A classification of SL(n) and translation covariant Minkowski valuations on log-concave functions is established. The moment vector and the recently introduced level set body of log-concave functions are characterized. Furthermore, analogs of the Euler characteristic and volume are characterized as SL(n) and translation invariant valuations on log-concave functions. 2000 AMS subject classificat...

This paper introduces new valuation schemes called actuarial-consistent valuations for insurance liabilities which depend on both financial and actuarial risks, imposes that all risks are priced via standard principles. We propose to extend principles by a procedure, we call ‘two-step valuations’. In the case coherent, show equivalent two-step valuations. also discuss connection with market-con...

We reexamine the graceful exit problem in the Pre-Big-Bang inflationary scenario. The dilaton-gravity action is generalized by adding the axion and a general axion/dilaton potential. We provide a phase space analysis of the dynamics which leads us to extend the previous no-go theorem and rule out the branch change necessary for graceful exit in this context. Submitted to Physics Letters B

We confront the recent proposal of Emerging Brane Inflation with WMAP3+SDSS, finding a scalar spectral index of ns = 0.9659 +0.0049 −0.0052 in excellent agreement with observations. The proposal incorporates a preceding phase of isotropic, non accelerated expansion in all dimensions, providing suitable initial conditions for inflation. Additional observational constraints on the parameters of t...

In this paper, we endow the space of continuous translation invariant valuations on convex sets generated by mixed volumes coupled with a suitable Radon measure tuples bodies two appropriate norms. This enables us to construct extension convolution operator smooth non-smooth valuations, which are in completion spaces respect these The novelty our approach lies fact that proof does not rely gene...

The Nash social welfare problem asks for an allocation of indivisible items to agents in order maximize the geometric mean agents' valuations. We give overview constant-factor approximation algorithm when have Rado valuations [Garg et al. 2021]. are a common generalization assignment (OXS) and weighted matroid rank functions. Our approach also gives first asymmetric under same valuations, provi...