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We also compute the Euler characteristic of the space of partial flags containingnt and give a connection with hyperplane arrangements.
      
Then theG0-orbit structure ofZ is described explicitly by the partial Cayley transforms of a certain hermitian symmetric sub-flagF?Z.
      
Semi-invariants of quivers can be constructed by taking admissible partial polarizations of the determinant of matrices containing sums of matrix components of the representation and the identity matrix as blocks.
      
We define a partial order on the set No,c of pairs (O,C), where O is a nilpotent orbit and C is a conjugacy class in A(O), Lusztig's canonical quotient of A(O).
      
We also give formulas for intersection pairings on resolutions of singularities (or more precisely partial resolutions, since orbifold singularities are allowed) of the quotients.
      
Intersection pairings on singular moduli spaces of bundles over a Riemann surface and their partial desingularisations
      
Partial sums of orthonormal bases preserving positivity-And martingales
      
We characterize, for finite measure spaces, those orthonormal bases with the following positivity property: if f is a non-negative function, then the partial sums in the expansion of f are non-negative.
      
The bases are necessarily generalized Haar functions and the partial sums are a martingale closed on the right by f.
      
As applications, we prove a partial converse of a well-known result of Nagel et al.
      
We study the analogs of some of the classical partial differential equations with Δ playing the role of the usual Laplacian.
      
Using methods developed for phase retrieval problems, we give here a partial answer for some classes of time limited (compactly supported) signals.
      
We give a partial positive answer to a problem posed by Coifman et al.
      
The low-frequency terms in the expansion involve an independent fractional Brownian motion evaluated at discrete times or, alternatively, partial sums of a stationary fractional ARIMA time series.
      
Some applications are given to control theory for partial differential equations.
      
The Carleson operator is closely related to the maximal partial sum operator for Fourier series.
      
The Banach envelopes of Besov and Triebel-Lizorkin spaces and applications to partial differential equations
      
The arclengths of the graphs Γ(sN(f)) of the partial sums sN(f) of the Fourier series of a piecewise smooth function f with a jump discontinuity grow at the rate O(logN).
      
A partial differential equation from polymer science is shown to be solvable using the operational properties of the Euclidean-group Fourier transform.
      
Connections to signal recovery for positive functions, as well as partial spectral analysis, are also discussed.
      
 

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