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21.
Jorgensen and Pedersen have proven that a certain fractal measure ν has no infinite set of complex exponentials which form an orthonormal set in L2(ν). We prove that any fractal measure μ obtained from an affine iterated function system possesses a sequence of complex exponentials which forms a Riesz basic sequence, or more generally a Bessel sequence, in L2(μ) such that the frequencies have positive Beurling dimension. 相似文献
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Integrating logical constraints into optimal control problems is not an easy task. In fact, optimal control problems are usually continuous while logical constraints are naturally expressed by integer (binary) variables. In this article we are interested is a particular form of an LQR optimal control problem: the energy (control L2 norm) is to be minimized, system dynamic is linear and logical constraints on the control use are to be fulfilled. Even if the starting continuous problem is not a complicated one, difficulties arise when integrating the additional logical constraints. First, we will present two different ways of modeling the problem, both of them leading us to Mixed Integer Problems. Furthermore, algorithms (Generalized Outer Approximation, Benders Decomposition and Branch and Cut) are applied on each model and results analyzed. We also present a Benders Decomposition algorithm variant that is adapted to our problem (taking into account its particular form) and we will conclude by looking at the optimal solutions obtained in an interesting physical example: the harmonic spring. 相似文献
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Dorin Ervin Dutkay 《Transactions of the American Mathematical Society》2006,358(12):5271-5291
We analyze representations of the Baumslag Solitar group that admit wavelets and show how such representations can be constructed from a given low-pass filter. We describe the direct integral decomposition for some examples and derive from it a general criterion for the existence of solutions for scaling equations. As another application, we construct a Fourier transform for some Hausdorff measures.
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Belhachmi Zakaria; Bucur Dorin; Sac-Epee Jean-Marc 《IMA Journal of Numerical Analysis》2006,26(4):790-810
** Email: belhach{at}poncelet.univ-metz.fr*** Email: bucur{at}math.univ-metz.fr**** Email: jmse{at}math.univ-metz.fr We study the NeumannLaplacian eigenvalue problem in domainswith multiple cracks. We derive a mixed variational formulationwhich holds on the whole geometric domain (including the cracks)and implements efficient finite-element discretizations forthe computation of eigenvalues. Optimal error estimates aregiven and several numerical examples are presented, confirmingthe efficiency of the method. As applications, we numericallyinvestigate the behaviour of the low eigenvalues in domainswith a large number of cracks. 相似文献
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Summary Defensins are small cationic peptides involved in innate immunity and are components of the first line of defence against invading pathogens. β-defensins are a subgroup of the defensin family that display a particular cysteine spacing and pattern of intramolecular bonding. These molecules are produced mostly by epithelia lining exposed surfaces and appear to have both antimicrobial and cell signalling functions. The unusually high degree of sequence variation in the mature peptide produced by the paralogous and in some cases orthologous genes implies extensive specialisation and species specific adaptation. Here we review recent functional data that are an important addition to our knowledge of the innate immune response and novel antibiotic design. We also consider the organisation and evolution of the genomic loci harbouring these genes where radical and rapid changes in β-defensin sequences have been shown to result from the interplay of both positive and negative selection. Consequently these genes provide some unusually clear glimpses of the processes of duplication and specialisation that have shaped the mammalian genome. 相似文献
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The object of the present study is to design a methodology to follow the kinetics of T1 precipitation, in an AA2198 alloy, in terms of precipitate size, morphology (thickness, diameter) and volume fraction, during a two-temperature isothermal heat treatment. We used in situ small-angle X-ray scattering (SAXS) as a way to measure the evolution of the T1 mean thickness and diameter during the heat treatment. Transmission electron microscopy (TEM) was then performed in order to calibrate these evolutions. Furthermore, we demonstrate that the volume fraction evolution can be described successfully using a simple analysis of the differential scanning calorimetry (DSC) thermograms. The latter was calibrated by selected observations in high angular annular dark field scanning transmission electron microscopy (HAADF-STEM). Microstructure evolution during DSC heating ramps was analysed using in situ SAXS: the T1 phase transformation is found to consist in a two-step thickening process explained by two consecutive diffusion stages. The enthalpy of formation of the T1 phase is deduced from the DSC measurements. 相似文献
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