Related papers: The inverse theorem for the nonlinear Roth configu…
We consider an inverse problem for Laplacians on rotationally symmetric manifolds, which are finite for the transversal direction and periodic with respect to the axis of the manifold, i.e., Laplacians on tori. We construct an infinite…
In this paper, we first prove that the absorption law for one-sided inverses along an element holds, deriving the absorption law for the inverse along an element. We then apply this result to obtain the absorption law for the inverse along…
We curry the elementary arithmetic operations of addition and multiplication to give monotone injections on N, and describe & study the inverse monoids that arise from also considering their generalised inverses. This leads to well-known…
This work belongs to the framework of inverse problems with linear model. The resolution of this type of problem consists in minimizing (possibly under constraints) a function of discrepancy between the measurements and a physical model of…
In this note we show that the Langlands lemma from the theory of Eisenstein series can be used to invert the recursion relation for the Poincar\'e series of the open substack of semi-stable $G$-bundles which was established by Atiyah/Bott…
The Ruelle-Perron-Frobenius (RPF) theorem is a powerful tool in the study of equilibrium measures and their statistical properties. We prove a nonstationary version of this theorem under general conditions involving an invariant sequence of…
This article presents original work combining a NURBS-based inverse analysis with both kinematic and constitutive nonlinearities to recover the applied loads and deformations of thin shell structures. The inverse formulation is tackled by…
We show that a general nonlinearity $a(x,u)$ is uniquely determined, possibly up to a gauge, in a neighborhood of a fixed solution from boundary measurements of the corresponding semilinear equation. The main theorems are low regularity…
We are interested in Poisson structures transverse to nilpotent adjoint orbits in a complex semi-simple Lie algebra, and we study their polynomial nature, introduced by R.Cushman and M.Roberts. Furthermore, in the case of sl(n), we…
The interrelations between the inverse problems of the representation theory and the categorical representation theory are discussed.
The inverse problem is studied in multi-body systems with nonlinear dynamics representing, e.g., phase-locked wave systems, standard multimode and random lasers. Using a general model for four-body interacting complex-valued variables we…
We consider second-order functional differential operators with a constant delay. Properties of their spectral characteristics are obtained and a nonlinear inverse problem is studied, which consists in recovering the operators from their…
In this article we study the inverse problem of determining a semilinear term appearing in an elliptic equation from boundary measurements. Our main objective is to develop flexible and general theoretical results that can be used for…
In the last decades the Moore-Penrose pseudoinverse has found a wide range of applications in many areas of Science and became a useful tool for physicists dealing, for instance, with optimization problems, with data analysis, with the…
This paper discusses the explicit inverse of a class of seven-diagonal (near) Toeplitz matrices, which arises in the numerical solutions of nonlinear fourth-order differential equation with a finite difference method. A non-recurrence…
An asymmetric operator of generalised translation is introduced in this paper. Using this operator, we define a generalised modulus of smoothness and prove direct and inverse theorems of approximation theory for it.
In this paper, we obtain a new estimate for uniform integrability under sublinear expectations. Based on this, we establish the limit theorems under nonlinear expectations dominated by sublinear expectations through tightness, and the limit…
In the paper, we prove an abstract KAM (Kolmogorov-Arnold-Moser) theorem for infinite dimensional reversible systems. Using this KAM theorem, we obtain the existence and linear stability of quasi-periodic solutions for a class of reversible…
In this paper, we establish universal approximation theorems for neural networks applied to general nonlinear ill-posed operator equations. In addition to the approximation error, the measurement error is also taken into account in our…
Given the cutting and spacer parameters for a rank-1 transformation, there is a simple condition which is easily seen to be sufficient to guarantee that the transformation under consideration is isomorphic to its inverse. Here we show that…