We discuss diagonalization of propagator for mixing fermions system based on the eigenvalue problem. The similarity transformation converting matrix into diagonal form is obtained. suggested has simple algebraic properties on-shell and can be used in renormalization fermion matrix.

We show that motivic Donaldson-Thomas invariants of a~symmetric quiver $Q$, captured by the generating function $P_Q$, can be encoded in another $Q^{(\infty)}$ (almost always) infinite size, whose only arrows are loops, and $P_{Q^{(\infty)}}$ is equal to $P_Q$ upon appropriate identification parameters. Consequences this statement include a generalization proof integrality Labastida-Mari\~{n}o-...

In this paper we explore several fundamental relations between formal systems, algorithms, and dynamical systems, focussing on the roles of undecidability, universality, diagonalization, and self-reference in each of these computational frameworks. Some of these interconnections are well-known, while some are clarified in this study as a result of a fine-grained comparison between recursive for...

The approximate joint diagonalization (AJD) is an important analytic tool at the base of numerous independent component analysis (ICA) and other blind source separation (BSS) methods, thus finding more and more applications in medical imaging analysis. In this work we present a new AJD algorithm named SDIAG (Spheric Diagonalization). It imposes no constraint either on the input matrices or on t...