Multiplicities of Points on Schubert Varieties in Grassmannians

We obtain an explicit determinantal formula for the multiplicity of any point on a classical Schubert variety.     

Approximating a solution set of nonlinear inequalities

In this paper we propose a method for solving systems of nonlinear inequalities with predefined accuracy based on nonuniform covering concept formerly adopted for global optimization. The method generates inner and outer approximations of the solution set. We describe the general concept and three ways of numerical implementation of the method. The first one is applicable only in a few cases when a minimum and a maximum of the constraints convolution function can be found analytically. The second implementation uses a global optimization method to find extrema of the constraints convolution function numerically. The third one is based on extrema approximation with Lipschitz under- and overestimations. We obtain theoretical bounds on the complexity and the accuracy of the generated approximations as well as compare proposed approaches theoretically and experimentally.     

Asymptotic velocity for fibered Hamiltonians

We show the existence of the asymptotic velocity for a large class of Hamiltonians with a fibered structure.     

Project screening with tiered evaluation

We study a Bayesian game of two-sided incomplete information in which an agent, who owns a project of unknown quality, considers proposing it to an evaluator, who has the choice of whether or not to accept it. There exist two distinct tiers of evaluation that differ in the benefits they deliver to the agent upon acceptance of a project. The agent has to select the tier to which the project is submitted for review. Making a proposal incurs a cost on the agent in the form of a submission cost. We examine the effect of changes in the payoff parameters at the two tiers of evaluation on the efficiency of the equilibrium outcome. We show that changes in these parameters that are aimed at increasing the level of self-screening exerted by the agent do not necessarily have beneficial effects either on the quality of projects submitted for review or on the quality of projects that are implemented. From a methodological viewpoint, our paper proposes a novel method of performing comparative statics in games whose equilibria are defined by a system of equations with no closed-form solution.