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For a fixed symmetric matrix A and symmetric perturbation E we develop purely deterministic bounds on how invariant subspaces of A and A+E can differ when measured by a suitable "row-wise" metric rather than via traditional measures of…

Mixed anomalies, higher form symmetries, two-group symmetries and non-invertible symmetries have proved to be useful in providing non-trivial constraints on the dynamics of quantum field theories. We study mixed anomalies involving discrete…

Motivated by a real problem in steel production, we introduce and analyze a general class of singularly perturbed linear hybrid systems with both switches and impulses, in which the slow or fast nature of the variables can be…

In this work we revisit and extend the method introduced by Lins Neto, Sad and Sc\'{a}rdua for detecting the non-existence of invariant algebraic curves other than some prescribed invariant nodal curve. We prove that, under the existence of…

Iterations of odd piecewise continuous maps with two discontinuities, i.e., symmetric discontinuous bimodal maps, are studied. Symbolic dynamics is introduced. The tools of kneading theory are used to study the homology of the discrete…

We introduce four invariants of algebraic varieties over imperfect fields, each of which measures either geometric non-normality or geometric non-reducedness. The first objective of this article is to establish fundamental properties of…

Random matrix models provide a phenomenological description of a vast variety of physical phenomena. Prominent examples include the eigenvalue statistics of quantum (chaotic) systems, which are conveniently characterized using the spectral…

Frames in separable Hilbert spaces gives stable analysis and reconstruction of each vector in the underlying space. In this paper, we study frame conditions for a collection of matrix-valued functions obtained by non-uniform shifts. We give…

Intercurrent events, common in clinical trials and observational studies, affect the existence or interpretation of final outcomes. Principal stratification addresses this challenge by defining local average treatment effect estimands…

We study transitions from convective to absolute instability near a trivial state in large bounded domains for prototypical model problems in the presence of transport and negative nonlinear feedback. We identify two generic scenarios,…

We prove uniqueness problems for meromorphic inner functions on the upper half-plane. In these problems we consider spectral data depending partially or fully on the spectrum, derivative values at the spectrum, Clark measure or the spectrum…

Invariant manifolds facilitate the understanding of nonlinear stochastic dynamics. When an invariant manifold is represented approximately by a graph for example, the whole stochastic dynamical system may be reduced or restricted to this…

Finite-order invariants of knots in arbitrary 3-manifolds (including non-orientable ones) are constructed and studied by methods of the topology of discriminant sets. Obstructions to the integrability of admissible weight systems to…

We study dynamics and bifurcations of 2-dimensional reversible maps having a symmetric saddle fixed point with an asymmetric pair of nontransversal homoclinic orbits (a symmetric nontransversal homoclinic figure-8). We consider…

It has been proved by S.L.Ziglin, for a large class of 2-degree-of-freedom (d.o.f) Hamiltonian systems, that transverse intersections of the invariant manifolds of saddle fixed points imply infinite branching of solutions in the complex…

Let $X$ be a regular geometrically integral variety over an imperfect field $K$. Unlike the case of characteristic $0$, $X':=X\times_{\mathrm{Spec}\,K}\mathrm{Spec}\,K'$ may have singular points for a (necessarily inseparable) field…

This paper presents results concerning bifurcations of 2D piecewise-smooth dynamical systems governed by vector fields. Generic three-parameter families of a class of Non-Smooth Vector Fields are studied and the bifurcation diagrams are…

We propose a method for learning dynamical systems from high-dimensional empirical data that combines variational autoencoders and (spatio-)temporal attention within a framework designed to enforce certain scientifically-motivated…

Two classes of time-periodic systems of ordinary differential equations with a small nonnegative parameter, those with fast and slow time, are studied. Right-hand sides of these systems are three times continuously differentiable with…

Within framework of basic-deformed and finite-difference calculi, as well as deformation procedures proposed by Tsallis, Abe, and Kaniadakis to be generalized by Naudts, we develop field-theoretical schemes of statistically distributed…