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math.AC2024
Extension of the Fundamental Theorem of Algebra for Polynomial Matrix Equations with Circulant Matrices
Vyacheslav M. Abramov
We establish an analogue of the fundamental theorem of algebra for polynomial matrix equations, in which the matrices-coefficients and unknown matrix are assumed to be circulant ma…
math.PR2024
A new criterion for recurrence of Markov chains with an infinitely countable set of states
Vyacheslav M. Abramov
For a class of irreducible Markov chains with an infinitely countable set of states, we establish a new verifiable necessary and sufficient condition for recurrence and transience.…