We study the problem of estimating the coefficients in an elliptic partial differential equation using noisy measurements of a solution to the equation. Although the unknown coefficients may vary on many scales we aim only at estimating their slowly varying parts, thus reducing the complexity of the inverse problem. However, ignoring the fine-scale fluctuations altogether introduces uncertainty...

The logistic Generalized Estimating Equations (logisticGEE) models have been extensively used for analyzing clustered binary data. However, assessing the goodness-of-fit and predictability of these models is problematic due to the fact that no likelihood is available and the observations can be correlated within a cluster. In this paper we propose a new measure for estimating the generalization...

In this paper we formulate a time-optimal control problem in the space of probability measures. The main motivation is to face situations in nitedimensional control systems evolving deterministically where the initial position of the controlled particle is not exactly known, but can be expressed by a probability measure on R. We propose for this problem a generalized version of some concepts fr...

This paper address a new vision for the generalized Mittag-Leffler stability of the fractional differential equations. We mainly focus on a new method, consisting of decomposing a given fractional differential equation into a cascade of many sub-fractional differential equations. And we propose a procedure for analyzing the generalized Mittag-Leffler stability for the given fractional different...

BACKGROUND Non-communicable diseases (NCDs) are rising among US Hispanics, but few studies have examined the preventive health behaviors for these NCDs among Hispanics. This study compared the preventive health behaviors of smoke-free living, physical activity, fruit and vegetable consumption, and avoidance of heavy alcohol use in Hispanics in the United States and Hispanics living along the US...

We analyze electromagnetic TM scattering from a diffraction grating consisting of a dielectric with possibly negative real part. The scattering problem can be reformulated as a strongly singular volume integral equation, a technique that attracts continuous interest in the engineering community, but rarely received rigorous theoretic treatment. In this paper, we provide (generalized) G̊arding es...

In this paper, the meshless local Petrov-Galerkin (MLPG) method is applied for solving a generalized Black-Scholes equation in financial problems. This equation is a PDE governing the price evolution of a European call or a European put under the Black-Scholes model. The θ-weighted method and MLPG are used for discretizing the governing equation in time variable and option pricing, respectively...

a general notion of completely monotone functionals on an ordered banach algebra b into a proper h*-algebra a with an integral representation for such functionals is given. as an application of this result we have obtained a characterization for the generalized completely continuous monotone functions on weighted foundation semigroups. a generalized version of bochner’s theorem on foundation se...

Summary: We consider the problem of estimating the first k coefficients in a regression equation with k + 1 variables. For this problem with known variance of innovations, the neutral Laplace weighted-average least-squares estimator was introduced in Magnus (2002). We investigate properties of this estimator in the case where the unknown variance is estimated by least squares. We find that the ...