Exact inversion of a compound conical Radon transform and a novel nuclear imaging principleInversion exacte d'une transformation conique de Radon composée et nouveau principe d'imagerie nucléaire

A new integral transform arising from a theory of imaging based on Compton scattering is introduced and the explicit expression for its inverse is established. Its properties serve as foundation to a new nuclear emission imaging principle. To cite this article: M.K. Nguyen, T.T. Truong, C. R. Acad. Sci. Paris, Ser. I 335 (2002) 213–217.     

Self-adaptive gradient projection algorithms for variational inequalities involving non-Lipschitz continuous operators

Numerical Algorithms - In this paper, we introduce a self-adaptive inertial gradient projection algorithm for solving monotone or strongly pseudomonotone variational inequalities in real Hilbert...     

Regularity of the solution for a final value problem for the Rayleigh‐Stokes equation

In this paper, we deal with the backward problem of determining initial condition for Rayleigh‐Stokes where the data are given at a fixed time. The problem has many applications in some non‐Newtonian fluids. We give some regularity properties of the solution to backward problem.     

Variable sampling interval Shewhart control charts for monitoring the multivariate coefficient of variation

In many industrial manufacturing processes, the ratio of the variance to the mean of a quantity of interest is an important characteristic to ensure the quality of the processes. This ratio is called the coefficient of variation (CV). A lot of control charts have been designed for monitoring the CV of univariate quantity in the literature. However, the CV control charts for multivariate quantity have not received much attention yet. In this paper, we investigate a variable sampling interval (VSI) Shewhart control chart for monitoring multivariate CV. The time between two consecutive samples is allowed to vary according to the previous value of the multivariate CV, which will help the chart to detect the process shifts faster. The comparison with the fixed sampling interval Shewhart chart is implemented to highlight the advantage of the VSI method. Finally, an illustrative example is demonstrated on real data.     

Remarks on the Emergence of Weak Euler Solutions in the Vanishing Viscosity Limit

Journal of Nonlinear Science - We prove that if the local second-order structure function exponents in the inertial range remain positive uniformly in viscosity, then any spacetime $$L^2$$ weak...     

Anisotropic Hardening of Sheet Metals at Elevated Temperature: Tension-Compressions Test Development and Validation

New test equipment has been developed to measure the in-plane cyclic behavior of sheet metals at elevated temperatures. The tester has clamping dies with adjustable side force to prevent the sheet specimens from buckling during compressive loading. In addition to the room temperature experiment, cartridge type heaters are inserted in the clamping dies so that the specimen can be heated up to 400 °C during the cyclic tests. For the strain measurement, a non-contact type laser extensometer is used. In order to validate the newly developed test device, the tension-compression (and compression-tension) tests under pre-strains and various temperatures have been performed. As model materials, the aluminum alloy sheet which exhibits a large Bauschinger effect and the magnesium alloy sheet which exhibits different amounts of asymmetry under cyclic loading are used. The developed device can be well-suited to measure the cyclic material behavior, especially the anisotropic and asymmetric hardening of light-weight materials.     

On σ(·, W)-Holomorphic Functions and Theorems of Vitali-Type

The aim of this paper is to give some criterions for holomorphy of F-valued σ(F, W)-holomorphic functions which are bounded on bounded sets in a domain D of Fréchet spaces E (resp. ${\mathbb{C}^n}$ ) where ${W \subset F'}$ defines the topology of Fréchet space F. Base on these results we consider the problem on holomorphic extension of F-valued σ(F, W)-holomorphic functions from non-rare subsets of D and from subsets of D which determines uniform convergence in H(D). As an application of the above, some theorems of Vitali-type for a locally bounded sequence ${\{f_i\}_{i \in \mathbb{N}}}$ of Fréchet-valued holomorphic functions are also proved.     

The smallest enclosing ball problem and the smallest intersecting ball problem: existence and uniqueness of solutions

In this paper we study the following problems and their further generalizations: given a finite number of nonempty closed subsets of a normed space, find a ball with the smallest radius that encloses all of the sets, and find a ball with the smallest radius that intersects all of the sets. These problems can be viewed as generalized versions of the smallest enclosing circle problem introduced in the nineteenth century by Sylvester which asks for the circle of smallest radius enclosing a given set of finite points in the plane. We will focus on sufficient conditions for the existence and uniqueness of an optimal solution for each problem, while the study of optimality conditions and numerical implementation will be addressed in our next projects.