Related papers: Fitting ideals for finitely presented algebraic dy…

I analyse a generalised Burger's equation to develop an accurate finite difference approximation to its dynamics. The analysis is based upon centre manifold theory so we are assured that the finite difference model accurately models the…

We consider the primal and dual forms of the optimality conditions for PDE-contrained optimization problems arising in Data-Driven Computational Mechanics when specialized to the reaction-diffusion context. Starting with the continuous…

In recent years, researchers have discovered various large algebraic structures that have surprising finiteness properties, such as FI-modules and Delta-modules. In this paper, we add another example to the growing list: we show that…

In this paper, we extend a classical vanishing result of Burnside from the character tables of finite groups to the character tables of commutative fusion rings, or more generally to a certain class of abelian normalizable hypergroups. We…

Combining results from Keller and Buchweitz, we describe the 1-periodic derived category of a finite dimensional algebra $A$ of finite global dimension as the stable category of maximal Cohen-Macaulay modules over some Gorenstein algebra…

We consider social systems in which agents are not only characterized by their states but also have the freedom to choose their interaction partners to maximize their utility. We map such systems onto an Ising model in which spins are…

We consider a multi-component version of the conserved Allen-Cahn equation proposed by J. Rubinstein and P. Sternberg in 1992 as an alternative model for phase separation. In our case, the free energy is characterized by a mixing entropy…

The thermodynamics of quantum systems coupled to periodically modulated heat baths and work reservoirs is developed. By identifying affinities and fluxes, the first and second law are formulated consistently. In the linear response regime,…

We describe the digraphs that are dual representations of finite lattices satisfying conditions related to meet-distributivity and modularity. This is done using the dual digraph representation of finite lattices by Craig, Gouveia and…

This paper is devoted to the study of some connections between coadjoint orbits in infinite dimensional Lie algebras, isospectral deformations and linearization of dynamical systems. We explain how results from deformation theory,…

We show that ideal submodules and closed ternary ideals in Hilbert modules are the same. We use this insight as a little peg on which to hang a little note about interrelations with other notions regarding Hilbert modules. In Section 3, we…

Homological algebra of modules over posets is developed, as closely parallel as possible to that of finitely generated modules over noetherian commutative rings, in the direction of finite presentations and resolutions. Centrally at issue…

We prove the approach to equilibrium of quenched isolated quantum systems for which the change in the Hamiltonian brought about by the quench satisfies a certain closed commutator algebra with all the extensive integrals of motion of the…

We classify the weak*-closed maximal left ideals of the measure algebra $M(G)$ for certain Hermitian locally compact groups $G$ in terms of the irreducible representations of $G$ and their asymptotic properties. In particular, we obtain a…

We propose an approach to the problem of finite temperature dynamical correlation functions in integrable one-dimensional models with a spectral gap. The approach is based on the analysis of the singularities of the operator matrix elements…

We study modules for the divided power algebra $D$ in a single variable over a commutative noetherian ring $k$. Our first result states that $D$ is a coherent ring. In fact, we show that there is a theory of Gr\"obner bases for finitely…

A collection of partial isometries whose range and initial projections satisfy a specified set of conditions often gives rise to a partial representation of a group. The C*-algebra generated by the partial isometries is thus a quotient of…

The study of images of noncommutative polynomials on algebras has attracted considerable attention. We investigate polynomial images and the additive structures they generate in associative algebras, focusing on sums and products of values.…

To study discrete dynamical systems of different types --- deterministic, statistical and quantum --- we develop various approaches. We introduce the concept of a system of discrete relations on an abstract simplicial complex and develop…

We study the quench dynamics of the one-dimensional Hubbard model through the Quench Action formalism. We introduce a class of integrable initial states -- expressed as product states over two sites -- for which we can provide an exact…