental UV/Vis data for the solvated compounds were in excellent agreement with the theoretical predictions. By attaching further functionalities, which allow the use of PP chromophores as linkers for the assembly of metal-organic frameworks (MOFs), we were able to exploit packing effects resulting in pronounced redshifts, which allowed further optimization of the photophysical properties of PP assemblies. Finally, we use a layer-by-layer method to assemble the PP linkers into surface-mounted MOFs (SURMOFs), thus obtaining high optical quality, homogeneous and crystalline multilayer films. Experimental results are in full accord with the calculations, demonstrating the huge potential of computational screening methods in tailoring MOF and SURMOF photophysical properties.  相似文献   
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We extend the method of Pizzo multiscale analysis for resonances introduced in [5] in order to infer analytic properties of resonances and eigenvalues (and their eigenprojections) as well as estimates for the localization of the spectrum of dilated Hamiltonians and norm-bounds for the corresponding resolvent operators, in neighborhoods of resonances and eigenvalues. We apply our method to the massless Spin–Boson model assuming a slight infrared regularization. We prove that the resonance and the ground-state eigenvalue (and their eigenprojections) are analytic with respect to the dilation parameter and the coupling constant. Moreover, we prove that the spectrum of the dilated Spin–Boson Hamiltonian in the neighborhood of the resonance and the ground-state eigenvalue is localized in two cones in the complex plane with vertices at the location of the resonance and the ground-state eigenvalue, respectively. Additionally, we provide norm-estimates for the resolvent of the dilated Spin–Boson Hamiltonian near the resonance and the ground-state eigenvalue. The topic of analyticity of eigenvalues and resonances has let to several studies and advances in the past. However, to the best of our knowledge, this is the first time that it is addressed from the perspective of Pizzo multiscale analysis. Once the multiscale analysis is set up our method gives easy access to analyticity: Essentially, it amounts to proving it for isolated eigenvalues only and use that uniform limits of analytic functions are analytic. The type of spectral and resolvent estimates that we prove are needed to control the time evolution including the scattering regime. The latter will be demonstrated in a forthcoming publication. The introduced multiscale method to study spectral and resolvent estimates follows its own inductive scheme and is independent (and different) from the method we apply to construct resonances.  相似文献   
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We study isometric embeddings of a Euclidean space or a Heisenberg group into a higher dimensional Heisenberg group, where both the source and target space are equipped with an arbitrary left-invariant homogeneous distance that is not necessarily sub-Riemannian. We show that if all infinite geodesics in the target are straight lines, then such an embedding must be a homogeneous homomorphism. We discuss a necessary and certain sufficient conditions for the target space to have this ‘geodesic linearity property’, and we provide various examples.  相似文献   
10.
The multicomponent assembly of pharmaceutically relevant N‐aryl‐oxazolidinones through the direct insertion of carbon dioxide into readily available anilines and dibromoalkanes is described. The addition of catalytic amounts of an organosuperbase such as Barton's base enables this transformation to proceed with high yields and exquisite substrate functional‐group tolerance under ambient CO2 pressure and mild temperature. This report also provides the first proof‐of‐principle for the single‐operation synthesis of elusive seven‐membered ring cyclic urethanes.  相似文献   
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