Non-isotrivial elliptic surfaces with non-zero average root number

Static solitons with non - zero Hopf number

We investigate a generalized non-linear O(3) σ-model in three space dimensions where the fields are maps from R3∪{∞} to S2. Such maps are classified by a homotopy invariant called the Hopf number which takes integer values. The model exhibits soliton solutions of closed vortex type which have a lower topological bound on their energies. We numerically compute the fields for topological charge 1...

Non-isotopic Lagrangian Tori in Elliptic Surfaces

We construct the first example of an infinite family of homotopic but pairwise smoothly non-isotopic Lagrangian tori in the rational elliptic surface E(1) = P2#9P2. Furthermore, we show that any two of these tori are smoothly equivalent, i.e., there exists an orientation-preserving selfdiffeomorphism of E(1) that carries one torus to the other. Our construction can be generalized for many other...

Non-zero probability of nearest neighbor searching

Nearest Neighbor (NN) searching is a challenging problem in data management and has been widely studied in data mining, pattern recognition and computational geometry. The goal of NN searching is efficiently reporting the nearest data to a given object as a query. In most of the studies both the data and query are assumed to be precise, however, due to the real applications of NN searching, suc...

The non-zero baryon number formulation of QCD

We discuss the non-zero baryon number formulation of QCD in the quenched limit at finite temperature. This describes the thermodynamics of gluons in the background of static quark sources. Although a sign problem remains in this theory, our simulation results show that it can be handled quite well numerically. The transition region gets shifted to smaller temperatures and the transition region ...

The Number of Non-zero Coefficients of Modular