The n-interior point variant of the Erdős-Szekeres problem is the following: for any n, n ≥ 1, does there exist a g(n) such that every point set in the plane with at least g(n) interior points has a convex polygon containing exactly n-interior points. The existence of g(n) has been proved only for n ≤ 3. In this paper, we show that, for point sets having at most logarithmic number of convex lay...

This paper describes a new technique for generating convex, strictly concave and indeenite (bilinear or not) quadratic programming problems. These problems have a number of properties that make them useful for test purposes. For example, strictly concave quadratic problems with their global maximum in the interior of the feasible domain and with an exponential number of local minima with distin...

We formulate a universal characterization of the many-particle quantum entanglement in the ground state of a topologically ordered two-dimensional medium with a mass gap. We consider a disk in the plane, with a smooth boundary of length L, large compared to the correlation length. In the ground state, by tracing out all degrees of freedom in the exterior of the disk, we obtain a marginal densit...

Camouflage is frequently used by animals and humans (usually for military purposes) in order to conceal objects from visual surveillance or inspection. Most camouflage methods are based on superpositioning multiple edges on the object that is supposed to be hidden, such that its familiar contours and texture are masked. In this work, we present an operator, (Darg), that is applied directly to t...

Interior operator games arose by abstracting some properties of several types of cooperative games (for instance: peer group games, big boss games, clan games and information market games). This reason allow us to focus on different problems in the same way. We introduced these games in Bilbao et al. (Ann. Oper. Res. 137:141–160, 2005) by a set system with structure of antimatroid, that determi...

In this paper we introduce the notion of fuzzy interior ideals in ternary semigroups and investigated relations between fuzzy ideals and fuzzy interior ideals in terms of regularity. Here a characterization of fuzzy interior ideals is obtained in terms of fuzzy translation operator. The notions of rough and rough fuzzy interior ideals in a ternary semigroup are introduced. Relation between cong...

We discuss the set of wavefunctions $\psi_V(t)$ that can be obtained from a given initial condition $\psi_0$ by applying flow Schr\"odinger operator $-\Delta + V(t,x)$ and varying potential $V(t,x)$. show this has empty interior, both as subset sphere in $L^2(\mathbb{R}^d)$ trajectories.

In this manuscript, we consider the inverse problem for non self-adjoint Sturm--Liouville operator $-D^2+q$ with eigenparameter dependent boundary and discontinuity conditions inside a finite closed interval. We prove by defining a new Hilbert space and using spectral data of a kind, the potential function can be uniquely determined by a set of value of eigenfunctions at an interior point and p...