New evidence for Green's conjecture on syzygies of canonical curves

We prove that two weakened forms of Green's conjectures for canonical curves are equivalent when the genus $g$ is odd.Comment: Tex-type: LaTe

Projective normality of flag varieties and Schubert varieties

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Some remarks on the instability flag

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Local Projections of Low-Momentum Potentials

Nuclear interactions evolved via renormalization group methods to lower resolution become increasingly non-local (off-diagonal in coordinate space) as they are softened. This inhibits both the development of intuition about the interactions and their use with some methods for solving the quantum many-body problem. By applying "local projections", a softened interaction can be reduced to a local effective interaction plus a non-local residual interaction. At the two-body level, a local projection after similarity renormalization group (SRG) evolution manifests the elimination of short-range repulsive cores and the flow toward universal low-momentum interactions. The SRG residual interaction is found to be relatively weak at low energy, which motivates a perturbative treatment

On semistable principal bundles over a complex projective manifold, II

Let (X, \omega) be a compact connected Kaehler manifold of complex dimension d and E_G a holomorphic principal G-bundle on X, where G is a connected reductive linear algebraic group defined over C. Let Z (G) denote the center of G. We prove that the following three statements are equivalent: (1) There is a parabolic subgroup P of G and a holomorphic reduction of the structure group of E_G to P (say, E_P) such that the bundle obtained by extending the structure group of E_P to L(P)/Z(G) (where L(P) is the Levi quotient of P) admits a flat connection; (2) The adjoint vector bundle ad(E_G) is numerically flat; (3) The principal G-bundle E_G is pseudostable, and the degree of the charateristic class c_2(ad(E_G) is zero.Comment: 15 page

Downlink scheduling in CDMA data networks

We identify optimality properties for scheduling downlink transmissions to data users in CDMA networks. For arbitrary-topology networks, we show that under certain idealizing assumptions it is optimal for a base station to transmit to only one data user at a time. Moreover, for data-only networks, we prove that a base station, when on, should transmit at maximum power for optimality. We use these two properties to obtain a mathematical programming formulation for determining the optimal transmission schedule in linear data-only networks, with time allocations playing the role of decision variables. The optimality conditions imply that there exist (i) subsets of outer users on either side of the cell that should be served when only the neighboring base station on the opposite side is on; (ii) a subset of inner users in the center of the cell that should be served when both neighbors are on; (iii) a subset of users in the intermediate regions that should receive transmissions when both neighbors are off. Exploiting these structural properties, we derive a simple search algorithm for finding the optimal transmission schedule in symmetric scenarios. Numerical experiments illustrate that scheduling achieves significant capacity gains over conventional CDMA