In this paper we propose a general coorbit space theory suitable to define coorbits of quasi-Banach spaces using an abstract continuous frame, indexed by a locally compact Hausdorff space, and an associated generalized voice transform. The proposed theory realizes a further step in the development of a universal abstract theory towards various function spaces and their atomic decompositions which has been initiated by Feichtinger and Gröchenig in the late 1980s. We combine the recent approaches in Rauhut and Ullrich (J Funct Anal 260(11):3299–3362, 2011) and Rauhut (Stud Math 180(3):237–253, 2007) to identify, in particular, various inhomogeneous (quasi-Banach) spaces of Besov–Lizorkin–Triebel type. To prove the potential of our new theory we apply it to spaces with variable smoothness and integrability which have attracted significant interest in the last 10 years. From the abstract discretization machinery we obtain atomic decompositions as well as wavelet frame isomorphisms for these spaces. 相似文献
A set of vertices of a graph is locating if every two distinct vertices outside have distinct neighbors in ; that is, for distinct vertices and outside , , where denotes the open neighborhood of . If is also a dominating set (total dominating set), it is called a locating-dominating set (respectively, locating-total dominating set) of . A graph is twin-free if every two distinct vertices of have distinct open and closed neighborhoods. It is conjectured (Garijo et al., 2014 [15]) and (Foucaud and Henning, 2016 [12]) respectively, that any twin-free graph without isolated vertices has a locating-dominating set of size at most one-half its order and a locating-total dominating set of size at most two-thirds its order. In this paper, we prove these two conjectures for the class of line graphs. Both bounds are tight for this class, in the sense that there are infinitely many connected line graphs for which equality holds in the bounds. 相似文献
The relaxation of slightly poly-disperse linear flexible polymers has been expressed in a simplified blending rule which is presumed to be a weighted linear superposition of the relaxation spectra of mono-disperse components which constitute the blend. Discrete components are characterized by their molecular weight Mi,weight fraction wi,and relaxation time spectrum Hi(). ). In contrast to broadly distributed blends in which the small molecules mobilize the large ones and vice versa, we introduce the term slightly polydisperse for blends with molecular weight distributions narrow enough to have very little change in the longest relaxation times of each molecular weight component. The properties of this blending rule are analyzed and dynamic data is calculated for slightly poly-disperse polystyrene. As an application, the blending rule is used to determine the characteristic mono-disperse parameters (BSW parameters) of two materials, poly (vinyl methyl ether) and polycarbonate, for which we could not determine their BSW parameters directly since they were not available in nearly monodisperse form. The proposed blending rule can only be applied to systems in which all components are above the entanglement molecular weight, i.e. MiMc.Dedicated to the memory of Professor Tasos C. Papanastasiou 相似文献
The drag of a sphere at highRe can be reduced to more than half its value by passive ventilation from the stagnation region to the base. Simultaneously, the flow field around the base is stabilized and made symmetric, leading to reduction of unsteady aerodynamic forces. At highRe, the vent flow breaks through the dead water region associated with the near wake and aerodynamically streamlines the base. The streamlining is done by virtue of a base-vortex-ring beyond the point of turbulent boundary layer separation. A mean flow model for the flow around the vented sphere is proposed.Smoke flow visualized on a laser light screen placed at two diameters behind the base of the sphere shows the effectiveness of the method in suppressing the flow oscillations.The drag reduction achieved is very sensitive to the quality of the external surface and relatively insensitive to disturbances in the internal flow. Surface roughness or boundary layer tripping wire on the external flow can completely offset the benefit obtained. 相似文献
Electro-rheological suspensions (ERS) are known to undergo liquid-to-solid transition under the application of an electric
field. Long-range interaction between neighboring particles results in sample-spanning particulate structures which behave
as soft solids. Here, we studied the rheological expression of this field-induced transition which has many similarities with
chemical gelation. This similarity shows in mechanical spectroscopy on a suspension of monodisperse silica in PDMS as model
ERS. Upon application of the electric field, dynamic moduli G′, G′′ grow by orders of magnitude and evolve in a pattern which is otherwise typical for gelation of network polymers (random
chemical or physical gelation). At the gel point, the slow dynamics is governed by power-law relaxation behavior (frequency-independent
tan δ). A low field strength is sufficient to reach the gel point and, correspondingly, the percolating particle structure
at the gel point is still very fragile. It can be broken by the imposition of low stress. For inducing a finite yield stress,
the field strength needs to be increased further until the long-range electrostatic interaction generates string-like particle
alignments which become clearly visible under the optical microscope. The onset of fragile connectivity was defined experimentally
by the tan δ method. The ERS was probed dynamically at low frequencies where the transition is most pronounced, and also in
steady shear where the rate of structure formation equals the rate of internal breaking.
Received: 1 May 2001 Accepted: 11 August 2001 相似文献
Microstructure heat exchangers have unique properties that make them useful for numerous scientific and industrial applications. The power transferred per unit volume is mainly a function of the distance between heat source and heat sink—the smaller this distance, the better the heat transfer. Another parameter governing for the heat transfer is the lateral characteristic dimension of the heat transfer structure; in the case of microchannels, this is the hydraulic diameter. Decreasing this characteristic dimension into the range of several 10s of micrometers leads to very high values for the heat transfer rate.
Another possible way of increasing the heat transfer rate of a heat exchanger is changing the flow regime. Microchannel devices usually operate within the laminar flow regime. By changing from microchannels to three dimensional structures, or to planar geometries with microcolumn arrays, a significant increase of the heat transfer rate can be achieved.
Microheat exchangers in the form of both microchannel devices (with different hydraulic diameters) and microcolumn array devices (with different microcolumn layouts) are presented and compared. Electrically heated microchannel devices are presented, and industrial applications are briefly described. 相似文献