Related papers: Response Functions from Integral Transforms with a…
Estimating the innovation probability density is an important issue in any regression analysis. This paper focuses on functional autoregressive models. A residual-based kernel estimator is proposed for the innovation density. Asymptotic…
This paper presents a two-phase method for learning interaction kernels of stochastic many-particle systems. After transforming stochastic trajectories of every particle into the particle density function by the kernel density estimation…
We present a novel approach for the inverse problem in electrical impedance tomography based on regularized quadratic regression. Our contribution introduces a new formulation for the forward model in the form of a nonlinear integral…
After a short critique of the Minkowski formulae for the electromagnetic constitutive laws in moving media, we argue that in actual fact the problem of Lorentz-covariant electromagnetic response theory is automatically solved within the…
The unpolarized response functions of the quasielastic $^{16}O(e,e^\prime p)^{15}N$ reaction are calculated for three different types of relativistic bound state wave functions. The wave functions are obtained from relativistic Hartree,…
We derive explicit formulas for the reconstruction of a function from its integrals over a family of spheres, or for the inversion of the spherical mean Radon transform. Such formulas are important for problems of thermo- and photo-…
Usually such area of mathematics as differential equations acts as a consumer of results given by functional analysis. This article will give an example of the reverse interaction of these two fields of knowledge. Namely, the derivation and…
In this paper we have chosen to work with two different approaches to solving the inverse problem of the calculus of variation. The first approach is based on an integral representation of the Lagrangian function that uses the first…
The possibility to resolve narrow structures in reaction cross sections in calculations with the Lorentz integral transform (LIT) method is studied. To this end we consider a fictitious two-nucleon problem with a low-lying and narrow…
In this paper, we analyze the properties of invertible neural networks, which provide a way of solving inverse problems. Our main focus lies on investigating and controlling the Lipschitz constants of the corresponding inverse networks.…
Spectral density functions quantify how environmental modes couple to quantum systems and govern their open dynamics. Inferring such frequency-dependent functions from time-domain measurements is an ill-conditioned inverse problem. Here, we…
Some results about existence, uniqueness, and attractive behaviour of solutions for nonlinear Volterra integral equations with non-convolution kernels are presented in this paper. These results are based on similar ones about nonlinear…
Inverted pendulums constitute one of the popular systems for benchmarking control algorithms. Several methods have been proposed for the control of this system, the majority of which rely on the availability of a mathematical model.…
Let $N$ be an integral operator of the form $\bigl(Nu\bigr)(x)=\int_{\mathbb R^c}n(x,x-y)\,u(y)\,dy$ acting in $L_p(\mathbb R^c)$ with a measurable kernel $n$ satisfying the estimate $|n(x,y)|\le\beta(y)$, where $\beta\in L_1$. It is proved…
The lower moments of the unpolarized and polarized deep-inelastic structure functions of the nucleon are calculated on the lattice. The calculation is done with Wilson fermions and for three values of the hopping parameter $\kappa$, so that…
We present a closed-form, exact analytical solution, valid at finite times, to a class of multiple integrals with highly oscillatory kernels. Our approach leverages the intimate connection between these integrals and the minimal…
Properties of the response functions for a two-dimensional quartic oscillator are studied based on the diagonalization of the Hamiltonian in a large model space. In particular, response functions corresponding to a given momentum transfer…
Robust stability problem of integral delay systems with uncertain kernel matrix functions is addressed in this paper. On the basis of characteristic equation and the argument principle, an algorithm is generated which is shown to outperform…
New index transforms with Weber type kernels, consisting of products of Bessel functions of the first and second kind are investigated. Mapping properties and inversion formulas are established for these transforms in Lebesgue spaces. The…
We presents a fully quantal version of the Langevin model for the total rate of exoergic ion-molecule reactions or inelastic processes. The model, which is derived from a rigorous multichannel quantum-defect formulation of bimolecular…