Afterglow light curves are constructed analytically for realistic gamma-ray burst remnants decelerating in either a homogeneous interstellar medium or a stellar wind environment, taking into account the radiative loss of the blast wave, which affects the temporal behaviors significantly. Inverse Compton scattering, which plays an important role when the energy equipartition factor ǫe of electro...

Not all approximations arise from information systems. The problem of fitting approximations, subjected to some rules (and related data), to information systems in a rough scheme of things is known as the inverse problem. The inverse problem is more general than the duality (or abstract representation) problems and was introduced by the present author in her earlier papers. From the practical p...

In this paper, a link between the Hyers–Ulam stability and the Moore–Penrose inverse is established, that is, a closed operator has the Hyers–Ulam stability if and only if it has a bounded Moore–Penrose inverse. Meanwhile, the stability constant can be determined in terms of the Moore– Penrose inverse. Based on this result, some conditions for the perturbed operators having the Hyers– Ulam stab...

The inverse spectral transform for the Zakharov-Shabat equation on the semi-line x > 0 is reconsidered as a Hilbert problem. The boundary data induce an essential singularity as k → ∞ to one of the basic solutions. Then solving the inverse problem means solving a Hilbert problem with particular prescribed behavior. It is demonstrated that the direct and inverse problems are solved in a consiste...

Abstract: This study proposes to examine the design methodology and the performances of an inverse dynamic model by fusion of statistical training and deterministic modeling. We carry out an inverse semi-physical model using a recurrent neural network and illustrate it on a didactic example. This technique leads to the realization of a neural network inverse problem solver (NNIPS). In the first...

Suppose that X1, X2, X3, . . . is a sequence of continua and fi : Xi+1 → 2Xi is an upper semi-continuous set-valued function for each positive integer i; let Gn = {x ∈ ∏n+1 i=1 Xi | xi ∈ fi(xi+1) for 1 ≤ i ≤ n}. We show that if Gn is a chainable continuum for each n ∈ N, then the inverse limit lim ←− is chainable. We use this to show that two well-studied examples of inverse limits on [0, 1] wi...

Hybrid inverse problems aim to combine two imaging modalities, one that displays large contrast and one that gives high resolution. Mathematically, quantitative reconstructions in such hybrid problems involve reconstructing coefficients in a partial differential equation (PDE) from point-wise functionals of the coefficients and the PDE solution. There are many settings in which such inverse pro...

We discuss the use of local basis expansions (LBEX) for solving linear inverse problems with continuous source spaces. The LBEX method is a generalisation, to the linear inverse problem, of the multitaper technique for spectral analysis. The multitaper technique employs Slepian sequences, that are maximally concentrated in the frequency domain. The analog for LBEX are combinations of lead field...

The response of JERS-1 and ERS-1 synthetic aperture radar (SAR) to the forest stem volume (biomass) was investigated by employing a digital stem volume map and weather information. The stem volume map was produced from the National Forest Inventory sample plot data together with a LANDSAT thematic mapper (TM) image. A new indirect inversion method was developed and tested to estimate the forest...

For a generator A of a C0 -semigroup T (·) on a Banach space X we consider the semi-norm Mk x := lim supt→0+ ‖t−1(T (t)− I)Ak−1x‖ on the Favard space Fk of order k associated with A . The use of this semi-norm is motivated by the functional analytic treatment of time-discretization methods of linear evolution equations. We show that sharp inequalities for bounded linear operators on D(Ak) can b...