Related papers: Newton flows for elliptic functions II Structural …

In this paper, we provide a classification of steady solutions to two-dimensional incompressible Euler equations in terms of the set of flow angles. The first main result asserts that the set of flow angles of any bounded steady flow in the…

Let $p$ be a prime number. Every $n$-variable polynomial $f(\underline x)$ over a finite field of characteristic $p$ defines an Artin--Schreier--Witt tower of varieties whose Galois group is isomorphic to $\mathbb{Z}_p$. Our goal of this…

We present a unified framework to systematically embed complex knotted and linked structures, beyond the torus family, into diverse topological phases, including Hopf insulators, classical spin liquids, topological semimetals, and…

We analyse the dynamics of an array of $N^2$ identical cells coupled in the shape of a torus. Each cell is a 2-dimensional ordinary differential equation of FitzHugh-Nagumo type and the total system is…

We study algebraic neural networks (AlgNNs) with commutative algebras which unify diverse architectures such as Euclidean convolutional neural networks, graph neural networks, and group neural networks under the umbrella of algebraic signal…

In this paper, we study the global existence of steady subsonic Euler flows through infinitely long nozzles without the assumption of irrotationality. It is shown that when the variation of Bernoulli's function in the upstream is…

In this paper we mainly study the existence of analytic normalization and the normal form of finite dimensional complete analytic integrable dynamical systems. More details, we will prove that any complete analytic integrable diffeomorphism…

We characterize the computational power of neural networks that follow the graph neural network (GNN) architecture, not restricted to aggregate-combine GNNs or other particular types. We establish an exact correspondence between the…

In this investigation we revisit the question of the linear stability analysis of 2D steady Euler flows characterized by the presence of compact regions with constant vorticity embedded in a potential flow. We give a complete derivation of…

Let $\mathcal{E}$ be a $\mathbb{Q}$-isogeny class of elliptic curves defined over $\mathbb{Q}$. The isogeny graph associated to $\mathcal{E}$ is a graph which has a vertex for each elliptic curve in the $\mathbb{Q}$-isogeny class…

Here we prove the linear stability of a family of `$n+1$'-dimensional Friedmann Lema\^{i}tre Robertson Walker (FLRW) cosmological models of general relativity. We show that the solutions to the linearized Einstein-Euler field equations…

Geometric graphs are a special kind of graph with geometric features, which are vital to model many scientific problems. Unlike generic graphs, geometric graphs often exhibit physical symmetries of translations, rotations, and reflections,…

This work shows that, Newton's Proposition 1 in the {\it Principia}, is an {\it exact} graphical representation of a canonical transformation, a first-order symplectic integrator generated at a finite time-step by the Hamiltonian. A…

Blood flow, dam or ship construction and numerous other problems in biomedical and general engineering involve incompressible flows interacting with elastic structures. Such interactions heavily influence the deformation and stress states…

We show existence, uniqueness and stability for a family of stationary subsonic compressible Euler flows with mass-additions in two-dimensional rectilinear ducts, subjected to suitable time-independent multi-dimensional boundary conditions…

Networks with phase-valued nodal variables are central in modeling several important societal and physical systems, including power grids, biological systems, and coupled oscillator networks. One of the distinctive features of phase-valued…

Morse theory relates algebraic topology invariants and the dynamics of the gradient flow of a Morse function, allowing to derive information about one out of the other. In the case of the homology, the construction extends to much more…

An elliptic curve may be immersed in ${\mathbf{P}}^{N-1}$ as a degree $N$ curve using level $N$ structure. In the case where $N$ is odd, there are well known classical results dating back to Bianchi and Klein. In this paper we study the…

Reasoning system dynamics is one of the most important analytical approaches for many scientific studies. With the initial state of a system as input, the recent graph neural networks (GNNs)-based methods are capable of predicting the…

Graph neural networks (GNNs) are a powerful architecture for tackling graph learning tasks, yet have been shown to be oblivious to eminent substructures such as cycles. We present TOGL, a novel layer that incorporates global topological…