Parameters for a two-state solution

It is now fashionable to bury the idea of a two-state solution, saying it is no longer practical. However, all who are quick to bury the idea are very slow to propose an alternative, possibly because no alternative exists. What follows is an attempt to delineate the parameters needed to end the protracted Israeli-Palestinian conflict. For such a momentous achievement of resolving a deep, entrenched conflict, three things are absolutely essential: • An Israeli leader who is committed to bring peace to his/her people and is willing to pay the necessary price; • A Palestinian leader who is committed to bring peace to his/her people and is willing to pay the necessary price; and • A shared belief by both leaders that the time is ripe for peace. This means both leaders believe that enough blood has been shed, that they need to seize the moment because things might worsen for their people, and that they have the ability to lead their respective people to accept the peace agreement in order to change reality for the better. At no given time during the past two decades have these three ingredients coexisted. In 1993 and 2000, Prime Ministers Yitzhak Rabin and Ehud Barak were committed to peace and felt that the time was ripe, but it’s debatable whether that commitment and feeling were shared by their Palestinian counterpart, Yasser Arafat. The three leaders did not have the full backing of their people and were either unable or unwilling to instill in their people a sense of urgency and yearning for peace, which must come at a high price. The way to escape the current deadlock is to rely on the Clinton Parameters, the Geneva Accord, the Arab Peace Initiative and the Olmert-Abbas Talks. These documents contain the foundations for resolving all contentious issues

Ground state solution of a noncooperative elliptic system

In this paper, we study the existence of a ground state solution, that is, a non trivial solution with least energy, of a noncooperative semilinear elliptic system on a bounded domain. By using the method of the generalized Nehari manifold developed recently by Szulkin and Weth, we prove the existence of a ground state solution when the nonlinearity is subcritical and satisfies a weak superquadratic condition.Comment: 9 page

H_2-Optimal Decentralized Control over Posets: A State-Space Solution for State-Feedback

We develop a complete state-space solution to H_2-optimal decentralized control of poset-causal systems with state-feedback. Our solution is based on the exploitation of a key separability property of the problem, that enables an efficient computation of the optimal controller by solving a small number of uncoupled standard Riccati equations. Our approach gives important insight into the structure of optimal controllers, such as controller degree bounds that depend on the structure of the poset. A novel element in our state-space characterization of the controller is a remarkable pair of transfer functions, that belong to the incidence algebra of the poset, are inverses of each other, and are intimately related to prediction of the state along the different paths on the poset. The results are illustrated by a numerical example.Comment: 39 pages, 2 figures, submitted to IEEE Transactions on Automatic Contro

Ground state solution of a nonlocal boundary-value problem

In this paper, we apply the method of the Nehari manifold to study the Kirchhoff type equation \begin{equation*} -\Big(a+b\int_\Omega|\nabla u|^2dx\Big)\Delta u=f(x,u) \end{equation*} submitted to Dirichlet boundary conditions. Under a general $4-$superlinear condition on the nonlinearity $f$, we prove the existence of a ground state solution; that is a nontrivial solution which has least energy among the set of nontrivial solutions. In case which $f$ is odd with respect to the second variable, we also obtain the existence of infinitely many solutions. Under our assumptions the Nehari manifold does not need to be of class $\mathcal{C}^1$.Comment: 8 page

Variational-Iterative Solution of Ground State for Central Potential

The newly developed iterative method based on Green function defined by quadratures along a single trajectory is combined with the variational method to solve the ground state quantum wave function for central potentials. As an example, the method is applied to discuss the ground state solution of Yukawa potential, using Hulthen solution as the trial function.Comment: 9 pages with 1 tabl