Some remarks on topological 4d-gravity

We show that the method of S. Wu to study topological 4d-gravity can be understood within a now standard method designed to produce equivariant cohomology classes. Next, this general framework is applied to produce some observables of the topological 4d-gravity.Comment: 10 pages, Late

Correspondence: CHEN Zhen to ZHOU Yan (about work(s) progress)

This letter is (mainly) scripted in Chinese. (Jerry Wu\u2723).https://digital.kenyon.edu/zhoudocs/1048/thumbnail.jp

Comment on "Statistical Distribution for Generalized Ideal Gas of Fractional-Statistics Particles", Phys. Rev. Lett. {\bf 73}, 922 (1994)

In Phys. Rev. Lett. 67, 937 (1991) [1], Haldane introduced the fruitful concept of fractional exclusion statistics (FES). One of the most influential papers in which the thermodynamics of FES systems was deduced is Y.-S. Wu, Phys. Rev. Lett. 73, 922 (1994). Unfortunately, some important, but eventually subtle, properties of the exclusion statistics parameters were overlooked in the original paper [1] and in all the papers after that, including [2]. This omission makes the thermodynamics of FES systems inconsistent when mutual exclusion statistics is manifesting in the system. By this Comment I want to point-out this error--an error that persisted for such a long time--and to give the correct statistical mechanics interpretation of FES.Comment: 1 page, submitted to PR

Comment on Cyclic quantum-evolution dependence on the Hamiltonian and geometric phase

It is shown that the analysis and the main result of the article by L-A. Wu [Phys. Rev. A 53, 2053 (1996)] are completely erroneous.Comment: LaTeX file, 2 page

Relatively Congruence-free Regular Semigroups

Yu, Wang, Wu and Ye call a semigroup S τ -congruence-free, where τ is an equivalence relation on S, if any congruence ρ on S is either disjoint from τ or contains τ . A congruence-free semigroup is then just an ω-congruence-free semigroup, where ω is the universal relation. They determined the completely regular semigroups that are τ -congruence-free with respect to each of the Green’s relations. The goal of this paper is to extend their results to all regular semigroups. Such a semigroup is J –congruence-free if and only if it is either a semilattice or has a single nontrivial J -class, J, say, and either J is a subsemigroup, in which case it is congruence-free, or otherwise its principal factor is congruence-free. Given the current knowledge of congruence-free regular semigroups, this result is probably best possible. When specialized to completely semisimple semigroups, however, a complete answer is obtained, one that specializes to that of Yu et al. A similar outcome is obtained for L and R. In the case of H, only the completely semisimple case is fully resolved, again specializing to those of Yu et al

The Investment Effects of Price Caps under Imperfect Competition. A Note.

This note analyzes a simple Cournot model where firms choose outputs and capacities facing varying demand and price-cap regulation. We find that binding price caps set above long-run marginal cost increase (rather than decrease) aggregate capacity investment. (author's abstract)Series: Working Papers / Research Institute for Regulatory Economic