Universally Kuratowski-Ulam spaces and open-open games

We examine the class of spaces in which the second player has a winning strategy in the open--open game. We show that this spaces are not universally Kuratowski-Ulam. We also show that the games G and G7 introduced by P. Daniels, K. Kunen, H. Zhou [Fund. Math. 145 (1994), no. 3, 205--220] are not equivalent

Splitters and Decomposers for Binary Matroids

Let $EX[M_1\dots, M_k]$ denote the class of binary matroids with no minors isomorphic to $M_1, \dots, M_k$. In this paper we give a decomposition theorem for $EX[S_{10}, S_{10}^*]$, where $S_{10}$ is a certain 10-element rank-4 matroid. As corollaries we obtain decomposition theorems for the classes obtained by excluding the Kuratowski graphs $EX[M(K_{3,3}), M^*(K_{3,3}), M(K_5), M^*(K_5)]$ and $EX[M(K_{3,3}), M^*(K_{3,3})]$. These decomposition theorems imply results on internally $4$-connected matroids by Zhou [\ref{Zhou2004}], Qin and Zhou [\ref{Qin2004}], and Mayhew, Royle and Whitte [\ref{Mayhewsubmitted}].Comment: arXiv admin note: text overlap with arXiv:1403.775

Price competition with consumer confusion

Copyright © 2013, INFORMS. Article posted with permission.This paper proposes a model in which identical sellers of a homogeneous product compete in both prices and price frames (i.e., ways to present price information). Frame choices affect the comparability of price offers and may cause consumer confusion and lower price sensitivity. In equilibrium, firms randomize their frame choices to obfuscate price comparisons and sustain positive profits. The nature of the equilibrium depends on whether frame differentiation or frame complexity is more confusing. Moreover, an increase in the number of competitors induces firms to rely more on frame complexity, and this may boost industry profits and lower consumer surplus

The Book of Poetry : Zhou dynastic building

“Woven” like many of the Da ya (Greater Odes) sings of two of the heroes who laid the groundwork for their grandson and son to overcome the Shang and establish the Zhou dynasty. The text lends itself to memorization and may have been part of early court ritual as our own Star-Spangled Banner celebrates an event in the early history of our country