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261.
We derive the order parameter equation which describes the evolution of spatio-temporal patterns close to the Bénard instability in a rotating large aspect ratio system for high Prandtl number fluids. Since this order parameter equation contains rather complicated nonlinear terms we present a model equation which can be obtained from the order parameter equation by suitable simplification of the nonlinearity. For this model equation we calculate the family of roll solutions and investigate their stability with respect to long scale instabilities and examine the onset of the Küppers-Lortz instability. Then we present spatiotemporal patterns which are obtained from a numerical evaluation of the model equation. 相似文献
262.
We obtain optimal bounds of order O(n
−1) for the rate of convergence to the semicircle law and to the Marchenko-Pastur law for the expected spectral distribution
functions of random matrices from the GUE and LUE, respectively.
Research supported by the DFG-Forschergruppe FOR 399/1. Partially supported by INTAS grant N 03-51-5018, by RFBR grant N 02-01-00233,
and by RFBR-DFG grant N 04-01-04000. 相似文献
263.
Helmut Friedrich 《Annales Henri Poincare》2007,8(5):817-884
We study formal expansions of asymptotically flat solutions to the static vacuum field equations which are determined by minimal
sets of freely specifyable data referred to as ‘null data’. These are given by sequences of symmetric trace free tensors at
space-like infinity of increasing order. They are 1 : 1 related to the sequences of Geroch multipoles. Necessary and sufficient
growth estimates on the null data are obtained for the formal expansions to be absolutely convergent. This provides a complete
characterization of all asymptotically flat solutions to the static vacuum field equations.
Submitted: October 26, 2006. Accepted: October 29, 2006. 相似文献
264.
The dyadic diaphony, introduced by Hellekalek and Leeb, is a quantitative measure for the irregularity of distribution of point sets in the unit-cube. In this paper we study the dyadic diaphony of digital nets over ℤ2. We prove an upper bound for the dyadic diaphony of nets and show that the convergence order is best possible. This follows from a relation between the dyadic diaphony and the
L2{\cal L}_2
discrepancy. In order to investigate the case where the number of points is small compared to the dimension we introduce the limiting dyadic diaphony, which is defined as the limiting case where the dimension tends to infinity. We obtain a tight upper and lower bound and we compare this result with the limiting dyadic diaphony of a random sample. 相似文献
265.
266.
267.
Friedrich Knop 《Mathematische Annalen》1993,295(1):333-363
Summary LetG be a reductive group defined over an algebraically closed fieldk and letX be aG-variety. In this paper we studyG-invariant valuationsv of the fieldK of rational functions onX. These objects are fundamental for the theory of equivariant completions ofX. LetB be a Borel subgroup andU the unipotent radical ofB. It is proved thatv is uniquely determined by its restriction toK
U
. Then we study the set of invariant valuations having some fixed restrictionv
0, toK
B
. Ifv
0 is geometric (i.e., induced by a prime divisor) then this set is a polyhedron in some vector space. In characteristic zero we prove that this polyhedron is a simplicial cone and in fact the fundamental domain of finite reflection groupW
X
. Thus, the classification of invariant valuations is almost reduced to the classification of valuations ofK
B
.
Unterstützt durch den Schweizerischen Nationalfonds zur Förderung der wissenschaftlichen Forschung. 相似文献
268.
We provide analogues of Carathéodory's theorem for integer cones and apply our bounds to integer programming and to the cutting stock problem. In particular, we provide an NP certificate for the latter, whose existence has not been known so far. 相似文献
269.
270.
Let (G,u) be an Archimedean norm-complete dimension group with order-unit. Continuing a previous paper, we study intervals (i.e., nonempty upward directed lower subsets) of G which are closed with respect to the canonical norm of (G,u). In particular, we establish a canonical one-to-one correspondence between closed intervals of G and certain affine lower semicontinuous functions on the state space of (G,u), which allows us to solve several problems of K. R. Goodearl about inserting affine continuous functions between convex upper semicontinuous and concave lower semicontinuous functions. This yields in turn new results about analogues of multiplier groups for norm-closed intervals. 相似文献