On the regularity over positively graded algebras

We study the relationship between the Tor-regularity and the local-regularity over a positively graded algebra defined over a field which coincide if the algebra is a standard graded polynomial ring. In this case both are characterizations of the so-called Castelnuovo--Mumford regularity. Moreover, we can characterize a standard graded polynomial ring as an algebra with extremal properties with respect to the Tor- and the local-regularity. For modules of finite projective dimension we get a nice formula relating the two regularity notions. Interesting examples are given to help to understand the relationship between the Tor- and the local-regularity in general.Comment: 13 pages; Revised version of the pape

Bounds for Betti numbers

In this paper we prove parts of a conjecture of Herzog giving lower bounds on the rank of the free modules appearing in the linear strand of a graded $k$-th syzygy module over the polynomial ring. If in addition the module is $\mathbb{Z}^n$-graded we show that the conjecture holds in full generality. Furthermore, we give lower and upper bounds for the graded Betti numbers of graded ideals with a linear resolution and a fixed number of generators.Comment: 15 page

Note on bounds for multiplicities

Let S=K[x_1,...,x_n] be a polynomial ring and R=S/I be a graded K-algebra where I is a graded ideal in S. Herzog, Huneke and Srinivasan have conjectured that the multiplicity of R is bounded above by a function of the maximal shifts in the minimal graded free resolution of R over S. We prove the conjecture in the case that codim(R)=2 which generalizes results in of Herzog, Srinivasan and Gold. We also give a proof for the bound in the case in which I is componentwise linear. For example, stable and squarefree stable ideals belong to this class of ideals.Comment: 10 pages; revised version accepted for publication in JPA

[Review of] William Oandasan. A Branch of California Redwood

One of the best ways to introduce readers to the diversity of Indian literatures (and, by implication, Indian experiences) is to expose them to poetry written in English by Indians. One-dimensional stereotypes about Nobel Savages simply cannot withstand the rich variety of a literature that extends at least back to the 19th-century attempts of a few Indian poets-such as William Wilson (Anishinabe), Emily Pauline Johnson (Mohawk), and Alexander Posey (Creek)-to imitate and modify English language poetic models up through the recent poems of hundreds of Indian writers whose backgrounds and poetic inclinations reflect numerous tribal, reservation, and urban experiences, as well as literary influences ranging from tribal chants and Japanese syllabic verse to 20th-century experiments with open verse and typography

Games with vector-valued payoffs and their application to competition between organizations

In 1959, Lloyd Shapley wrote a short paper on games with vector payoffs. He analyzed zero-sum matrix games. Here, we extend Shapley's equilibrium concept to general games with vector payoffs, introduce an organizational interpretation of the concept, elaborate the relationship of the original concept to another equilibrium concept where each player can be viewed as running a bargaining game among internal ‘factions,'' and finally comment upon its relationship to the concept of party unanimity Nash equilibrium (PUNE).

Political Competition (A theory with applications to the distribution of income)

The formal model of political competition almost ubiquitously employed by students of political economy is one in which political parties play no role. That model, introduced by Anthony Downs (1957) over forty years ago, portrays a competition between candidates, whose sole motivation for engaging in politics is to enjoy the power and perquisites of office holding. Although voters care about policies, the candidates do not; for them, a policy is simply an instrument to be used, opportunistically, as an entry ticket to a prosperous career. Political parties, however, have, throughout the history of democracy, cared about policies, perhaps because they are formed by interest groups of citizens. Therefore the Downsian model cannot be viewed as an historically accurate model of party competition.