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991.
Block-diagonalization of sparse equivariant discretization matrices is studied. Such matrices typically arise when partial
differential equations that evolve in symmetric geometries are discretized via the finite element method or via finite differences.
By considering sparse equivariant matrices as equivariant graphs, we identify a condition for when block-diagonalization via
a sparse variant of a generalized Fourier transform (GFT) becomes particularly simple and fast.
Characterizations for finite element triangulations of a symmetric domain are given, and formulas for assembling the block-diagonalized
matrix directly are presented. It is emphasized that the GFT preserves symmetric (Hermitian) properties of an equivariant
matrix.
By simulating the heat equation at the surface of a sphere discretized by an icosahedral grid, it is demonstrated that the
block-diagonalization is beneficial. The gain is significant for a direct method, and modest for an iterative method.
A comparison with a block-diagonalization approach based upon the continuous formulation is made. It is found that the sparse
GFT method is an appropriate way to discretize the resulting continuous subsystems, since the spectrum and the symmetry are
preserved.
AMS subject classification (2000) 43A30, 65T99, 20B25 相似文献
992.
We prove both geometric ergodicity and regular variation of the stationary distribution for a class of nonlinear stochastic recursions that includes nonlinear AR-ARCH models of order 1. The Lyapounov exponent for the model, the index of regular variation and the spectral measure for the regular variation all are characterized by a simple two-state Markov chain. 相似文献
993.
Jing-na Li Xiao-feng Wang Zheng-an Yao 《应用数学学报(英文版)》2007,23(3):421-432
In this paper, we propose a model in studying soft ferromagnetic films, which is readily accessible experimentally. By using penalty approximation and compensated compactness, we prove that the dynamical equation in thin film has a local weak solution. Moreover, the corresponding linear equation is also dealt with in great detail. 相似文献
994.
A flow visualization of the two-dimensional rigid fling-clap motions of the flat-plate wing is performed to get the knowledge
of fling-clapping mechanism that might be employed by insects during flight. In this numerical visualization, the time-dependent
Navier-Stokes equations are solved for two types of wing motion; ‘fling followed by clap and pause motion’ and ‘cyclic fling-clapping
motion’. The result is observed regarding the main flow features such as the sequential development of the two families of
separation vortex pairs and their movement. For the ‘fling followed by clap and pause motion’, a strong separation vortex
pair of counterrotation develops in the opening between the wings in the fling phase and they then move out from the opening
in the following clap phase. For ‘the cyclic fling-clapping motion’, the separation vortex pair developed in the outside space
in the clap phase move into the opening in the following fling phase. The separation vortex pair in the opening developed
in the fling phase of the cyclic motion is observed to be stronger than those of the ‘fling followed by clap and pause motion’.
Regarding the strong fling separation vortex and the weak clap separation vortex above it in the opening, the flow pattern
of the fling phase of the cyclic fling and clap motion is different to that of the fling phase of the first cycle. The flow
pattern of the third cycle of the cyclic fling-clapping motion is observed to be almost same as that of the second cycle.
Therefore, a periodicity of the flow pattern is established after the second cycle. 相似文献
995.
D Shaw 《The Journal of the Operational Research Society》2006,57(7):830-841
Problem-structuring group workshops can be used in organizations as a consulting tool and as a research tool. One example of the latter is using a problem-structuring method (PSM) to help a group tackle an organizational issue; meanwhile, researchers collect the participants’ initial views, discussion of divergent views, the negotiated agreement, and the reasoning for outcomes emerging. Technology can help by supporting participants in freely sharing their opinions and by logging data for post-workshop analyses. For example, computers let participants share views anonymously and without being influenced by others (as well as logging those views), and video-cameras can record discussions and intra-group dynamics. This paper evaluates whether technology-supported Journey Making workshops can be effective research tools that can capture quality research data when compared against theoretical performance benchmarks and other qualitative research tools. 相似文献
996.
S. S. Dragomir Y. J. Cho S. S. Kim J. Roumeliotis 《Journal of Applied Mathematics and Computing》2006,20(1-2):279-292
A reverse of Bessel’s inequality in 2-inner product spaces and companions of Grüss inequality with applications for determinantal integral inequalities are given. 相似文献
997.
998.
Alexander Semenov Aurélia Charlot Rachel Auzély-Velty Marguerite Rinaudo 《Rheologica Acta》2007,46(5):541-568
Dynamics of associating polymer solutions above the reversible gelation point are studied. Each macromolecule consists of
a soluble backbone (B) and a small fraction of specific strongly interacting groups (A or C stickers) attached to B. A mixture
of B–A and B–C associating polymers with 1:1 stoichiometric ratio is considered. As a result of AC association, the polymers
reversibly gelate above the overlap concentration. It is shown that (1) the network strands are linear complexes (double chains)
of B–A and B–C; (2) “diffusion” of the network junction points is characterized by an apparent activation energy, which can
be significantly higher than the energy of one AC bond; (3) most importantly, the randomness of sticker distribution along
the chain can significantly slow down the network relaxation leading to a markedly non-Maxwellian viscoelastic behavior. The
theory elucidates the most essential features of rheological behavior of polysaccharide associating systems (with A = adamantyl
moiety, C = β-cyclodextrin, B = either chitosan or hyaluronan) including similar behavior of G
′ and G
″ in a wide frequency range, strong temperature dependence of the characteristic frequency ω
x
, and an extremely strong effect of added free stickers (fC) on the dynamics.
This paper was presented at Annual European Rheology Conference (AERC) held in Hersonisos, Crete, Greece, April 27–29, 2006. 相似文献
999.
Jing Ping YANG Shi Hong CHENG Xiao Qian WANG 《数学学报(英文版)》2007,23(3):467-478
This paper investigates bivariate recursive equations on excess-of-loss reinsurance. For an insurance portfolio, under the assumptions that the individual claim severity distribution has bounded continuous density and the number of claims belongs to R1 (a, b) family, bivariate recursive equations for the joint distribution of the cedent's aggregate claims and the reinsurer's aggregate claims are obtained. 相似文献
1000.
Meghan Griffith 《Acta Analytica》2007,22(1):16-28
In this paper, I argue that trying is the locus of freedom and moral responsibility. Thus, any plausible view of free and
responsible action must accommodate and account for free tryings. I then consider a version of agent causation whereby the
agent directly causes her tryings. On this view, the agent is afforded direct control over her efforts and there is no need
to posit—as other agent-causal theorists do—an uncaused event. I discuss the potential advantages of this sort of view, and
its challenges. 相似文献