Related papers: On the Stewart-Lyth Inverse Problem
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 study the stability of a scalar inflaton field and analyze its point attractors in the phase space. We show that the value of the inflaton field in the vacuum is a bifurcation parameter and prove the possible existence of a limit cycle…
The Sturm-Liouville operator on a star-shaped graph is considered. We assume that the potential is known a priori on all the edges except one, and study the partial inverse problem, which consists in recovering the potential on the…
The resolvent approach is applied to the spectral analysis of the heat equation with non decaying potentials. The special case of potentials with spectral data obtained by a rational similarity transformation of the spectral data of a…
For an expensive to evaluate computer simulator, even the estimate of the overall surface can be a challenging problem. In this paper, we focus on the estimation of the inverse solution, i.e., to find the set(s) of input combinations of the…
Starting from the hypothesis of scaling solutions, the general exact form of the scalar field potential is found. In the case of two fluids, it turns out to be a negative power of hyperbolic sine. In the case of three fluids the analytic…
The inverse problem of spectral analysis for the non-self-adjoint matrix Sturm-Liouville operator on a finite interval is investigated. We study properties of the spectral characteristics for the considered operator, and provide necessary…
Sharp shapes in the inflaton potentials often lead to short departures from slow roll which, in turn, result in deviations from scale invariance in the scalar power spectrum. Typically, in such situations, the scalar power spectrum exhibits…
The inverse spectral problem is studied for the Sturm-Liouville operator with a complex-valued potential and arbitrary entire functions in one of the boundary conditions. We obtain necessary and sufficient conditions for uniqueness, and…
The paper deals with two inverse problems for Sturm--Liouville operator $Ly=-y" +q(x)y$ on the finite interval $[0,\pi]$. The first one is the problem of recovering of a potential by two spectra. We associate with this problem the map $F:\,…
We investigate the impact of modified-gravity models on the Lyman-$\alpha$ power spectrum. Building a simple analytical modeling, based on a truncated Zeldovich approximation, we estimate the intergalactic medium power spectrum and the…
In this work, we consider the inverse scattering transform and multi-solition solutions of the sextic nonlinear Schr\"{o}dinger equation. The Jost functions of spectrum problem are derived directly, and the scattering data with $t=0$ are…
We consider a more general initial condition satisfying the minimal uncertainty relationship. We calculate the power spectrum of a simple model in inflationary cosmology. The results depend on perturbations generated below a fundamental…
In this paper we propose a perturbative method for the reconstruction of the covariance matrix of a multinormal distribution, under the assumption that the only available information amounts to the covariance matrix of a spherically…
It is believed that some numerical technique must be employed for the determination of the system parameters of a visual binary or a star with a planet because the relevant equations are not only highly nonlinear but also transcendental…
We use a numerical code for accurate computation of the amplitude of linear density perturbations and gravitational waves generated by single-field inflation models to study the accuracy of existing analytic results based on the slow-roll…
We study cosmological tensor perturbations generated during de Sitter inflation in the conformal gravity with mass parameter $m^2=2H^2$. It turns out that tensor power spectrum is scale-invariant.
The inverse eigenvalue problem of a graph studies the real symmetric matrices whose off-diagonal pattern is prescribed by the adjacencies of the graph. The strong spectral property (SSP) is an important tool for this problem. This note…
Motivated by the prospect of testing inflation from precision cosmic microwave background observations, we present analytic results for scalar and tensor perturbations in single-field inflation models based on the application of uniform…
We argue that in models of inflation with two scalar fields and non-canonical kinetic terms there is a possibility of obtaining a red tilt of the power spectrum of curvature perturbations from noncanonicality-induced interactions between…