The \(\alpha \)-modulation transform is a time-frequency transform generated by square-integrable representations of the affine Weyl–Heisenberg group modulo suitable subgroups. In this paper we prove new conditions that guarantee the admissibility of a given window function. We also show that the generalized coorbit theory can be applied to this setting, assuming specific regularity of the windows. This then yields canonical constructions of Banach frames and atomic decompositions in \(\alpha \)-modulation spaces. In particular, we prove the existence of compactly supported (in time domain) vectors that are admissible and satisfy all conditions within the coorbit machinery, which considerably go beyond known results. 相似文献
We consider the heat flow of corotational harmonic maps from \(\mathbb {R}^3\) to the three-sphere and prove the nonlinear asymptotic stability of a particular self-similar shrinker that is not known in closed form. Our method provides a novel, systematic, robust, and constructive approach to the stability analysis of self-similar blowup in parabolic evolution equations. In particular, we completely avoid using delicate Lyapunov functionals, monotonicity formulas, indirect arguments, or fragile parabolic structure like the maximum principle. As a matter of fact, our approach reduces the nonlinear stability analysis of self-similar shrinkers to the spectral analysis of the associated self-adjoint linearized operators. 相似文献
In this paper, we will present some coupled fixed point theorems on a metric space endowed with two b-metrics. The approach is based on the application of a fixed point theorem for an appropriate operator on the Cartesian product of the given spaces. An application to a boundary value problem for a system of second order differential equations is also presented. 相似文献
We give a probabilistic numerical approach for the nonlinear Dirichlet problem associated with a branching process. Main tools are the probabilistic representation of the solution with the measure-valued branching process, as well as specific techniques for the numerical solution of linear partial differential equations, introduced and developed by Milstein and Tretyakov, and Monte Carlo methods. 相似文献
A reagentless third generation electrochemical glucose biosensor was fabricated based on wiring the template enzyme glucose oxidase (GOx) with graphene nanoribbons (GN) in order to create direct electron transfer between the co-factor (flavin adenine dinucleotide, FAD) and the electrode. The strategy involved: (i) isolation of the apo-enzyme by separating it from its co-enzyme; (ii) preparation of graphene nanoribbons (GN) by oxidative unzipping of multi-walled carbon nanotubes; (iii) adsorptive immobilization of GNs on the surface of a screen printed carbon electrode (SPCE); (iv) covalent attachment of FAD to the nanoribbons; (v) recombination of the apo-enzyme with the covalently bound FAD to the holoenzyme; and (vi) stabilization of the bio-layer with a thin membrane of Nafion. The biosensor (referred to as GN/FAD/apo-GOx/Nafion/SPCE) is operated at a potential of +0.475 V vs Ag/AgCl/{3 M KCl} in flow-injection mode with an oxygen-free phosphate buffer (pH 7.5) acting as a carrier. The signals are linearly proportional to the concentration of glucose in the range from 50 to 2000 mg?L?1 with a detection limit of 20 mg?L?1. The repeatability (10 measurements, at 1000 mg?L?1 glucose) is ±1.4% and the reproducibility (5 sensors, 1000 mg?L?1 glucose) is ±1.8%. The biosensor was applied to the determination of glucose in human serum.
Graphical abstract Wiring of the apo-enzyme of glucose oxidase (apo-GOx) with graphene nanoribbons (GN) bound to FAD at a screen-printed carbon electrode (SPCE). Cyclic voltammetric and amperometric responses to various glucose concentrations.
