This work is concerned with the semiclassical approximation of the SchrödingerPoisson equation modeling ballistic transport in a 1D periodic potential by means of WKB techniques. It is derived by considering the mean-field limit of a N -body quantum problem, then K-multivalued solutions are adapted to the treatment of this weakly nonlinear system obtained after homogenization without taking int...

Functional dependencies, a notion originated in Relational Database Theory, are known to admit interesting characterizations in terms of Formal Concept Analysis. In database terms, two successive, natural extensions of the notion of functional dependency are the socalled degenerate multivalued dependencies, and multivalued dependencies proper. We propose here a new Galois connection, based on a...

The study of fixed points for multivalued contractions and nonexpansive maps using the Hausdorff metric was initiated by Markin [17]. Later, an interesting and rich fixed point theory for such maps has been developed. The theory of multivalued maps has applications in control theory, convex optimization, differential inclusions, and economics (see, e.g., [3, 8, 16, 22]). The theory of multivalu...

Implementation of silicon-quantum-dots (Si-QDs) as a floating gate in metal-oxide-semiconductor field-effect transistors (MOSFETs) has received increasing attention because of its potential advantage for multivalued memories operating reliably even at room temperature and above [1-3]. In this work, we focused on electron storage in Si-QDs stack structures and studied electron charging, discharg...

In this paper, we introduce a new class of bifunction variational inequalities, which is called the multivalued mixed quasi bifunction variational inequalities. Using the auxiliary principle technique, we suggest and analyze a proximal point method for solving the multivalued mixed quasi bifunction variational inequalities. It is shown that the convergence of the proposed method requires only p...

The use of multivalued controls derived from a special maximal monotone operator are studied in this note. Starting with a strictly passive linear system (with possible parametric uncertainty and external disturbances) a multivalued control law is derived, ensuring regulation of the output to a desired value. The methodology used falls in a passivity-based control context, where we study how th...

Department of Mathematics, Lund Institute of Technology P.O. Box 118, S-221 00 LUND, Sweden email:[email protected] Abstract. In the exponential Radon transform in R2 , the integrals of a scalar function f over lines, with exponential weight functions, are determined. In this paper we demonstrate how to define two different kinds of exponential Radon transforms for vector fields in R2 in a natu...

We describe an approach to define contours of 3D vector fields and employ them as an interactive flow visualization tool. Although contours are well-defined and commonly used for surfaces and 3D scalar fields, they have no straightforward extension in vector fields. Our approach is to extract and visualize specific stream lines which show the most similar behavior to contours on surfaces. This ...

Diffraction and reflection of an arbitrarily polarized plane wave by an arbitrarily oriented spheroid in the short-wavelength limit are considered in the context of ray theory. A closed-form solution for both diffraction and reflection is obtained, and the polarization character of the diffracted plus reflected electric field is obtained. It is found that the magnitude of the reflected electric...