A dynamic free-entry oligopoly with sluggish entry and exit adjustments

We study a dynamic free-entry oligopoly with sluggish entry and exit of firms under general demand and cost functions. We show that the number of firms in a steady-state open-loop solution for a dynamic free-entry oligopoly is smaller than that at static equilibrium and that the number of firms in a steady-state memoryless closed-loop solution is larger than that in an open-loop solution.     

Aerobic oxidation of alcohols using bismuth bromide as a catalyst

We developed an environmentally friendly method for aerobic oxidation of alcohols using a commercially available, relatively benign bismuth salt as a catalyst. We found that the catalytic combination of BiBr₃ with nitric acid is key for enhancing the reactivity. The reaction proceeds well under air, making the use of pure oxygen unnecessary. Each of the primary or secondary alcohols tested was oxidized to the corresponding aldehydes or ketones using this protocol.     

Extension of the LP-Newton method to conic programming problems via semi-infinite representation

Numerical Algorithms - The LP-Newton method solves linear programming (LP) problems by repeatedly projecting a current point onto a certain relevant polytope. In this paper, we extend the...     

Distance-based classifier by data transformation for high-dimension,strongly spiked eigenvalue models

Annals of the Institute of Statistical Mathematics - We consider classifiers for high-dimensional data under the strongly spiked eigenvalue (SSE) model. We first show that high-dimensional data...     

On the rate of convergence of solutions in free boundary problems via penalization

The rate of convergence of approximate solutions via penalization for free boundary problems are concerned. A key observation is to obtain global bounds of penalized terms which give necessary estimates on integrations by the nonlinear adjoint method by L.C. Evans.     

9,10‐Diaminoanthracenes Revisited: The Influence of N‐Substituents on Their Electronic States

The electronic and molecular structures of 9,10‐diamino‐substituted anthracenes with different N‐substituents have been re‐examined. In particular, different N‐substituents influence both the electronic and molecular structures of the oxidized species of 9,10‐diaminoanthracenes. The anthrylene moiety of 9,10‐bis(N,N‐di(p‐anisyl)amino)anthracene retains its planarity during the course of two successive one‐electron oxidations, whereas 9,10‐bis(N,N‐dimethylamino)anthracene and 9,10‐bis(N‐p‐anisyl‐N‐methylamino)anthracene undergo a substantial structural change to a butterfly‐like structure through a two‐electron oxidation process. The structural changes observed for the oxidized states are ascribed to significant differences in the frontier molecular orbitals of the above‐mentioned three kinds of 9,10‐diaminoanthracenes due to different extents of mixing between the amine‐localized and anthrylene‐localized orbitals.     

Triply Linked Corrole Dimers

The oxidation of 10–10′ singly linked corrole dimers with DDQ at low concentration in CHCl₃ afforded meso–meso, β–β, β–β triply linked 2H‐corrole dimers (with two inner NH groups in each corrole unit), which exhibited characteristic ¹H NMR and absorption spectra attributable to their nonaromatic electronic networks. These 2H‐corrole dimers were reduced with NaBH₄ to aromatic 3H‐corrole dimers, which were unstable and easily oxidized back to the 2H‐corrole dimers upon exposure to air. Bis(zinc(II)) complexes of the 2H‐corrole dimers were synthesized and characterized as rare examples of nonaromatic zinc(II) corrole complexes.