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11.
In this paper we consider a wavelet algorithm for the piecewise constant collocation method applied to the boundary element solution of a first kind integral equation arising in acoustic scattering. The conventional stiffness matrix is transformed into the corresponding matrix with respect to wavelet bases, and it is approximated by a compressed matrix. Finally, the stiffness matrix is multiplied by diagonal preconditioners such that the resulting matrix of the system of linear equations is well conditioned and sparse. Using this matrix, the boundary integral equation can be solved effectively. 相似文献
12.
In circuit-switched networks call streams are characterized by their mean and peakedness (two-moment method). The GI/M/C/0 system is used to model a single link, where the GI-stream is determined by fitting moments appropriately. For the moments of the overflow traffic of a GI/M/C/0 system there are efficient numerical algorithms available. However, for the moments of the freed carried traffic, defined as the moments of a virtual link of infinite capacity to which the process of calls accepted by the link (carried arrival process) is virtually directed and where the virtual calls get fresh exponential i.i.d. holding times, only complex numerical algorithms are available. This is the reason why the concept of the freed carried traffic is not used. The main result of this paper is a numerically stable and efficient algorithm for computing the moments of freed carried traffic, in particular an explicit formula for its peakedness. This result offers a unified handling of both overflow and carried traffics in networks. Furthermore, some refined characteristics for the overflow and freed carried streams are derived. 相似文献
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The finite-size corrections, central chargesc, and scaling dimensionsx of tricritical hard squares and critical hard hexagons are calculated analytically. This is achieved by solving the special functional equation or inversion identity satisfied by the commuting row transfer matrices of these lattice models at criticality. The results are expressed in terms of Rogers dilogarithms. For tricritical hard squares we obtainc=7/10,x=3/40, 1/5, 7/8, 6/5 and for hard hexagons we obtainc=4/5,x=2/15, 4/5, 17/15, 4/3, 9/5, in accord with the predictions of conformal and modular invariance. 相似文献
15.
Aspects of Generic Entanglement 总被引:4,自引:4,他引:0
Patrick Hayden Debbie W. Leung Andreas Winter 《Communications in Mathematical Physics》2006,265(1):95-117
We study entanglement and other correlation properties of random states in high-dimensional bipartite systems. These correlations
are quantified by parameters that are subject to the ``concentration of measure' phenomenon, meaning that on a large-probability
set these parameters are close to their expectation. For the entropy of entanglement, this has the counterintuitive consequence
that there exist large subspaces in which all pure states are close to maximally entangled. This, in turn, implies the existence
of mixed states with entanglement of formation near that of a maximally entangled state, but with negligible quantum mutual
information and, therefore, negligible distillable entanglement, secret key, and common randomness. It also implies a very
strong locking effect for the entanglement of formation: its value can jump from maximal to near zero by tracing over a number
of qubits negligible compared to the size of the total system. Furthermore, such properties are generic. Similar phenomena
are observed for random multiparty states, leading us to speculate on the possibility that the theory of entanglement is much
simplified when restricted to asymptotically generic states. Further consequences of our results include a complete derandomization
of the protocol for universal superdense coding of quantum states. 相似文献
16.
We investigate an operator renormalization group method to extract and describe the relevant degrees of freedom in the evolution of partial differential equations. The proposed renormalization group approach is formulated as an analytical method providing the fundamental concepts of a numerical algorithm applicable to various dynamical systems. We examine dynamical scaling characteristics in the short-time and the long-time evolution regime providing only a reduced number of degrees of freedom to the evolution process. 相似文献
17.
Andreas Speiser 《Monatshefte für Mathematik》1939,48(1):240-244
Ohne Zusammenfassung 相似文献
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Selecting, modifying or creating appropriate problems for mathematics class has become an activity of increaing importance in the professional development of German mathematics teachers. But rather than asking in general: “What is a good problem?” there should be a stronger emphasis on considering the specific goal of a problem, e.g.: “What are the ingredients that make a problem appropriate for initiating a learning process” or “What are the characteristics that make a problem appropriate for its use in a central test?” We propose a guiding scheme for teachers that turns out to be especially helpful, since the newly introduced orientation on outcome standards a) leads to a critical predominance of test items and b) expects teachers to design adequate problems for specific learning processes (e.g. problem solving, reasoning and modelling activities). 相似文献