In the discrete setting of one-dimensional finite-differences we prove a Carleman estimate for a semi-discretization of the parabolic operator ∂t − ∂x(c∂x) where the diffusion coefficient c has a jump. As a consequence of this Carleman estimate, we deduce consistent nullcontrollability results for classes of semi-linear parabolic equations.

Abstract A 3D coefficient inverse problem for a hyperbolic equation with non-overdetermined data is considered. The forward the Cauchy initial condition being delta function concentrated at single plane (i.e. wave). certain associated operator written in finite differences respect to two out of three spatial variables, i.e. “partial differences”. grid step size bounded from below by fixed numbe...

abstract for seismic design, it is important to estimate the, maximum lateral displacement (inelastic displacement) of the structures due to earthquakes for several reasons. seismic design provisions estimate the maximum roof and storey drifts occurring in major earthquakes by amplifying the roof displacement and drifts of the structures obtained by elastic analysis subjected to seismic design ...

to investigate the possibility of using ultrasound to estimate carcass composition, 38 moghani male lambs were made use of. subcutaneous fat depth (usft) and longissimus dorsi muscle depth (ulmd) and area (ulma) were assessed in the site between 12th and 13th ribs by using ultrasound equipped with an 8 mhz probe. the lambs were then slaughtered. carcasses were cold stored at 4°c for 24 hours an...

The role of the Lambert-Beer law in ocean optics is critically examined. The Lambert-Beer law and the three-parameter model of the submarine light field are used to construct an optical energy budget for any hydrosol. It is further applied to the analytical exponential decay coefficient of the light field and used to estimate the optical properties and effects of the dissolved/suspended compone...

A composite score is the sum of a set of components. For example, a total test score can be defined as the sum of the individual items. The reliability of composite scores is of interest in a wide variety of contexts due to their widespread use and applicability to many disciplines. The psychometric literature has devoted considerable time to discussing how to best estimate the population relia...

Motivated by recent work on studying massive imaging data in various neuroimaging studies, we propose a novel spatially varying coefficient model (SVCM) to capture the varying association between imaging measures in a three-dimensional (3D) volume (or 2D surface) with a set of covariates. Two stylized features of neuorimaging data are the presence of multiple piecewise smooth regions with unkno...