There are two classes of nonlinear expectations, one is the Choquet expectation given by Choquet (1955), the other is the Peng’s g-expectation given by Peng (1997) via backward differential equations (BSDE). Recently, Peng raised the following question: can a g-expectation be represented by a Choquet expectation? In this paper, we provide a necessary and sufficient condition on g-expectations u...

We prove a translative mean value formula for simple valuations, taken at the intersection of a fixed and a translated convex body. MSC 2000: 52A22 (primary); 52B45 (secondary)

In this paper we study the existence of critical points for noncoercive functionals, whose principal part has a degenerate coerciveness. A bifurcation result at zero for the associated differential operator is established.

We prove results generalizing the classical Riemann Singularity Theorem to the case of integral, singular curves. The main result is a computation of the multiplicity of the theta divisor of an integral, nodal curve at an arbitrary point. We also suggest a general formula for the multiplicity of the theta divisor of a singular, integral curve at a point and present some evidence that this formu...

The monotone convergence theorem holds for the Riemann integral, provided (of course) it is assumed that the limit function is Riemann integrable. It might be thought, though, that this would be difficult to prove and inappropriate for an undergraduate course. In fact the identity is elementary: in the Lebesgue theory it is only the integrability of the limit function that is deep. This article...

We present a coherent picture of the spin-statistics theorem in path integral formulation. The local path integral measure and Lorentz invariant local Lagrangian, when combined with Green’s functions defined in terms of time ordered products, ensure causality regardless of statistics. The Feynman’s m−iǫ prescription ensures the positive energy condition regardless of statistics, and the abnorma...

Two subjects are addressed. A series of mass distributions is explicitly presented, that generate zero gravitation …eld in an open set in E. Second, an explicit reconstruction formula in E from data of spherical means with centers in an algebraic set. For both constructions, the same geometric method is applied based on properties of a special class of polynomials. Key words oscillatory set hyp...

We generalise the definition of the characteristic of an integral triangle to integral sim-plices and prove that each simplex in an integral point set has the same characteristic. This theorem is used for an efficient construction algorithm for integral point sets. Using this algorithm we are able to provide new exact values for the minimum diameter of integral point sets.