In this paper we study relations between the minimax, risk averse and nested formulations of multistage stochastic programming problems. In particular, we discuss conditions for time consistency of such formulations of stochastic problems. We also describe a connection between law invariant coherent risk measures and the corresponding sets of probability measures in their dual representation. F...

Let Fn denote the distribution function of the normalized sum Zn = (X1+ · · ·+Xn)/σ √ n of i.i.d. random variables with finite fourth absolute moment. In this paper, polynomial rates of convergence of Fn to the normal law with respect to the Kolmogorov distance, as well as polynomial approximations of Fn by the Edgeworth corrections (modulo logarithmically growing factors in n) are given in ter...

The classical Kramer sampling theorem is, in the subject of self-adjoint boundary value problems, one of the richest sources to obtain sampling expansions. It has become very fruitful in connection with discrete Sturm-Liouville problems. In this paper, a discrete version of the analytic Kramer sampling theorem is proved. Orthogonal polynomials arising from indeterminate Hamburger moment problem...

We define spinc prequantization of a symplectic manifold to be a spinc structure and a connection which are compatible with the symplectic form. We describe the cutting of an S-equivariant spinc prequantization. The cutting process involves a choice of a spinc prequantization for the complex plane. We prove that the cutting is possible if and only if the moment map level set along which the cut...

Abstract We study a system of equations on compact complex manifold, that couples the scalar curvature Kähler metric with spectral function first-order deformation structure. The comes from an infinite-dimensional reduction, which is hyperkähler reduction for particular choice function. main tool studying flat connection space deformations structure, allows to obtain formal complexification mom...

A fundamentally new understanding of the classical electromagnetic interaction of a point charge and a magnetic dipole moment through order v/c is suggested. This relativistic analysis connects together hidden momentum in magnets, Solem’s strange polarization of the classical hydrogen atom, and the Aharonov-Bohm phase shift. First we review the predictions following from the traditional particl...