We prove two relative local variational principles of topological pressure functions P (T,F ,U , y) and P (T,F ,U|Y ) for a given factor map π, an open cover U and a subadditive sequence of real-valued continuous functions F . By proving the upper semi-continuity and affinity of the entropy maps h{·}(T,U | Y ) and h+{·}(T,U | Y ) on the space of all invariant Borel probability measures, we show...

The potentially large spatial footprint of earthquake disasters and the increased concentration population values in dense urban areas call for an explicit consideration seismic risk at a regional, building portfolio level. relation between building-level portfolio-level is helpful if one wants to meet specific regional tolerance level by specifying targets individual buildings. We examine four...

In this paper, we study the problem of maximizing welfare in combinatorial auctions with k(> 1)duplicates of each item, where k is a fixed constant (i.e. k is not the part of the input) and bidders are submodular or subadditive. We exhibit some upper and lower approximation bounds for k-duplicates combinatorial auctions. First, we show that it is NP-hard to approximate the maximum welfare for k...

In Song and Yan (2006), we introduced risk measures which are comonotonic subadditive or comonotonic convex, and gave their representations in terms of Choquet integrals. Independently, Heyde et al. (2006) proposed a data based risk measure in which the comonotonic subadditivity is taken as an axiom. The present paper proposes an axiomatic approach to some new risk measures and gives their repr...

We consider three equilibrium concepts proposed in the literature for time-inconsistent stopping problems, including mild equilibria (introduced Huang and Nguyen-Huu (2018)), weak Christensen Lindensjö strong Bayraktar et al. (2021)). The discount function is assumed to be log subadditive underlying process one-dimensional diffusion. first provide necessary sufficient conditions characterizatio...

Abstract We continue our study of strongly unbounded colorings, this time focusing on subadditive maps. In Part I series, we showed that, for many pairs infinite cardinals $\theta < \kappa $ , the existence a coloring $c:[\kappa ]^2 \rightarrow \theta is theorem $\textsf{ZFC}$ . Adding requirement subadditivity to significant strengthening, though, and here see that in cases independent conn...

This paper gives a new flavor of what Peter Jagers and his co-authors call ‘the path to extinction’. In a neutral population with constant size N , we assume that each individual at time 0 carries a distinct type, or allele. We consider the joint dynamics of these N alleles, for example the dynamics of their respective frequencies and more plainly the nonincreasing process counting the number o...