We study diagonal estimates for the Bergman kernels of certain model domains in C near boundary points that are of infinite type. To do so, we need a mild structural condition on the defining functions of interest that facilitates optimal upper and lower bounds. This is a mild condition; unlike earlier studies of this sort, we are able to make estimates for non-convex pseudoconvex domains as we...

The infinite configuration space of an integrable vertex model based on Uq gl(2|2) 1 is studied at q = 0. Allowing four particular boundary conditions, the infinite configurations are mapped onto the semi-standard supertableaux of pairs of infinite border strips. By means of this map, a weight-preserving one-to-one correspondence between the infinite configurations and the normal forms of a pai...

We propose a relation between the $\eta$ invariant on manifold with boundary, invariants of edge states, and in an infinite volume limit. With example planar fermions bag chiral boundary conditions we show that this holds whenever states are sufficiently well-localized near boundary. As by-product spectrum modes for is linear but bounded.

We consider unsteady ballistic heat transport in a semi-infinite Hooke chain with free end and arbitrary initial temperature profile. An analytical description of the evolution kinetic is proposed both discrete (exact) continuum (approximate) formulations. By comparison descriptions field, we reveal some restrictions to latter. Specifically, far-field well described by solution, which, however,...

Keywords: Stefan problem Non-classical heat equation Free boundary problem Similarity solution Nonlinear heat sources Volterra integral equation a b s t r a c t We prove the existence and uniqueness, local in time, of the solution of a one-phase Stefan problem for a non-classical heat equation for a semi-infinite material with a convective boundary condition at the fixed face x = 0. Here the he...

This letter investigates the design of a class infinite-dimensional observers for one dimensional (1D) boundary controlled port-Hamiltonian systems (BC-PHS) defined by differential operators order N≥1. The convergence proposed observer depends on number and location available measurements. Asymptotic is assured N≥1, provided that enough measurements are available, exponential can be cases N=1 N...