Geometric lower bounds for generalized ranks

We revisit a geometric lower bound for Waring rank of polynomials (symmetric rank of symmetric tensors) of Landsberg and Teitler and generalize it to a lower bound for rank with respect to arbitrary varieties, improving the bound given by the "non-Abelian" catalecticants recently introduced by Landsberg and Ottaviani. This is applied to give lower bounds for ranks of multihomogeneous polynomials (partially symmetric tensors); a special case is the simultaneous Waring decomposition problem for a linear system of polynomials. We generalize the classical Apolarity Lemma to multihomogeneous polynomials and give some more general statements. Finally we revisit the lower bound of Ranestad and Schreyer, and again generalize it to multihomogeneous polynomials and some more general settings.Comment: 43 pages. v2: minor change

Using a Multiple-Case Studies Design to Investigate the Information-Seeking Behavior of Arts Administrators

The case study method, and in particular the multiple???case studies design, offers LIS researchers a proven tool for achieving a deep understanding of a specific phenomenon???-for example, the information- seeking behavior of a particular user group. Although the case study method has been dismissed by critics who question the rigor of the approach, numerous studies over the past twenty years have demonstrated that the case study method can be used successfully to probe beneath the surface of a situation and to provide a rich context for understanding the phenomena under study. This article summarizes the application of the multiple???case studies design, in which a literal and theoretical replication strategy is used to identify consistent patterns of behavior and to uncover new and/or divergent themes. The motivation behind arts administrators??? decisions to seek information is investigated using this approach and examples are given of sample selection, data collection, and analysis. Specific issues associated with the case study method are identified and practical steps used to address them are suggested.published or submitted for publicatio

Unemployment Compensation in Ohio: Already weak Coverage is Threatened

For years, relatively fewer unemployed Ohioans have qualified for unemployment compensation than their counterparts in other states. Ohio's tough earnings standard and disqualification of jobless workers who would be eligible for benefits elsewhere contribute to this dismal record. For instance, most states allow part-time workers who lose their jobs to seek similar part-time work and qualify for benefits, assuming they have earned enough and meet the other criteria. Ohio does not. Ohio's current requirement that workers average at least $222 a week for at least 20 weeks over a year's time is among the most stringent in the country.1 For instance, it disqualifies those earning this year's minimum wage of$7.70 an hour and working 28 hours a week. A retail employee who has worked for years at such a job would be left without benefits if she or he was laid off

Municipal Income Tax "Fix" is a Flub: Legislators should cut tax avoidance, not invite it

A major rewrite of the state law governing Ohio municipal income tax is being discussed in Columbus. A proposal to overhaul the tax -- House Bill 601 -- was introduced late last year, and the General Assembly will see a revised version afterit convenes this month. A significant effort to overhaul Ohio's municipal income tax should crack down on tax avoidance, guarantee a broad tax base, and ensure that those most able to pay are in fact doing so. In some instances, however, House Bill 601 allows tax avoidance to continue, or even creates new avenues to avoid the tax. When this issue is taken up in the next General Assembly, this should be corrected

Philosophy Without Belief

Should we believe our controversial philosophical views? Recently, several authors have argued from broadly conciliationist premises that we should not. If they are right, we philosophers face a dilemma: If we believe our views, we are irrational. If we do not, we are not sincere in holding them. This paper offers a way out, proposing an attitude we can rationally take toward our views that can support sincerity of the appropriate sort. We should arrive at our views via a certain sort of ‘insulated’ reasoning – that is, reasoning that involves setting aside certain higher-order worries, such as those provided by disagreement – when we investigate philosophical questions