35,762 research outputs found
On the Combinatorial Structure of Primitive Vassiliev Invariants, III - A Lower Bound
We prove that the dimension of the space of primitive Vassiliev invariants of
degree n grows - as n tends to infinity - faster than Exp(c Sqrt(n)) for any c
< Pi Sqrt (2/3).
The proof relies on the use of the weight systems coming from the Lie algebra
gl(N). In fact, we show that our bound is - up to multiplication with a
rational function in n - the best possible that one can get with gl(N)-weight
systems.Comment: 11 pages, 12 figure
Invariants for E_0-semigroups on II_1 factors
We introduce four new cocycle conjugacy invariants for E_0-semigroups on II_1
factors: a coupling index, a dimension for the gauge group, a super product
system and a C*-semiflow. Using noncommutative It\^o integrals we show that the
dimension of the gauge group can be computed from the structure of the additive
cocycles. We do this for the Clifford flows and even Clifford flows on the
hyperfinite II_1 factor, and for the free flows on the free group factor
. In all cases the index is 0, which implies they have trivial
gauge groups. We compute the super product systems for these families and,
using this, we show they have trivial coupling index. Finally, using the
C*-semiflow and the boundary representation of Powers and Alevras, we show that
the families of Clifford flows and even Clifford flows contain infinitely many
mutually non-cocycle-conjugate E_0-semigroups.Comment: 51 page
Guide to Spectral Proper Orthogonal Decomposition
This paper discusses the spectral proper orthogonal decomposition and its use in identifying modes, or structures, in flow data. A specific algorithm based on estimating the cross-spectral density tensor with Welch’s method is presented, and guidance is provided on selecting data sampling parameters and understanding tradeoffs among them in terms of bias, variability, aliasing, and leakage. Practical implementation issues, including dealing with large datasets, are discussed and illustrated with examples involving experimental and computational turbulent flow data
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