2 citations · 2 across the 7 of their papers we have counts for
9 papers
Non-existence of co-spectral simple connected graphs with small number of edges
O. Boyko, D. Kaliuzhnyi-Verbovetskyi, V. Pivovarchik
We prove that if the number of edges does not exceed 7 then the asymptotics of eigenvalues of the Dirichlet problem uniquely determine the shape of the graph.
Integrability of Free Noncommutative Functions
Dmitry Kaliuzhnyi-Verbovetskyi, Leonard Stevenson, Victor Vinnikov
Noncommutative functions are graded functions between sets of square matrices of all sizes over two vector spaces that respect direct sums and similarities. They possess very stron…
Sparse Monte Carlo method for nonlocal diffusion problems
Dmitry Kaliuzhnyi-Verbovetskyi, Georgi S. Medvedev
A class of evolution equations with nonlocal diffusion is considered in this work. These are integro-differential equations arising as models of propagation phenomena in continuum…
The mean field equation for the Kuramoto model on graph sequences with non-Lipschitz limit
Dmitry Kaliuzhnyi-Verbovetskyi, Georgi S. Medvedev
The Kuramoto model (KM) of coupled phase oscillators on graphs provides the most influential framework for studying collective dynamics and synchronization. It exhibits a rich repe…
Rational inner functions on a square-matrix polyball
Anatolii Grinshpan, Dmitry S. Kaliuzhnyi-Verbovetskyi, Victor Vinnikov +1
We establish the existence of a finite-dimensional unitary realization for every matrix-valued rational inner function from the Schur--Agler class on a unit square-matrix polyball.…
Contractive determinantal representations of stable polynomials on a matrix polyball
Anatolii Grinshpan, Dmitry S. Kaliuzhnyi-Verbovetskyi, Victor Vinnikov +1
We show that an irreducible polynomial with no zeros on the closure of a matrix unit polyball, a.k.a. a cartesian product of Cartan domains of type I, and such that , a…