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981.
C. Carstensen. 《Mathematics of Computation》2004,73(247):1153-1165
All first-order averaging or gradient-recovery operators for lowest-order finite element methods are shown to allow for an efficient a posteriori error estimation in an isotropic, elliptic model problem in a bounded Lipschitz domain in . Given a piecewise constant discrete flux (that is the gradient of a discrete displacement) as an approximation to the unknown exact flux (that is the gradient of the exact displacement), recent results verify efficiency and reliability of
in the sense that is a lower and upper bound of the flux error up to multiplicative constants and higher-order terms. The averaging space consists of piecewise polynomial and globally continuous finite element functions in components with carefully designed boundary conditions. The minimal value is frequently replaced by some averaging operator applied within a simple post-processing to . The result provides a reliable error bound with .
in the sense that is a lower and upper bound of the flux error up to multiplicative constants and higher-order terms. The averaging space consists of piecewise polynomial and globally continuous finite element functions in components with carefully designed boundary conditions. The minimal value is frequently replaced by some averaging operator applied within a simple post-processing to . The result provides a reliable error bound with .
This paper establishes and so equivalence of and . This implies efficiency of for a large class of patchwise averaging techniques which includes the ZZ-gradient-recovery technique. The bound established for tetrahedral finite elements appears striking in that the shape of the elements does not enter: The equivalence is robust with respect to anisotropic meshes. The main arguments in the proof are Ascoli's lemma, a strengthened Cauchy inequality, and elementary calculations with mass matrices.
982.
Julien Bichon 《Algebras and Representation Theory》2004,7(4):343-362
Let A be a compact quantum group, let nN
* and let A
aut(X
n
) be the quantum permutation group on n letters. A free wreath product construction A*w
A
aut(X
n
) is introduced. This construction provides new examples of quantum groups, and is useful to describe the quantum automorphism group of the n-times disjoint union of a finite connected graph. 相似文献
983.
ShaoJiFENG DeXingFENG 《数学学报(英文版)》2004,20(6):1057-1072
For wave equations with variable coefficients on regions which are not necessarily smooth, we study the energy decay rate when a nonlinear damping is applied on a suitable subrigion. 相似文献
984.
Zhi-Hui Geng Pu-Kun Liu 《International Journal of Infrared and Millimeter Waves》2004,25(7):1133-1142
The beam-wave interaction in a Ka-band, two-cavity fundamental gyroklystron amplifier is studied by using a self-consistent nonlinear simulation code. The electron efficiency for this gyroklystron amplifier is calculated, and the effect of various parameters, such as beam voltage, beam current, electron guiding center radius, velocity pitch ratio and drift tube length on the electron efficiency is discussed in detail. 相似文献
985.
A theorem proved by R. Høegh-Krohn in Comm. Math. Phys. 38(1974), 195–224, which yields a possibility to define states of systems of quantum particles by their values on the products
, where \mathfraka
t
, t
are time automorphisms and F
j
are multiplication operators, is generalized and extended. In particular, it is shown that the algebras generated by such products with F
j
taken from the families of multiplication operators satisfying certain conditions are dense in the algebras of observables in the -weak topology, in which normal states are continuous. This result was obtained for the systems with two types of kinetic energy: the usual one expressed by means of the Laplacian; the relativistic kinetic energy defined by a pseudo-differential operator. 相似文献
986.
987.
For two covariant differential *-calculi, the twisted cyclic cocycle associated with the volume form is represented in terms of commutators
for some self-adjoint operator
and some *-representation of the underlying *-algebra. 相似文献
988.
It is known that the Whittaker functions w(q) associated with the group GL(N) are eigenfunctions of the Hamiltonians of the open Toda chain, hence satisfy a set of differential equations in the Toda variables q
i
. Using the expression of the q
i
for the closed Toda chain in terms of Sklyanin variables
i
, and the known relations between the open and the closed Toda chains, we show that Whittaker functions also satisfy a set of new difference equations in
i
. 相似文献
989.
Based on the ansatz to the wave functions, the quasi-exact solutions of the 2D Schrödinger equation with some anharmonic potentials are reviewed and analyzed if admitting restrictions on the parameters of the potential and the angular momentum m. These potentials are taken as the screened Coulomb potential V(r)=a/r+b/(r+), the singular one-fraction power one V(r)=ar
–1/2+br
–3/2 and the singular two-fraction one V(r)=ar
2/3+br
–2/3+cr
–4/3. The latter one is found that the hidden symmetry exists if substituting r–ir. It will reverse the signs of E and c of quantum system, leaving the remaining parameters invariant. 相似文献
990.
I. V. Avilov É. I. Zen'kevich I. V. Filatov A. M. Shul'ga 《Journal of Applied Spectroscopy》2003,70(2):257-264
Quantum-chemical investigation of the electronic structure and properties of the excited states of porphyrin dimers, in which monomeric subunits are linked by the phenyl spacer, is performed by semiempirical methods. The molecular orbitals of the monomeric subunits are shown to interact with each other via molecular orbitals of the phenyl ring. Comparison of the experimental absorption data and quantum-chemical calculations of electronic absorption spectra for different conformations of Zn-tetraphenylporphyrin dimer is performed and the main conformation of the dimer in a solution at 295 K, in which the planes of tetrapyrrole macrocycles are located at an angle of about 60°, is substantiated. 相似文献