NON-COERCIVE RICCI FLOW INVARIANT CURVATURE CONES

This note is a study of nonnegativity conditions on curvature preserved by the Ricci flow. We focus on a specific class of curvature conditions which we call non-coercive: These are the conditions for which nonnegative curvature and vanishing scalar curvature does not imply flatness. We show, in dimensions greater than 4, that if a Ricci flow invariant nonnegativity condition is satisfied by all Einstein curvature operators with nonnegative scalar curvature, then this condition is just the nonnegativity of scalar curvature. As a corollary, we obtain that a Ricci flow invariant curvature condition, which is stronger than a nonnegative scalar curvature, cannot be strictly satisfied by curvature operators (other than multiples of the identity) of compact Einstein symmetric spaces. We also investigate conditions which are satisfied by all conformally flat manifolds with nonnegative scalar curvature.

L-infinity norms of holomorphic modular forms in the case of compact quotient

We prove a sub-convex estimate for the sup-norm of L-2-normalized holomorphic modular forms of weight k on the upper half plane, with respect to the unit group of a quaternion division algebra over Q. More precisely we show that when the L-2 norm of an eigenfunction f is one, parallel to f parallel to(infinity) <<(epsilon) k(1/2-1/33+epsilon) for any epsilon > 0 and for all k sufficiently large.

QoS Aware Trust Metric based Framework for Wireless Sensor Networks

Wireless Sensor Networks have gained popularity due to their real time applications and low-cost nature. These networks provide solutions to scenarios that are critical, complicated and sensitive like military fields, habitat monitoring, and disaster management. The nodes in wireless sensor networks are highly resource constrained. Routing protocols are designed to make efficient utilization of the available resources in communicating a message from source to destination. In addition to the resource management, the trustworthiness of neighboring nodes or forwarding nodes and the energy level of the nodes to keep the network alive for longer duration is to be considered. This paper proposes a QoS Aware Trust Metric based Framework for Wireless Sensor Networks. The proposed framework safeguards a wireless sensor network from intruders by considering the trustworthiness of the forwarder node at every stage of multi-hop routing. Increases network lifetime by considering the energy level of the node, prevents the adversary from tracing the route from source to destination by providing path variation. The framework is built on NS2 Simulator. Experimental results show that the framework provides energy balance through establishment of trustworthy paths from the source to the destination. (C) 2015 The Authors. Published by Elsevier B.V.

Exact Phase Retrieval in Principal Shift-Invariant Spaces

We address the problem of phase retrieval from Fourier transform magnitude spectrum for continuous-time signals that lie in a shift-invariant space spanned by integer shifts of a generator kernel. The phase retrieval problem for such signals is formulated as one of reconstructing the combining coefficients in the shift-invariant basis expansion. We develop sufficient conditions on the coefficients and the bases to guarantee exact phase retrieval, by which we mean reconstruction up to a global phase factor. We present a new class of discrete-domain signals that are not necessarily minimum-phase, but allow for exact phase retrieval from their Fourier magnitude spectra. We also establish Hilbert transform relations between log-magnitude and phase spectra for this class of discrete signals. It turns out that the corresponding continuous-domain counterparts need not satisfy a Hilbert transform relation; notwithstanding, the continuous-domain signals can be reconstructed from their Fourier magnitude spectra. We validate the reconstruction guarantees through simulations for some important classes of signals such as bandlimited signals and piecewise-smooth signals. We also present an application of the proposed phase retrieval technique for artifact-free signal reconstruction in frequency-domain optical-coherence tomography (FDOCT).

Moduli spaces of vector bundles on a singular rational ruled surface

We study moduli spaces M-X (r, c(1), c(2)) parametrizing slope semistable vector bundles of rank r and fixed Chern classes c(1), c(2) on a ruled surface whose base is a rational nodal curve. We showthat under certain conditions, these moduli spaces are irreducible, smooth and rational (when non-empty). We also prove that they are non-empty in some cases. We show that for a rational ruled surface defined over real numbers, the moduli space M-X (r, c(1), c(2)) is rational as a variety defined over R.