Related papers: On the complex moment problem as a dynamic inverse…
This paper derives recursion equations for a robust smoothing problem for a class of nonlinear systems with uncertainties in modeling and exogenous noise sources. The systems considered operate in discrete-time and the uncertainties are…
The general entire solution to a linear system of moment differential equations is obtained in terms of a moment kernel function for generalized summability, and the Jordan decomposition of the matrix defining the problem. The growth at…
In this work we study an inverse dynamical problem for a bipartite quantum system governed by the time local master equation: to find the class of generators which give rise to a certain time evolution with the constraint of fixed reduced…
The truncated moment problem asks to characterize finite sequences of real numbers that are the moments of a positive Borel measure on Rn. Its tracial analog is obtained by integrating traces of symmetric matrices and is the main topic of…
In this work we consider the problem of extracting a set of interaction parameters from an high-dimensional dataset describing T independent configurations of a complex system composed of N binary units. This problem is formulated in the…
The inverse problem which arises in the Camassa--Holm equation is revisited for the class of discrete densities. The method of solution relies on the use of orthogonal polynomials. The explicit formulas are obtained directly from the…
We derive a moment formula for generalized fractional polynomial processes, i.e., for polynomial-preserving Markov processes time-changed by an inverse L\'evy-subordinator. If the time change is inverse $\alpha$-stable, the time-derivative…
In this work we develop a new numerical approach for recovering a spatially dependent source component in a standard parabolic equation from partial interior measurements. We establish novel conditional Lipschitz stability and H\"{o}lder…
We define discrete Hamiltonian systems in the framework of discrete embeddings. An explicit comparison with previous attempts is given. We then solve the discrete Helmholtz's inverse problem for the discrete calculus of variation in the…
We consider an inverse source problem in the two-time-scale mobile-immobile fractional diffusion model from partial interior observation. Theoretically, we combine the fractional Duhamel's principle with the weak vanishing property to…
For a general class of diffusion processes with multiplicative noise, describing a variety of physical as well as financial phenomena, mostly typical of complex systems, we obtain the analytical solution for the moments at all times. We…
The large moment method can be used to compute a large number of moments of physical quantities that are described by coupled systems of linear differential equations. Besides these systems the algorithm requires a certain number of initial…
The inverse problem in Seismology is tackled in this paper under three particular circumstances. First, the inverse problem is defined as the determination of the seismic-moment tensor from the far-field seismic waves (P and S waves). We…
This paper proposes direct and inverse results for the Dirichlet and Dirichlet to Neumann problems for complex curves with nodal type singularities. As an application, we give a method to reconstruct the conformal structure of a compact…
We study a class of projective transformations of spectraplexes associated with self-dual cones and, on this basis, propose a polynomial-time algorithm for convex feasibility problems with positive definite constraints. At each iteration of…
We consider $\sigma$-harmonic mappings, that is mappings $U$ whose components $u_i$ solve a divergence structure elliptic equation ${\rm div} (\sigma \nabla u_i)=0$, for $i=1,\ldots,n $. We investigate whether, with suitably prescribed…
We study the inverse problem for the fractional Laplace equation with multiple nonlinear lower order terms. We show that the direct problem is well-posed and the inverse problem is uniquely solvable. More specifically, the unknown…
We discuss a quantum mechanical indirect measurement method to recover a position dependent Hamilton matrix from time evolution of coherent quantum mechanical states through an object. A mathematical formulation of this inverse problem…
The uniform probability measure on a convex polytope induces piecewise polynomial densities on its projections. For a fixed combinatorial type of simplicial polytopes, the moments of these measures are rational functions in the vertex…
We present a complexity measure for any finite time series. This measure has invariance under any monotonic transformation of the time series, has a degree of robustness against noise, and has the adaptability of satisfying almost all the…