Virtual Element Method for fourth order problems: L2−L^2-estimates

We analyse the family of $C^1$-Virtual Elements introduced in \cite{Brezzi:Marini:plates} for fourth-order problems and prove optimal estimates in $L^2$ and in $H^1$ via classical duality arguments

Homology over local homomorphisms

The notions of Betti numbers and of Bass numbers of a finite module N over a local ring R are extended to modules that are only assumed to be finite over S, for some local homomorphism f: R --> S. Various techniques are developed to study the new invariants and to establish their basic properties. In several cases they are computed in closed form. Applications go in several directions. One is to identify new classes of finite R-modules whose classical Betti numbers or Bass numbers have extremal growth. Another is to transfer ring theoretical properties between R and S in situations where S may have infinite flat dimension over R. A third is to obtain criteria for a ring equipped with a `contracting' endomorphism -- such as the Frobenius endomorphism -- to be regular or complete intersection; these results represent broad generalizations of Kunz's characterization of regularity in prime characteristic.Comment: To appear in the American Journal of Mathematics; new version has minor changes in the presentation; table of content removed; 52 page

Corruption and Reform: An Introduction

The United States today, according to most studies, is among the least corrupt nations in the world. But America's past was checkered with political scandal and widespread corruption that would not seem unusual compared with the most corrupt developing nation today. We construct a "corruption and fraud index" using word counts from a large number of newspapers for 1815 to 1975, supplemented with other historical facts. The index reveals that America experienced a substantial decrease in corruption from 1870 to 1920, particularly from the late-1870s to the mid-1880s and again in the 1910s. At its peak in the 1870s the "corruption and fraud index" is about five times its level from the end of the Progressive Era to the 1970s. If the United States was once considerably more corrupt than it is today, then America's history should offer lessons about how to reduce corruption. How did America become a less corrupt polity, economy, and society? We review the findings and insights from a series of essays for a conference volume, Corruption and Reform: Lessons from America's History, for which this paper is the introduction that attempt to understand the remarkable evolution of corruption and reform in U.S. history.

Women, Children, and Industrialization in the Early Republic: Evidence from the Manufacturing Censuses

The first half of the nineteenth century was a critical juncture regarding the emergence of female participation in the market economy, the increase in the wage of females relative to that of adult males, and the evolution of large scale firms in both mechanized and non-mechanized industries. We present the first systematic and comprehensive description of these events as they evolved in the states of the Northeast to 1850. Our sources are primarily samples taken from three early censuses and reports of manufacturing, 1820, 1832, and 1850. Our principal findings are: (1) that women and children composed a large share (over 40% in 1832) of the entire manufacturing labor force during the initial period of industrialization in the U.S., but that this share began a secular decline as early as 1840; (2) that the wage of females (and boys) relative to that of adult males rose wherever large scale manufacturing establishments spread and that by 1850 this ratio had risen to almost 90% its long-term level; (3) that the labor force participation of young unmarried women in the industrial counties of the Northeast was, in 1832, high by late nineteenth century standards; and (4) that the employment of females and boys was closely associated with production processes used by large-scale establishments. Women and children had been a previously under-utilized and large segment of the potential labor force, and their harnessing by manufacturing was a critical factor in the industrialization of the Northeast.

The processing of ambiguous sentences by first and second language learners of English

This study compares the way English-speaking children and adult second language learners of English resolve relative clause attachment ambiguities in sentences such as The dean liked the secretary of the professor who was reading a letter. Two groups of advanced L2 learners of English with Greek or German as their L1 participated in a set of off-line and on-line tasks. While the participants ' disambiguation preferences were influenced by lexical-semantic properties of the preposition linking the two potential antecedent NPs (of vs. with), there was no evidence that they were applying any structure-based ambiguity resolution strategies of the type that have been claimed to influence sentence processing in monolingual adults. These findings differ markedly from those obtained from 6 to 7 yearold monolingual English children in a parallel auditory study (Felser, Marinis, & Clahsen, submitted) in that the children's attachment preferences were not affected by the type of preposition at all. We argue that whereas children primarily rely on structure-based parsing principles during processing, adult L2 learners are guided mainly by non-structural informatio

The compact group--fossil group connection: observations of a massive compact group at z=0.22

It has been suggested that fossil groups could be the cannibalized remains of compact groups, that lost energy through tidal friction. However, in the nearby universe, compact groups which are close to the merging phase and display a wealth of interacting features (such as HCG 31 and HCG 79) have very low velocity dispersions and poor neighborhoods, unlike the massive, cluster-like fossil groups studied to date. In fact, known z=0 compact groups are very seldom embedded in massive enough structures which may have resembled the intergalactic medium of fossil groups. In this paper we study the dynamical properties of CG6, a massive compact group at z=0.220 that has several properties in common with known fossil groups. We report on new g' and i' imaging and multi-slit spectroscopic performed with GMOS on Gemini South. The system has 20 members, within a radius of 1 h_70^-1 Mpc, a velocity dispersion of 700 km/s and has a mass of 1.8 x 10^14 h_70^-1 Msun, similar to that of the most massive fossil groups known. The merging of the four central galaxies in this group would form a galaxy with magnitude M_r' ~ -23.4, typical for first-ranked galaxies of fossil groups. Although nearby compact groups with similar properties to CG 6 are rare, we speculate that such systems occurred more frequently in the past and they may have been the precursors of fossil groups.Comment: 7 pages, 3 figures (one color, low resolution), uses emulateapj.sty. Accepted for publication in ApJ Lette

The Relative Productivity Hypothesis of Industrialization: The American Case, 1820-1850

The American Northeast industrialized rapidly from about 1820 to 1850, while the South remained agricultural. Industrialization in the Northeast was substantially powered during these decades by female and child labor, who comprised about 45% of the manufacturing work force in 1832. Wherever manufacturing spread in the Northeast, the wages of females and children relative to those of adult men increased greatly from levels in the agricultural sector which were previously quite low. Our hypothesis of early industrialization is that such development proceeds first in areas whose agriculture, for various reasons, puts a low value on females and children relative to adult men. The lower the "relative productivity" of females and children in the pre-industrial agricultural or traditional economy the earlier will manufacturing evolve, the proportionately greater will the relative wages for females and children increase, and the relatively more manufactured goods will the economy produce. A two-sector model which incorporates a difference in "relative productivity" between two economies is used to develop seven propositions relating to the process of early industrialization. Data from two early censuses of manufactures, 1832 and 1850, and other sources provide evidence for our hypothesis, demonstrating, for example, the low relative productivity of females and children in the Northeast agricultural sector, and the increase in relative wages for these laborers with industrialization. We conclude that factors with low relative productivity in agriculture were instrumental in the initial adoption of the factory system and of industrialization in general in the U.S., and we believe these results are applicable to contemporary phenomena in developing countries.