Using two methods we show that a quantized discrete breather in a 1D lattice is stable. One method uses path integrals and compares correlations for a (linear) local mode with those of the quantum breather. The other takes a local mode as the zeroth order system relative to which numerical, cutoff-insensitive diagonalization of the Hamiltonian is performed.

We apply persistent homology to four collaboration networks. We show that the intervals for the zeroth and first Betti numbers correspond to tangible features of the structure of these networks. Finally, we use persistent homology to distinguish collaboration networks from similar random networks.

Isolated horizons [1], much like Killing horizons [2], were introduced in order to deal with the more practical problems involving black holes. Both formulations are local, in contrast with the global nature of event horizons [3]. However, isolated horizons, unlike Killing horizons, do not require a Killing vector field in their neighbourhood. Thus, isolated horizons are characterized by a weak...

We show that the central charge $k$ reduction of universal extension elliptic Hall algebra is isomorphic to trace, or zeroth Hochschild homology, quantum Heisenberg category $k$. As an application, we construct large families representations algebra.

In this paper, we obtain the sharp uniqueness for an inverse $ x $-source problem a one-dimensional time-fractional diffusion equation with zeroth-order term by minimum possible lateral Cauchy data. The key ingredient is unique continuation which holds weak solutions.

We study the homology of dual de Rham complex as functors on category abelian groups. give a description up to degree 7 for free groups and present corrected version proof Jean’s computations zeroth group.

This paper considers stochastic convex optimization problems with two sets of constraints: (a) deterministic constraints on the domain variable, which are difficult to project onto; and (b) or that admit efficient projection. Problems this form arise frequently in context semidefinite programming as well when various NP-hard solved approximately via relaxation. Since projection onto first set i...