Patrolling games were recently introduced by Alpern, Morton and Papadaki to model the problem of protecting the nodes of a network from an attack. Time is discrete and in each time unit the Patroller can stay at the same node or move to an adjacent node. The Attacker chooses when to attack and which node to attack, and needs m consecutive time units to carry it out. The Attacker wins if the Pat...

Rosamine derivative RC-1, bearing macrocyclic ligand [15]aneNO(2)S(2) as receptor, was synthesized as an enhanced fluorescent chemosensor for Ag(+) in absolute aqueous solution. The fluorescence images in living cells show the potential application of RC-1. The difference of fluorescence enhancement process after binding with Ag(+)/Hg(2+) in acetonitrile/water solution was first proved by theor...

We introduce a new notion of viscosity solutions for the level set formulation of the motion by crystalline mean curvature in three dimensions. The solutions satisfy the comparison principle, stability with respect to an approximation by regularized problems, and we also show the uniqueness and existence of a level set flow for bounded crystals.

A randomized-controlled study compared the preparatory effects of problem-posing on learning from subsequent instruction. Students engaged in problem-posing either with solution generation (where they generated problems and solutions to a novel situation) or problem-posing without solution generation (where they generated only problems) prior to learning a novel math concept. Problem-posing wit...

The author studies on a hedging problem for an European contingent claim in a certain incomplete market model by using a homogeneous filtered value measure. He considers the minimal hedging risk in discrete time model and its continuous limit. As a result, he shows that this limit is described by a viscosity solution of some HamiltonJacobi-Bellman equation.

Natural compounds still play an increasingly important role in many areas of research and development. Their structural diversity is enhanced by the synthetic potential of combinatorial chemistry. Fractionation and separation of samples obtained from nature remain time-consuming, tedious and extremely expensive even though the assays for testing these samples have become faster and more cost-ef...

In this paper we prove that a function u ∈ C(Ω) is the continuous value of the Tug-of-War game described in [19] if and only if it is the unique viscosity solution to the infinity laplacian with mixed boundary conditions

This paper is devoted to the study of the maximum principle for the elliptic equation with a deviated argument. We will consider viscosity solutions of this equation.

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