We consider the optimal control of initial-boundary value problems for entropy solutions of scalar hyperbolic conservation laws. In particular, we consider initial-boundary value problems where the initial and boundary data switch between different C-functions at certain switching points and both, the functions and the switching points, are controlled. We show that the control-tostate mapping i...

Let (μα) be a net of Radon sub-probability measures on R, and (tα) be a net in ]0,+∞[ converging to 0. Assuming that the generalized log-moment generating function L(λ) exists for all λ in a nonempty open interval G, we give conditions on the left or right derivatives of L|G, implying vague (and thus narrow when 0 ∈ G) large deviations. The rate function (which can be nonconvex) is obtained as ...

In this paper, the problem of the global robust asymptotic stability (GRAS) for a class of interval neural networks described by nonlinear delayed differential equations of the neutral type is investigated. A series of sufficient criteria for such problems are obtained by employing Lyapunov-Krasovskii functional and LMI technique. These conditions are dependent on the size of the time delay, wh...

Zaj́ıček has recently shown that for a lower semi-continuous real-valued function on an Asplund space, the set of points where the function is Fréchet subdifferentiable but not Fréchet differentiable is first category. We introduce another variant of Fréchet differentiability, called Fréchet directional differentiability, and show that for any realvalued function on a normed linear space, the se...

In this paper, we aim to explore properties of a class of NCP-functions and investigate a related semismooth Newton method for complementarity problems. Some favorite properties about the class of NCP-functions and its merit function are discussed including strong semismoothness, continuous differentiability and the nonsingularity of the element in C-subdifferential. In particular, we present a...

Fuzzy differential equations are used in modeling problems in science and engineering. For instance, it is known that the knowledge of dynamical systems modeled by ordinary differential equations is often incomplete or vague. While, fuzzy differential equations represent a proper way to model dynamical systems under uncertainty and vagueness. In this paper, two methods for solving first order l...

A class of semismooth Newton methods for unilaterally constrained variational problems modelling cracks under a non-penetration condition are introduced and investigated. On the continuous level, a penalization technique is applied which allows to argue generalized differentiability of the nonlinear mapping associated to its first order optimality characterization. It is shown that the correspo...

A formulation of the second-order Hadamard differentiability of (extended) statistical functionals and some related theoretical results are established. These results are applied to derive the limiting distributions of a class of generalized Crame r von Mises type test statistics, which include some proposed new ones for the tests of goodness of fit in the 3-sample problems, the tests in linear...

Abstract. A generalized Cauchy problem for quasilinear hyperbolic functional differential systems is considered. A theorem on the local existence of weak solutions is proved. The initial problem is transformed into a system of functional integral equations for an unknown function and for their partial derivatives with respect to spatial variables. The existence of solutions for this system is p...

We study sun-products on R, i.e. generalized Abelian deformations associated with star-products for general Poisson structures on R. We show that their cochains are given by differential operators. As a consequence, the weak triviality of sun-products is established and we show that strong equivalence classes are quite small. When the Poisson structure is linear (i.e., on the dual of a Lie alge...