A combinatorial analysis of barred preferential arrangements

For a non-negative integer n an ordered partition of a set Xn with n distinct elements is called a preferential arrangement (PA). A barred preferential arrangement (BPA) is a preferential arrangement with bars in between the blocks of the partition. An integer sequence an associated with the counting PA's of Xn has been intensely studied over a century and a half in many different contexts. In this thesis we develop a unified combinatorial framework to study the enumeration of BPAs and a special subclass of BPAs. The results of the study lead to a positive settlement of an open problem and a conjecture by Nelsen. We derive few important identities pertaining to the number of BPAs and restricted BPAs of an n element set using generating- functionology. Later we show that the number of restricted BPAs of Xn are intricately related to well-known numbers such as Eulerian numbers, Bell numbers, Poly-Bernoulli numbers and the number of equivalence classes of fuzzy subsets of Xn under some equivalent relation

BREAKING THE STAINED GLASS CEILING: INTERSECTIONALITY AND THE FEMALE ORDINATION MOVEMENT IN THE ROMAN CATHOLIC CHURCH

This thesis examines the female ordination movement within the Catholic Church as a feminist social justice collective seeking to overturn gender based oppression within this religious institution. Through a study of three communities, Mary Mother of Jesus, Good Shepherd, and Mary Magdalene Apostolic Catholic Community, this thesis explores the emancipatory strategies utilized by the female ordination movement to instil equality within the Church and within society. Each community’s commitment to gender inclusivity intersects with additional areas of structural reform, including LGBTIQ equality, racial justice, social welfare provision for the poor and the elimination of power and hierarchy within organized religion. This study is thus motivated by the question of how the female ordination movement is incorporating intersectional considerations within its fight of oppression in the Roman Catholic Church. Informed by a feminist epistemology, this thesis integrates the theoretical frameworks of intersectionality and kyriarchy to explore the positioning of the female ordination movement around multiple axes of domination within the Catholic Church, including sexism, racism, homophobia and classism. The methodology is triangulated. Firstly, semi-structured interviews were conducted with members of this movement and were evaluated through narrative analysis. Second, participation observation of the communities’ liturgies was evaluated through ritual analysis. This dual methodological approach addresses both the core beliefs and communal acts of these communities and understands their activism as both ideological and performative in nature. Given that women have been noticeably absent from the androcentric history of the Roman Catholic Church, and given also that there have been few fieldwork-based studies to date of feminist Catholic communities, the inclusion of these women’s voices and experiences represents an important contribution to scholarly inquiries investigating sexism and feminist activism within religious structures. This thesis draws upon their voices and their communal activities to fill a lacuna in research surrounding the tensions between feminism and patriarchy, and the ways in which intersectional feminism is transforming the structures and nature of Catholicism

Untouchable bureaucracy : unrepresentative bureaucracy in a North Indian State.

Under the impetus of “reservations” -an elaborate government policy of affirmative action- over the past six decades hundreds of thousands of Indian untouchables -individuals ranked extremely low in the Hindu caste hierarchy- have managed to secure highly valued civil service jobs. The question explored in this study is why these untouchable bureaucrats are not much inclined -as those who introduced reservations had hoped and anticipated they would- to use their new-found positions of power and influence to extend special help to untouchable clients outside bureaucracy. In an effort to account for this puzzling phenomenon of unrepresentative bureaucracy the author conducted prolonged ethnographic fieldwork in a dust-level rural development bureaucracy in north India. He introduces the reader to a complex and vibrant local universe in which an array of actors, factors and considerations conspire to simultaneously limit untouchable bureaucrats’ opportunities and motives for acting as active representatives of untouchable interests and constrain untouchable clients’ possibilities for claiming special treatment. Affirmative action in civil service recruitment, it is concluded, seems to be of doubtful use as a social engineering tool, at least in the case of stigmatized ethnic  minority groups in patronage democracies. LEI Universiteit LeidenThe politics and administration of institutional chang

Interpretation of the Statutory Modification of Joint and Several Liability: Resisting the Deconstruction of Tort Reform

This Article defends RCW 4.22.070 and opposes the deconstruction of legislative tort reform. The Article’s premise is that the legislature did indeed intend to accomplish a significant reform of the liability system and to take a long, purposeful stride toward the implementation of comparative fault as applied to all parties in tort litigation. The Article concludes that the legislature adopted language that adequately, if sometimes imperfectly, achieves that purpose. The Article discusses the following: the meaning of “fault” as applicable through RCW 4.22.070; the nature of the entities to whom fault must be allocated; the responsibility for raising the culpability of an unjoined entity and the burden of proof on allocation of fault; the manner in which damages are to be apportioned among the culpable parties; the separate rule for parties acting in concert or as agents; the limited form of joint and several liability that applies when the plaintiff is without fault; the provisions for settlement and contribution under the statute; and the three exceptions to the statute. Additionally, the Article examines two areas in which RCW 4.22.070 must be read in conjunction with other statutes to as to give the fullest possible effect to both legislative enactments. First, the article outlines a recent Washington Supreme Court decision concerning the application of comparative responsibility principles to the workers compensation program. Second, the Article looks at the application of the comparative fault principles of the 1986 modification of joint and several liability in the context of the 1981 retailer relief provision, which granted broad relief to retailers but left them exposed to liability in certain circumstances, such as when the manufacturer of the product was insolvent. Lastly, the Article offers some ruminations on the future course of the common law as it develops with respect to joint and several liability in those few areas that fall outside the express mandate of the 1986 statute

Proceedings of the Seventh Congress of the European Society for Research in Mathematics Education

International audienceThis volume contains the Proceedings of the Seventh Congress of the European Society for Research in Mathematics Education (ERME), which took place 9-13 February 2011, at Rzeszñw in Poland

Manager’s and citizen’s perspective of positive and negative risks for small probabilities

So far „risk‟ has been mostly defined as the expected value of a loss, mathematically PL, being P the probability of an adverse event and L the loss incurred as a consequence of the event. The so called risk matrix is based on this definition. Also for favorable events one usually refers to the expected gain PG, being G the gain incurred as a consequence of the positive event. These “measures” are generally violated in practice. The case of insurances (on the side of losses, negative risk) and the case of lotteries (on the side of gains, positive risk) are the most obvious. In these cases a single person is available to pay a higher price than that stated by the mathematical expected value, according to (more or less theoretically justified) measures. The higher the risk, the higher the unfair accepted price. The definition of risk as expected value is justified in a long term “manager‟s” perspective, in which it is conceivable to distribute the effects of an adverse event on a large number of subjects or a large number of recurrences. In other words, this definition is mostly justified on frequentist terms. Moreover, according to this definition, in two extreme situations (high-probability/low-consequence and low-probability/high-consequence), the estimated risk is low. This logic is against the principles of sustainability and continuous improvement, which should impose instead both a continuous search for lower probabilities of adverse events (higher and higher reliability) and a continuous search for lower impact of adverse events (in accordance with the fail-safe principle). In this work a different definition of risk is proposed, which stems from the idea of safeguard: (1Risk)=(1P)(1L). According to this definition, the risk levels can be considered low only when both the probability of the adverse event and the loss are small. Such perspective, in which the calculation of safeguard is privileged to the calculation of risk, would possibly avoid exposing the Society to catastrophic consequences, sometimes due to wrong or oversimplified use of probabilistic models. Therefore, it can be seen as the citizen‟s perspective to the definition of risk