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91.
92.
93.
The C. Neumann system describes a particle on the sphere S
n
under the influence of a potential that is a quadratic form. We study the case that the quadratic form has ℓ +1 distinct eigenvalues with multiplicity. Each group of m
σ
equal eigenvalues gives rise to an O(m
σ
)-symmetry in configuration space. The combined symmetry group G is a direct product of ℓ + 1 such factors, and its cotangent lift has an Ad*-equivariant momentum mapping. Regular reduction leads to the Rosochatius
system on S
ℓ
, which has the same form as the Neumann system albeit for an additional effective potential. 相似文献
94.
Let \((M,\Omega )\) be a connected symplectic 4-manifold and let \(F=(J,H) :M\rightarrow \mathbb {R}^2\) be a completely integrable system on M with only non-degenerate singularities. Assume that F does not have singularities with hyperbolic blocks and that \(p_1,\ldots ,p_n\) are the focus–focus singularities of F. For each subset \(S=\{i_1,\ldots ,i_j\}\), we will show how to modify F locally around any \(p_i, i \in S\), in order to create a new integrable system \(\widetilde{F}=(J, \widetilde{H}) :M \rightarrow \mathbb {R}^2\) such that its classical spectrum \(\widetilde{F}(M)\) contains j smooth curves of singular values corresponding to non-degenerate transversally hyperbolic singularities of \(\widetilde{F}\). Moreover the focus–focus singularities of \(\widetilde{F}\) are precisely \(p_i\), \(i \in \{1,\ldots ,n\} \setminus S\). The proof is based on Eliasson’s linearization theorem for non-degenerate singularities, and properties of the Hamiltonian Hopf bifurcation. 相似文献
95.
The reaction matrix of a cavity with attached waveguides connects scattering properties to properties of a corresponding closed billiard for which the waveguides are cut off by straight walls. On the one hand, this matrix is directly related to the S-matrix, on the other hand it can be expressed by a spectral sum over all eigenfunctions of the closed system. However, in the physically relevant situation where these eigenfunctions vanish on the impenetrable boundaries of the closed billiard, the spectral sum for the reaction matrix, as it was used before, fails to converge and does not reliably reproduce the scattering properties. We derive here a convergent representation of the reaction matrix in terms of eigenmodes satisfying Dirichlet boundary conditions and demonstrate its validity in the rectangular and the Sinai billiards. 相似文献
96.
We present a new bound for suprema of a special type of chaos process indexed by a set of matrices, which is based on a chaining method. As applications we show significantly improved estimates for the restricted isometry constants of partial random circulant matrices and time‐frequency structured random matrices. In both cases the required condition on the number m of rows in terms of the sparsity s and the vector length n is m ? s log2 s log2 n. © 2014 Wiley Periodicals, Inc. 相似文献
97.
Richard Kueng Holger Rauhut Ulrich Terstiege 《Applied and Computational Harmonic Analysis》2017,42(1):88-116
We study the recovery of Hermitian low rank matrices from undersampled measurements via nuclear norm minimization. We consider the particular scenario where the measurements are Frobenius inner products with random rank-one matrices of the form for some measurement vectors , i.e., the measurements are given by . The case where the matrix to be recovered is of rank one reduces to the problem of phaseless estimation (from measurements ) via the PhaseLift approach, which has been introduced recently. We derive bounds for the number m of measurements that guarantee successful uniform recovery of Hermitian rank r matrices, either for the vectors , , being chosen independently at random according to a standard Gaussian distribution, or being sampled independently from an (approximate) complex projective t-design with . In the Gaussian case, we require measurements, while in the case of 4-designs we need . Our results are uniform in the sense that one random choice of the measurement vectors guarantees recovery of all rank r-matrices simultaneously with high probability. Moreover, we prove robustness of recovery under perturbation of the measurements by noise. The result for approximate 4-designs generalizes and improves a recent bound on phase retrieval due to Gross, Krahmer and Kueng. In addition, it has applications in quantum state tomography. Our proofs employ the so-called bowling scheme which is based on recent ideas by Mendelson and Koltchinskii. 相似文献
98.
99.
Kamil J. Kuder Magdalena Kotaska Katarzyna Szczepaska Kamil Mika David Reiner-Link Holger Stark Katarzyna Kie-Kononowicz 《Molecules (Basel, Switzerland)》2021,26(8)
In an attempt to find new dual acting histamine H3 receptor (H3R) ligands, we designed a series of compounds, structurally based on previously described in our group, a highly active and selective human histamine H3 receptor (hH3R) ligand KSK63. As a result, 15 obtained compounds show moderate hH3R affinity, the best being the compound 17 (hH3R Ki = 518 nM). Docking to the histamine H3R homology model revealed two possible binding modes, with key interactions retained in both cases. In an attempt to find possible dual acting ligands, selected compounds were tested for antioxidant properties. Compound 16 (hH3R Ki = 592 nM) showed the strongest antioxidant properties at the concentration of 10−4 mol/L. It significantly reduced the amount of free radicals presenting 50–60% of ascorbic acid activity in the 2,2-diphenyl-1-picrylhydrazyl (DPPH) assay, as well as showed antioxidative properties in the ferric reducing antioxidant power (FRAP) assay. Despite the yet unknown antioxidation mechanism and moderate hH3R affinity, 16 (QD13) constitutes a starting point for the search of potential dual acting H3R ligands-promising tools for the treatment of neurological disorders associated with increased neuronal oxidative stress. 相似文献
100.