We demonstrate that Coxeter groups allow for complex PT -symmetric deformations across the boundaries of all Weyl chambers. We compute the explicit deformations for the A2 and G2-Coxeter group and apply these constructions to Calogero-MoserSutherland models invariant under the extended Coxeter groups. The eigenspecta for the deformed models are real and contain the spectra of the undeformed cas...

The general KdV equation (gKdV) derived by T. Chou is one of the famous (1 + 1) dimensional soliton equations with variable coefficients. It is well-known that the gKdV equation is integrable. In this paper a higher-dimensional gKdV equation, which is integrable in the sense of the Painlevé test, is presented. A transformation that links this equation to the canonical form of the Calogero–Bogoy...

We construct families of Hamiltonians extending the Calogero model and such that a finite number of eigenvectors can be computed algebraically.

It is shown that Rota’s basis conjecture follows from a similar conjecture that involves just three bases instead of n bases.

A graph is said to be reconstructible if it is determined up to isomorphism from the collection of all its one-vertex deleted unlabeled subgraphs. Reconstruction Conjecture (RC) asserts that all graphs on at least three vertices are reconstructible. In this paper, we prove that interval-regular graphs and some new classes of graphs are reconstructible and show that RC is true if and only if all...

In this paper, we show that for any even integer t ≥ 4, every 3-connected graph with no K3,t-minor has a spanning tree whose maximum degree is at most t − 1. This result is a common generalization of the result by Barnette [1] and the one by Chen, Egawa, Kawarabayashi, Mohar and Ota [4].

BACKGROUND Limited efficacy of IV recombinant tissue plasminogen activator (rt-PA) for large vessel occlusions (LVO) raises doubts about its utility prior to endovascular therapy. PURPOSE To compare outcomes and hospital costs for anterior circulation LVOs (middle cerebral artery, internal carotid artery terminus (ICA-T)) treated with either primary endovascular therapy alone (EV-Only) or bri...