相关论文: Lax Liftings and Lax Distributive Laws
We present four classes of nonlinear systems which may be considered discrete analogues of the Garnier system. These systems arise as discrete isomonodromic deformations of systems of linear difference equations in which the associated Lax…
We provide bicategorical analogs of several aspects of the notion of geometry in the sense of the theory of spectrum. We first introduce a notion of local right biadjoint, and prove it to be equivalent to a notion of bistable pseudofunctor,…
We propose a functional lifting-based convex relaxation of variational problems with Laplacian-based second-order regularization. The approach rests on ideas from the calibration method as well as from sublabel-accurate continuous…
A lattice Maxwell system is developed with gauge-symmetry, symplectic structure and discrete space-time symmetry. Noether's theorem for Lie group symmetries is generalized to discrete symmetries for the lattice Maxwell system. As a result,…
We introduce a criterion that a given bihamiltonian structure allows a local coordinate system where both brackets have constant coefficients. This criterion is applied to the bihamiltonian open Toda lattice in a generic point, which is…
We prove an Alt-Caffarelli-Friedman montonicity formula for pairs of functions solving elliptic equations driven by different ellipticity matrices in their positivity sets. As application, we derive Liouville-type theorems for subsolutions…
The main result of the paper is a flat extension theorem for positive linear functionals on *-algebras. The theorem is applied to truncated moment problems on cylinder sets, on matrices of polynomials and on enveloping algebras of Lie…
Two new generalizations of the relation of comonotonicity of lattice-valued vectors are introduced and discussed. These new relations coincide on distributive lattices and they share several properties with the comonotonicity for the…
A generator matrix of a linear code $\C$ over $\gf(q)$ is also a matrix of the same rank $k$ over any extension field $\gf(q^\ell)$ and generates a linear code of the same length, same dimension and same minimum distance over $\gf(q^\ell)$,…
We study the problem of extension and lifting of operators belonging to certain operator ideals, as well as that of their associated polynomials and holomorphic functions. Our results provide a characterization of $\mathcal{L}_1$ and…
Potential functionals have been introduced recently as an important tool for the analysis of coupled scalar systems (e.g. density evolution equations). In this contribution, we investigate interesting properties of this potential. Using the…
The pinning of flux lattices by weak impurity disorder is studied in the absence of free dislocations using both the gaussian variational method and, to $O(\epsilon=4-d)$, the functional renormalization group. We find universal logarithmic…
A key idea in convex optimization theory is to use well-structured affine functions to approximate general functions, leading to impactful developments in conjugate functions and convex duality theory. This raises the question: what are the…
We define a new logic-induced notion of bisimulation (called $\rho$-bisimulation) for coalgebraic modal logics given by a logical connection, and investigate its properties. We show that it is structural in the sense that it is defined only…
The basic disentanglement theorem established by the present authors states that estimates on a weighted geometric mean over (convex) families of functions can be disentangled into quantitatively linked estimates on each family separately.…
The paper introduces the notion of a weak bisimulation for coalgebras whose type is a monad satisfying some extra properties. In the first part of the paper we argue that systems with silent moves should be modelled coalgebraically as…
We use a minimal model for a dense suspension undergoing thickening and thinning to investigate microstructural changes in 2d simulations. Our simulations show that in steady flow the contact network contains distinct building blocks which…
We study bisimulation and context equivalence in a probabilistic $\lambda$-calculus. The contributions of this paper are threefold. Firstly we show a technique for proving congruence of probabilistic applicative bisimilarity. While the…
The Hochschild cohomology of a tensor product of algebras is isomorphic to a graded tensor product of Hochschild cohomology algebras, as a Gerstenhaber algebra. A similar result holds when the tensor product is twisted by a bicharacter. We…
The isomonodromy deformation method is applied to the scaling limits in the linear NxN matrix equations with rational coefficients to obtain the deformation equations for the algebraic curves which describe the local behavior of the reduced…