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Nonparametric Instrumental Variables (NPIV) analysis is based on a conditional moment restriction. We show that if this moment condition is even slightly misspecified, say because instruments are not quite valid, then NPIV estimates can be…
Avila recently introduced a new method for the study of the discrete Schr\"odinger Operator with limit periodic potential. I adapt this method to the context of orthogonal polynomials in the unit circle with limit periodic Verblunsky…
For studying the objectivity and the quality of a given form of the Periodic system as a single whole we compare plots of functions presenting properties of elements in pairs of periods. Using mathematical statistics we introduce a…
Mathematical method of quantum phase space is very useful in physical applications like quantum optics and non-relativistic quantum mechanics. However, attempts to generalize it for the relativistic case lead to some difficulties. One of…
We complete the study of some periods of polynomials in (n+1) variables with (n+2) monomials in computing the behavior of these periods in the natural parameter for such a polynomial.
The behavior of many critical phenomena at large distances is expected to be invariant under the full conformal group, rather than only isometries and scale transformations. When studying critical phenomena, approximations are often…
The least squares method allows fitting parameters of a mathematical model from experimental data. This article proposes a general approach of this method. After introducing the method and giving a formal definition, the transitivity of the…
We analyze transition potentials $(V(r) \stackrel{r\sim 0}{\rightarrow} {\alpha r^{-2}})$ in non-relativistic quantum mechanics using the techniques of supersymmetry. For the range $-1/4 < \alpha < 3/4$, the eigenvalue problem becomes…
Efficient modeling of dispersive materials via time-domain simulations of the Maxwell equations relies on the technique of auxiliary differential equations. In this approach, a material's frequency-dependent permittivity is represented via…
We present a method that allows to distinguish between nearly periodic and strictly periodic time series. To this purpose, we employ a conservative criterion for periodicity, namely that the time series can be interpolated by a periodic…
The main purpose of this paper is to demonstrate and illustrate, once again, the potency of the variational technique as an approximation procedure for the quantization of quantum mechanical systems. By choosing particle-in-a-box…
We use Lyapunov-like functions and convex optimization to propagate uncertainty in the initial condition of nonlinear systems governed by ordinary differential equations. We consider the full nonlinear dynamics without approximation,…
A procedure for asymptotic bias reduction of maximum likelihood estimates of generic estimands is developed. The estimator is realized as a plug-in estimator, where the parameter maximizes the penalized likelihood with a penalty function…
We introduce a minimization formulation for the determination of a finite-dimensional, time-dependent, orthonormal basis that captures directions of the phase space associated with transient instabilities. While these instabilities have…
The Petermann factor and the phase rigidity are convenient measures for various aspects of open quantum and wave systems, such as the sensitivity of energy eigenvalues to perturbations or the magnitude of quantum excess noise in lasers. We…
Estimating the parameters of ordinary differential equations (ODEs) is of fundamental importance in many scientific applications. While ODEs are typically approximated with deterministic algorithms, new research on probabilistic solvers…
We propose a general framework for solving quantum state estimation problems using the minimum relative entropy criterion. A convex optimization approach allows us to decide the feasibility of the problem given the data and, whenever…
The explicit semiclassical treatment of logarithmic perturbation theory for the nonrelativistic bound states problem is developed. Based upon $\hbar$-expansions and suitable quantization conditions a new procedure for deriving perturbation…
The resonant dynamics of a charged particle, governed by the Lorentz force equation in an electromagnetic field generated by a current-carrying wire with a small harmonic modulation, is considered in this study. When regarded as a…
A model Hamiltonian that exhibits asymptotic freedom and a bound state, is used to show on example that similarity renormalization group procedure can be tuned to improve convergence of perturbative derivation of effective Hamiltonians,…