Here we define the concept of L-regularity for coherent sheaves on the Grassmannian G(1, 4) as a generalization of Castelnuovo-Mumford regularity on Pn. In this setting we prove analogs of some classical properties. We use our notion of L-regularity in order to prove a splitting criterion for rank 2 vector bundles with only a finite number of vanishing conditions. In the second part we give the...

We study the systems of Euler equations which arise from agent-based dynamics driven by velocity alignment. It is known that smooth solutions of such systems must flock, namely — the large time behavior of the velocity field approaches a limiting “flocking” velocity. To address the question of global regularity, we derive sharp critical thresholds in the phase space of initial configuration whi...

We study boundary regularity for conformally compact Einstein metrics in even dimensions by generalizing the ideas of Michael Anderson found in [And03] and [And06]. Our method of approach is to view the vanishing of the Ambient Obstruction tensor as an nth order system of equations for the components of a compactification of the given metric. This, together with boundary conditions that the com...

We discuss local convergence of Newton’s method to a singular solution x∗ of the nonlinear equations F (x) = 0, for F : IR → IR. It is shown that an existing proof of Griewank, concerning linear convergence to a singular solution x∗ from a starlike domain around x∗ for F twice Lipschitz continuously differentiable and x∗ satisfying a particular regularity condition, can be adapted to the case i...

Orthographic regularity is important for processing Chinese characters. However, the issues how orthographic regularity influences the visual recognition of real Chinese characters and whether common processes related to the potential effect exist between successive (SUCC) and concurrent (CONC) conditions with asynchronous presentation of S1 and S2 are still unclear. In the current study, event...