Comments on the 'China model'

This paper reviews the articles by Pan and by Zhu on the China Model. The review of Pan is critical, that of Zhu sympathetic. Pan is criticised for taking an unquestioning attitude towards state supporting ideologies and failing to adequately account for the effects of changes in family structure and class structure in China over the past 50 years. The reviewer broadly agrees with Zhu's comments about a future steady state economy. The article provides statistical data from the recent economic and demographic histories of China and Japan to back up the general conclusions drawn by Zhu

Agricultural Engineering in China

Rosana G. Moreira, Editor-in-Chief; Texas A&M UniversityThis is an Invited Paper from International Commission of Agricultural Engineering (CIGR, Commission Internationale du Genie Rural) E-Journal Volume 5 (2003): X. Zhou, R. Dong, S. Li, G. Peng, L. Zhang, J. Hou, J. Xiao and B. Zhu. Agricultural Engineering in China. Vol. V. September 2003

Asymmetric coloring games on incomparability graphs

Consider the following game on a graph $G$: Alice and Bob take turns coloring the vertices of $G$ properly from a fixed set of colors; Alice wins when the entire graph has been colored, while Bob wins when some uncolored vertices have been left. The game chromatic number of $G$ is the minimum number of colors that allows Alice to win the game. The game Grundy number of $G$ is defined similarly except that the players color the vertices according to the first-fit rule and they only decide on the order in which it is applied. The $(a,b)$-game chromatic and Grundy numbers are defined likewise except that Alice colors $a$ vertices and Bob colors $b$ vertices in each round. We study the behavior of these parameters for incomparability graphs of posets with bounded width. We conjecture a complete characterization of the pairs $(a,b)$ for which the $(a,b)$-game chromatic and Grundy numbers are bounded in terms of the width of the poset; we prove that it gives a necessary condition and provide some evidence for its sufficiency. We also show that the game chromatic number is not bounded in terms of the Grundy number, which answers a question of Havet and Zhu

The Minimal Total Irregularity of Graphs

In \cite{2012a}, Abdo and Dimitov defined the total irregularity of a graph $G=(V,E)$ as \hskip3.3cm $\rm irr_{t}$$(G) = \frac{1}{2}\sum_{u,v\in V}|d_{G}(u)-d_{G}(v)|,$ \noindent where $d_{G}(u)$ denotes the vertex degree of a vertex $u\in V$. In this paper, we investigate the minimal total irregularity of the connected graphs, determine the minimal, the second minimal, the third minimal total irregularity of trees, unicyclic graphs, bicyclic graphs on $n$ vertices, and propose an open problem for further research.Comment: 13 pages, 4 figure

On a theorem of Ax and Katz

The well-known theorem of Ax and Katz gives a p-divisibility bound for the number of rational points on an algebraic variety V over a finite field of characteristic p in terms of the degree and number of variables of defining polynomials of V. It was strengthened by Adolphson-Sperber in terms of Newton polytope of the support set G of V. In this paper we prove that for every generic algebraic variety over a number field supported on G the Adolphson-Sperber bound can be achieved on special fibre at p for a set of prime p of positive density in SpecZ. Moreover we show that if G has certain combinatorial conditional number nonzero then the above bound is achieved at special fiber at p for all but finitely many primes p.Comment: 11 page