In the paradigm of von Neumann and Morgenstern, a representation of a ne preferences in terms of an expected utility can be obtained under the assumption of weak continuity. Since the weak topology is coarse, this requirement is a priori far from being negligible. In this work, we replace the assumption of weak continuity by monotonicity. More precisely, on the space of lotteries on a real open...

A graph drawn in the plane is called k-quasi-planar if it does not contain k pairwise crossing edges. It has been conjectured for a long time that for every fixed k, the maximum number of edges of a k-quasi-planar graph with n vertices is O(n). The best known upper bound is n(logn) . In the present note, we improve this bound to (n logn)2 c k (n) in the special case where the graph is drawn in ...

We study a Dirichlet optimal control problem for a quasi-linear monotone elliptic equation, the so-called weighted p-Laplace problem. The coefficient of the p-Laplacian, the weight u, we take as a control in BV (Ω) ∩ L∞(Ω). In this article, we use box-type constraints for the control such that there is a strictly positive lower and some upper bound. In order to handle the inherent degeneracy of...

Qualitative models are more suitable than classical quantitative models in many tasks like Model-based Diagnosis (MBD), explaining system behavior, and designing novel devices from first principles. Monotonicity is an important feature to leverage when constructing qualitative models. Detecting monotone pieces robustly and efficiently from sensor or simulation data remains an open problem. This...

The minimax identity for a nondecreasing upper-semicontinuous utility function satisfying mild growth assumption is studied. In contrast to the classical setting, concavity of not asumed. By considering concave envelope function, equalities and inequalities between robust functionals an initial its concavification are obtained. Furthermore, similar proved in case implementing upper bound on fin...

Let + := {(x1, . . . , xN ) ; xi 0, i = 1, 2, . . . , N} and + := + . Assume that f : + → + is monotone which means that it is monotone with respect to each variable. We denote f ↓, when f is decreasing (= nonincreasing) and f ↑ when f is increasing (= nondecreasing). Throughout this paper ω, u, v are positive measurable functions defined on + , N 1. A function P on [0,∞) is called a modular fu...

Let E be a topological vector space and X be a non-empty subset of E. Let S : X → 2X and T : X → 2E be two maps. Then the generalized quasi-variational inequality (GQVI) problem is to find a point ŷ ∈ S(ŷ) and a point ŵ ∈ T (ŷ) such that Re〈ŵ, ŷ − x〉 ≤ 0 for all x ∈ S(ŷ). We shall use Chowdhury and Tan’s 1996 generalized version of Ky Fan’s minimax inequality as a tool to obtain some general th...

‎‎In this paper‎, ‎the existence and uniqueness of positive solutions for a class of nonlinear initial value problem for a finite fractional difference equation obtained by constructing the upper and lower control functions of nonlinear term without any monotone requirement‎ .‎The solutions of fractional difference equation are the size of tumor in model tumor growth described by the Gompertz f...