The strong Lefschetz property for coinvariant rings of finite reflection groups

In this paper we prove that a deformed tensor product of two Lefschetz algebras is a Lefschetz algebra. We then use this result in conjunction with some basic Schubert calculus to prove that the coinvariant ring of a finite reflection has the strong Lefschetz property.Comment: 31 page

Artinian algebras and Jordan type

The Jordan type of an element $\ell$ of the maximal ideal of an Artinian k-algebra A acting on an A-module M of k-dimension n, is the partition of n given by the Jordan block decomposition of the multiplication map $m_\ell$ on M. In general the Jordan type has more information than whether the pair $(\ell,M)$ is strong or weak Lefschetz. We develop basic properties of the Jordan type and their loci for modules over graded or local Artinian algebras. We as well study the relation of generic Jordan type of $A$ to the Hilbert function of $A$. We introduce and study a finer invariant, the Jordan degree type. In our last sections we give an overview of topics such as the Jordan types for Nagata idealizations, for modular tensor products, and for free extensions, including examples and some new results. We as well propose open problems.Comment: 53 pages. Added results, examples for Jordan degree type (Section 2.4) and Jordan type and initial ideal (Section 2.5

In Search Of Satanists Examining The Accounts Of Deviant Religious Practitioners

Despite the glut of literature focusing on numerous aspects of mainline American religious life, there is a surprising dearth of information regarding deviant religious practitioners. Importantly, there remains a lack of focus on the specificities of religious and spiritual deviance, and the accounts of those who engage in such practices. This exploratory study closely examines the members of one such religion; specifically, the Church of Satan. Despite the stigma associated with Satanism, individuals continue to willfully engage in such practices. Research uses face-toface, semi-structured interviews to better discern the rationale behind Satanic worship as understood by modern-day believers. Particular attention is given to the accounts of Satanists to examine motivations for engaging in such practices, as well as identity management techniques for dealing with potential stigma. Results of the analysis show that Satanists utilize a variety of accounts when speaking about their spiritual choices and the potential stigma that surrounds such choices. These results are discussed and directions for additional research are presented

Estimating Cost Growth in Engineering and Schedule Cost Categories Using a Two-Pronged Regression Approach

This research confirms the usefulness of the logistic and multiple regression two-step procedure for assessing cost growth in major DoD weapon systems. We compile programmatic data from the Selected Acquisition Reports (SARs) between 1990 and 2002 for programs covering all defense departments. Our analysis concentrates on cost growth in the procurement appropriations of the Engineering and Manufacturing Development phase of acquisitions. We investigate the use of logistic regression in cost growth analysis to predict whether or not cost growth will occur in a program. If applicable, multiple regression is implemented to predict how much cost growth will occur. Our study focuses on the engineering and schedule SAR cost variance categories within the procurement appropriations. We study each of these categories individually for significant cost growth characteristics and develop predictive models for each. We discover the two-step logistic and multiple regression approach produces desirable results