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51.
52.
Andreas Tittl Aurelian John‐Herpin Aleksandrs Leitis Eduardo R. Arvelo Hatice Altug 《Angewandte Chemie (International ed. in English)》2019,58(42):14810-14822
Molecular spectroscopy provides unique information on the internal structure of biological materials by detecting the characteristic vibrational signatures of their constituent chemical bonds at infrared frequencies. Nanophotonic antennas and metasurfaces have driven this concept towards few‐molecule sensitivity by confining incident light into intense hot spots of the electromagnetic fields, providing strongly enhanced light‐matter interaction. In this Minireview, recently developed molecular biosensing approaches based on the combination of dielectric metasurfaces and imaging detection are highlighted in comparison to traditional plasmonic geometries, and the unique potential of artificial intelligence techniques for nanophotonic sensor design and data analysis is emphasized. Because of their spectrometer‐less operation principle, such imaging‐based approaches hold great promise for miniaturized biosensors in practical point‐of‐care or field‐deployable applications. 相似文献
53.
We consider interpolation on a finite uniform grid by means of one of the radial basis functions (RBF) φ(r)=rγ for γ>0, γ2
or φ(r)=rγ ln r for γ2
+. For each positive integer N, let h=N−1 and let {xi: i =1, 2, …, (N+1)d} be the set of vertices of the uniform grid of mesh-size h on the unit d-dimensional cube [0, 1]d. Given f: [0, 1]d→
, let sh be its unique RBF interpolant at the grid vertices: sh(xi)=f(xi), i=1, 2, …, (N+1)d. For h→0, we show that the uniform norm of the error f−sh on a compact subset K of the interior of [0, 1]d enjoys the same rate of convergence to zero as the error of RBF interpolation on the infinite uniform grid h
d, provided that f is a data function whose partial derivatives in the interior of [0, 1]d up to a certain order can be extended to Lipschitz functions on [0, 1]d. 相似文献
54.
We give a proof of the realization theorem of N.J. Young which states that analytic functions which are symbols of bounded Hankel operators admit par-balanced realizations. The main tool used in this proof is the induced Hilbert spaces and a lifting lemma of Kreîn-Reid-Lax-Dieudonné. Alternatively one can use the Loewner inequality. A short proof of the uniqueness of par-balanced realizations is included. As an application, it is proved that par-balanced realizations of real symmetric transfer functions areJ-self-adjoint.Research supported in part by the Romanian Academy grant GAR-6645/1996.This research was supported in part by NSF grant DMS-9501223. 相似文献
55.
The Markovian time evolution of the entropy production rate is studied as a measure of irreversibility generated in a bipartite quantum system consisting of two coupled bosonic modes immersed in a common thermal environment. The dynamics of the system is described in the framework of the formalism of the theory of open quantum systems based on completely positive quantum dynamical semigroups, for initial two-mode squeezed thermal states, squeezed vacuum states, thermal states and coherent states. We show that the rate of the entropy production of the initial state and nonequilibrium stationary state, and the time evolution of the rate of entropy production, strongly depend on the parameters of the initial Gaussian state (squeezing parameter and average thermal photon numbers), frequencies of modes, parameters characterising the thermal environment (temperature and dissipation coefficient), and the strength of coupling between the two modes. We also provide a comparison of the behaviour of entropy production rate and Rényi-2 mutual information present in the considered system. 相似文献
56.
57.
Ciprian Preda Petre Preda Aurelian Craciunescu 《Journal of Mathematical Analysis and Applications》2012,385(1):572-581
We point out versions of a well-known theorem of R. Datko for nonuniform exponential contractions. More precisely, we obtain theorems that characterize the nonuniform exponential stability and the nonuniform exponential dichotomy for nonuniform exponential contractions. Thus, we generalize the results in Datko (1972) [8] and Preda and Megan (1985) [14]. 相似文献
58.
We prove that a generalized version, essentially obtained by R.M. Loynes, of the B. Sz.-Nagy??s Dilation Theorem for ${\mathcal{B}^*(\mathcal{H})}$ -valued (here ${\mathcal{H}}$ is a VH-space in the sense of Loynes) positive semidefinite maps on *-semigroups is equivalent with a generalized version of the W.F. Stinespring??s Dilation Theorem for ${\mathcal{B}^*(\mathcal{H})}$ -valued completely positive linear maps on B *-algebras. This equivalence result is a generalization of a theorem of F.H. Szafraniec, originally proved for the case of operator valued maps (that is, when ${\mathcal{H}}$ is a Hilbert space). 相似文献
59.
We propose a general concept of triplet of Hilbert spaces with closed embeddings, instead of continuous ones, and we show how rather general weighted $L^2$ spaces yield this kind of generalized triplets of Hilbert spaces for which the underlying spaces and operators can be explicitly calculated. Then we show that generalized triplets of Hilbert spaces with closed embeddings can be naturally associated to any pair of Dirichlet type spaces $\mathcal{D }_\alpha (\mathbb{D }^N)$ of holomorphic functions on the unit polydisc $\mathbb{D }^N$ and we explicitly calculate the associated operators in terms of reproducing kernels and radial derivative operators. We also point out a rigging of the Hardy space $H^2(\mathbb{D }^N)$ through a scale of Dirichlet type spaces and Bergman type spaces. 相似文献
60.
Tudor Rosu Elena Pahontu Catalin Maxim Rodica Georgescu Nicolae Stanica Gabriela Laura Almajan Aurelian Gulea 《Polyhedron》2010
Coordination compounds of Cu(II), VO(II), Ni(II), and Mn(II) with the Schiff base obtained through the condensation of 4-amino-2,3-dimethyl-1-phenyl-3-pyrazolin-5-one with 3-formyl-6-methyl-chromone were synthesized. The characterization of the newly formed compounds was done by 1H NMR, UV–Vis, IR, ESR spectroscopy, elemental analysis and molar electric conductibility. The crystal structure of 1-phenyl-2,3-dimethyl-4-(N-3-formyl-6-methyl-chromone)-3-pyrazolin-5-one (HL) has been determined by X-ray diffraction studies, as well as the one of its copper(II) complex [CuL(OAc)]·CH3OH which contains an anionic ligand and an acetate in the coordination sphere of the metal. The single crystal X-ray structure for (HL) was analyzed for its various weak H-bonding and dimeric association. 相似文献