Related papers: An algebraic approach for the weak coupling of mul…
The notion of quantum symmetry has recently been extended to include reduced-dimensional transformations and algebraic structures beyond groups. Such generalized symmetries lead to exotic phases of matter and excitations that defy Landau's…
In this paper, we would like to consider the Cauchy problem for a weakly coupled system of semi-linear damped wave equations with mixed nonlinear terms. Our main objective is to draw conclusions about the critical curve of this problem…
A dual pair formulation for asymmetric locally convex spaces is developed that strictly generalises the ordinary vector space setting. The concept of a polar topology carries over to the asymmetric case and some familiar results are…
In this paper, we consider a parabolic system from a bounded domain in a Euclidean space or a closed Riemannian manifold into a unit sphere in a compact Lie algebra $\mathfrak{g}$, which can be viewed as the extension of Landau-Lifshtiz…
Euler alignment systems appear as hydrodynamic limits of interacting self-propelled particle systems such as the (generalized) Cucker-Smale model. In this work, we study weak solutions to an Euler alignment system on smooth, bounded,…
We consider the Cauchy problem for a semilinear stochastic differential inclusion in a Hilbert space. The linear operator generates a strongly continuous semigroup and the nonlinear term is multivalued and satisfies a condition which is…
Given a linear closed but not necessarily densely defined operator $A$ on a Banach space $E$ with nonempty resolvent set and a multivalued map $F\colon I\times E\map E$ with weakly sequentially closed graph, we consider the…
A system of two operator equations is considered - one of pseudomonotone type and the other of strongly monotone type - both being strongly coupled. Conditions are given that allow to reduce the solvability of this system to a single…
We study a system of functional relations among a commuting family of row-to-row transfer matrices in solvable lattice models. The role of exact sequences of the finite dimensional quantum group modules is clarified. We find a curious…
We consider a class of monotone operators which are appropriate for symbolic representation and manipulation within a computer algebra system. Various structural properties of the class (e.g., closure under taking inverses, resolvents) are…
A tensor is a multi-dimensional array of complex numbers, and the Lohe tensor model is an aggregation model on the space of tensors with the same rank and size. It incorporates previously well-studied aggregation models on the space of…
In this paper, we establish the well-posedness of Cauchy problems for weak solutions to second-order degenerate parabolic equations with a non-smooth, time-dependent degenerate elliptic part that includes both bounded and unbounded…
This paper deals with the notion of weak Lawvere-Tierney topology on a topos. Our motivation to study such a notion is based on the observation that the composition of two Lawvere-Tierney topologies is no longer idempotent, when seen as a…
Classifier fusion is established as an effective methodology for boosting performance in different settings and one-class classification is no exception. In this study, we consider the one-class classifier fusion problem by modelling the…
For a class of weakly hyperbolic systems of the form D_t - A(t,x,D_x), where A(t,x,D_x) is a first-order pseudodifferential operator whose principal symbol degenerates like t^{l_*} at time t=0, for some integer l_* \geq 1, well-posedness of…
Recently, a set of thermodynamic Bethe ansatz equations is proposed by Dorey, Pocklington and Tateo for unitary minimal models perturbed by \phi_{1,2} or \phi_{2,1} operator. We examine their results in view of the lattice analogues, dilute…
Consider an operator equation $F(u)=0$ in a real Hilbert space. Let us call this equation ill-posed if the operator $F'(u)$ is not boundedly invertible, and well-posed otherwise. If $F$ is monotone $C^2_{loc}(H)$ operator, then we construct…
A lattice model of critical dense polymers is solved exactly for finite strips. The model is the first member of the principal series of the recently introduced logarithmic minimal models. The key to the solution is a functional equation in…
We present a first-order aggregation model on the space of complex matrices which can be derived from the Lohe tensor model on the space of tensors with the same rank and size. We call such matrix-valued aggregation model as "the…
We study the dynamics of systems consisting of two spatially segregated ODE compartments coupled through a one-dimensional bulk diffusion field. For this coupled PDE-ODE system, we first employ a multi-scale asymptotic expansion to derive…