We consider a zero sum differential game with lack of observation on one side. The initial state of the system is drawn at random according to some probability μ0 on IR N . Player I is informed of the initial position of state while player II knows only μ0. Moreover Player I observes Player II’s moves while Player II is blind and has no further information. We prove that in this game with a ter...

The Dirichlet problem for the 2D Helmholtz equation in an exterior domain with cracks is studied. The compatibility conditions at the tips of the cracks are assumed. The existence of a unique classical solution is proved by potential theory. The integral representation for a solution in the form of potentials is obtained. The problem is reduced to the Fredholm equation of the second kind and of...

We analyze the set of continuous viscosity solutions of the infinity Laplace equation −∆∞w(x) = f(x), with generally sign-changing right-hand side in a bounded domain. The existence of a least and a greatest continuous viscosity solutions, up to the boundary, is proved through a Perron’s construction by means of a strict comparison principle. These extremal solutions are proved to be absolutely...

Employment is one of the bread-and –butter issues requiring urgent attention and careful handling. With the accelerating of the urbanization, a large number of surplus labors have appeared in rural areas of China. At the same time, in the course of the deepening reform of state-owned enterprises, there are more and more laid-off workers, so the problem of unemployment sticks out. In this paper,...

An inventory model for a deteriorating item with price sensitive demand is developed under deterioration rate, which is assumed to follow weibull distribution with known parameter. In addition, we allow for multiple price changes about an item, but the number of price changes isn’t given. The purpose of this paper is to find the optimal number of price settings, the optimal dynamic prices and t...

X iv :0 90 8. 30 57 v1 [ m at h. A P] 2 1 A ug 2 00 9 EXISTENCE AND REGULARITY FOR THE GENERALIZED MEAN CURVATURE FLOW EQUATIONS RONGLI HUANG AND JIGUANG BAO Abstract. By making use of the approximation method, we obtain the existence and regularity of the viscosity solutions for the generalized mean curvature flow. The asymptotic behavior of the flow is also considered. In particular, the Diri...

The design studio 'Flying Bricks' was held during the summer semester 2015. Its main objective was to redesign an existing building with the use of facing bricks algorithmically, utilizing algorithmic thinking and programming as a means for form generation. The purpose of having students express their designs in terms of code was to emphasize problem thinking over solution generation, which has...

In this paper we consider a free boundary problem which is used to describe the motion of contact lines of a liquid droplet on a flat surface. The elliptic nature of the equation for droplet shape and the monotonic dependence of contact line velocity on contact angle allows us to introduce a notion of “viscosity” solutions for this problem. Unlike similar free boundary problems, a comparison pr...

i2b2 has proven to be a valuable tool for a variety of tasks in clinical and translational research. But to establish an extended IT infrastructure, several clinical information systems have to be connected seamlessly and routine data integration processes have to be defined. In this position paper, we will outline a number of options that would enhance the existing software stack with regards ...

The nonnegative viscosity solutions to the infinite heat equation with homogeneous Dirichlet boundary conditions are shown to converge as t → ∞ to a uniquely determined limit after a suitable time rescaling. The proof relies on the half-relaxed limits technique as well as interior positivity estimates and boundary estimates. The expansion of the support is also studied.