Related papers: Cohomological equations for linear involutions
In this note, we give a shorter proof of the result of Zheng, Yu, and Pei on the explicit formula of inverses of generalized cyclotomic permutation polynomials over finite fields. Moreover, we characterize all these cyclotomic permutation…
Semilinear stochastic evolution equations with multiplicative L\'evy noise and monotone nonlinear drift are considered. Unlike other similar work we do not impose coercivity conditions on coefficients. Existence and uniqueness of the mild…
Nonlinear and nonlinear evolution equations of the form $u_t=\L u \pm|\nabla u|^q$, where $\L$ is a pseudodifferential operator representing the infinitesimal generator of a L\'evy stochastic process, have been derived as models for growing…
We consider integrable boundary conditions for both discrete and continuum classical integrable models. Local integrals of motion generated by the corresponding transfer matrices give rise to time evolution equations for the initial Lax…
We prove exponential mixing for the Rauzy-Veech-Zorich induction map on the space of interval exchange transformations (Theorem 3)
We show that, for certain evolution partial differential equations, the solution on a finite interval $(0,\ell)$ can be reconstructed as a superposition of restrictions to $(0,\ell)$ of solutions to two associated partial differential…
We compute the local intersection cohomology of the irreducible components of varieties of complexes, by using Lusztig's geometric approach to quantum groups and explicit constructions of elements of Lusztig's canonical bases.
It is shown how a system of evolution equations can be developed both from the structure equations of a submanifold embedded in three-space as well as from a matrix SO(6) Lax pair. The two systems obtained this way correspond exactly when a…
A cohomology theory for lambda-rings is developed. This is then applied to study deformations of lambda-rings.
In this paper, we define the cohomology of a modified Rota-Baxter Leibniz algebra with coefficients in a suitable representation. As applications of our cohomology, we study formal one-parameter deformations and abelian extensions of…
An integrable hierarchies connected with linear stationary Schr\"odinger equation with energy dependent potentials (in general case) are considered. Galilei-like and scaling invariance transformations are constructed. A symmetry method is…
Noncommutative Euclidean spaces -- otherwise known as Moyal spaces or quantum Euclidean spaces -- are a standard example of a non-compact noncommutative geometry. Recent progress in the harmonic analysis of these spaces gives us the…
We derive new Lax representations for the hyper-CR equation of Einstein--Weyl structures and for the associated integrable hierarchy.
We present a list of (1+1)-dimensional second-order evolution equations all connected via a proposed generalised hodograph transformation, resulting in a tree of equations transformable to the linear second-order autonomous evolution…
This article surveys some recent developments on the cohomology of the compactified Jacobian associated with a locally planar integral curve. Topics discussed here include the Ng\^o support theorem, the perverse filtration, connections to…
We survey some recent progress on modulation spaces and the well-posedness results for a class of nonlinear evolution equations by using the frequency-uniform localization techniques.
We solve the classification problem for integrable lattices of the form $u_{,t}=f(u_{-2},\dots,u_2)$ under the additional assumption of invariance with respect to the group of linear-fractional transformations. The obtained list contains 5…
We completely revised the paper after the referee's comments. In the new version, we replaced two erroneous examples, studied a link with earlier work of Koh and Stilmann, and strengthened the main theorem.
A new form of a binary Darboux transformation is used to generate analytical solutions of a nonlinear Liouville-von Neumann equation. General theory is illustrated by explicit examples.
A criterion for unique ergodicity for points of a curve in the space of interval exchange transformation is given.