Krull-Schmidt categories and projective covers

Krull-Schmidt categories are additive categories such that each object decomposes into a finite direct sum of indecomposable objects having local endomorphism rings. We provide a self-contained introduction which is based on the concept of a projective cover

Trading on Preconceptions: Why World War I Was Not a Failure of Economic Interdependence

World War I is generally viewed by both advocates and critics of commercial liberal theory as the quintessential example of a failure of economic integration to maintain peace. Yet this consensus relies on both methodologically flawed inference and an incomplete accounting of the antecedents to the war. Crucially, World War I began in a weakly integrated portion of Europe with which highly integrated powers were entangled through the alliance system. Crises among the highly interdependent European powers in the decades leading up to the war were generally resolved without bloodshed. Among the less interdependent powers in Eastern Europe, however, crises regularly escalated to militarized violence. Moreover, the crises leading to the war created increased incentives for the integrated powers to strengthen commitments to their less interdependent partners. In attempting to make these alliances more credible, Western powers shifted foreign policy discretion to the very states that lacked strong economic disincentives to fight. Had globalization pervaded Eastern Europe, or if the rest of Europe had been less locked into events in the east, Europe might have avoided a “Great War.” </jats:p

An Analysis of Traditional Secondary Band Pedagogical Practices and their Benefits and Detriments to Individual Performers

Certain pedagogical practices present in ensemble settings overlook individual achievement. This adherence to methods that do not directly benefit individual performers may result in students who are following performance practices not well suited to their specific instruments. This negative impact on a student\u27s sound and technique within a band classroom has the potential to put them at a further disadvantage to those who are able to afford external performance privileges such as private lessons and summer programs, and can impact the sound of the ensemble as a whole. This research analyzed common band pedagogical practices. In doing so, the relevance of Social Emotional Learning and a learner-centered approach were uncovered and applied to these pedagogical techniques. This approach to learning was applied to an analysis of relevant band literature in regards to how this music may provide the greatest impact on individual tone, intonation, air support, and general musicality, regardless of ensemble or individual skill level. High school and collegiate band directors were contacted regarding their personal pedagogical practices and beliefs within their own program. This research further demonstrated that a mindset shift towards a learner-centered approach to pedagogy is vital in the face of shifting classroom environments and a greater need for individual achievement

Prime ends for domains in metric spaces

In this paper we propose a new definition of prime ends for domains in metric spaces under rather general assumptions. We compare our prime ends to those of Carath\'eodory and N\"akki. Modulus ends and prime ends, defined by means of the \p-modulus of curve families, are also discussed and related to the prime ends. We provide characterizations of singleton prime ends and relate them to the notion of accessibility of boundary points, and introduce a topology on the prime end boundary. We also study relations between the prime end boundary and the Mazurkiewicz boundary. Generalizing the notion of John domains, we introduce almost John domains, and we investigate prime ends in the settings of John domains, almost John domains and domains which are finitely connected at the boundary.Comment: 46 pages, 4 figure

Integration of Transit Systems Summary

The objective of this report is to assess the potential for interagency and intermodal integration of transit systems in U.S. urban areas, drawing on an analysis of the successful experience of European systems. Vol. l documents the need for transit integration in U.S. urban areas, presents the conceptual and evaluative frame-work, and reviews current transit integration efforts by Federal, state, and local governments. Vol. 2 describes in detail four major European transit systems (London, Hamburg, Paris, and Munich); gives brief descriptions of six others (Newcastle upon Tyne, Edinburgh, Stockholm, Gothenburg, Copenhagen, and Oslo); and summarizes and appraises the applicability to U.S. transit systems of techniques which have contributed to the success of these European systems. Vol. 3 deals with the application of these techniques to three major U.S. cities (Philadelphia, San Francisco, and Seattle) and to an archetypal smaller urban area, Middletown. II The report is summarized in the fourth volume. Appendices include contacts in U.S. cities, UMTA study grants, and questionnaire forms. Approximately 150 references are listed at the ends of individual sections

Integration of Transit System

The objective of this report is to assess the potential for interagency and intermodal integration of transit systems in u.s. urban areas, drawing on an analysis of the successful experience of European systems. Vol. 1 documents the need for transit integration in U.S. urban areas, presents the conceptual and evaluative frame­work, and reviews current transit integration efforts by Federal, state, and local governments. Vol. 2 describes in detail four major European transit systems (London, Hamburg, Paris, and Munich); give brief descriptions of six others (Newcastle upon Tyne, Edinburgh, Stockholm, Gothenburg, Copenhagen, and Oslo); and summarizes and appraises the applicability to U.S. transit systems of techniques which have contributed to the success of these European systems. Vol. 3 deals with the application of these techniques to three major U.S. cities (Philadelphia, San Francisco, and Seattle) and to an archetypal smaller urban area, Middletown. The report is summar­ized in the fourth volume. Appendices include contacts in u.s. cities, UMTA study grants, and questionnaire forms. Approximately 150 references are listed at the ends of individual sections and in a bibliography in the summary volume

Completely dissociative groupoids

Consider arbitrarily parenthesized expressions on the $k$ variables $x_0, x_1, ..., x_{k-1}$, where each $x_i$ appears exactly once and in the order of their indices. We call these expressions {\em formal $k$--products}. $F^\sigma(k)$ denotes the set of formal $k$--products. For ${{\bf u},{\bf v}}\subseteq F^\sigma(k)$, the claim, that ${\bf u}$ and ${\bf v}$ produce equal elements in a groupoid $G$ for all values assumed in $G$ by the variables $x_i$, attributes to $G$ a {\em generalized associative law}. Many groupoids are {\em completely dissociative}; i.e., no generalized associative law holds for them; two examples are the groupoids on ${0,1}$ whose binary operations are implication and NAND. We prove a variety of results of that flavor.Comment: 29 page

A sense of place, many times over - pattern formation and evolution of repetitive morphological structures

Fifty years ago, Lewis Wolpert introduced the concept of "positional information" to explain how patterns form in a multicellular embryonic field. Using morphogen gradients, whose continuous distributions of positional values are discretized via thresholds into distinct cellular states, he provided, at the theoretical level, an elegant solution to the "French Flag problem." In the intervening years, many experimental studies have lent support to Wolpert's ideas. However, the embryonic patterning of highly repetitive morphological structures, as often occurring in nature, can reveal limitations in the strict implementation of his initial theory, given the number of distinct threshold values that would have to be specified. Here, we review how positional information is complemented to circumvent these inadequacies, to accommodate tissue growth and pattern periodicity. In particular, we focus on functional anatomical assemblies composed of such structures, like the vertebrate spine or tetrapod digits, where the resulting segmented architecture is intrinsically linked to periodic pattern formation and unidirectional growth. These systems integrate positional information and growth with additional patterning cues that, we suggest, increase robustness and evolvability. We discuss different experimental and theoretical models to study such patterning systems, and how the underlying processes are modulated over evolutionary timescales to enable morphological diversification