Differential forms, Fukaya A∞A_\infty algebras, and Gromov-Witten axioms

Consider the differential forms $A^*(L)$ on a Lagrangian submanifold $L \subset X$. Following ideas of Fukaya-Oh-Ohta-Ono, we construct a family of cyclic unital curved $A_\infty$ structures on $A^*(L),$ parameterized by the cohomology of $X$ relative to $L.$ The family of $A_\infty$ structures satisfies properties analogous to the axioms of Gromov-Witten theory. Our construction is canonical up to $A_\infty$ pseudoisotopy. We work in the situation that moduli spaces are regular and boundary evaluation maps are submersions, and thus we do not use the theory of the virtual fundamental class.Comment: 51 pages, 6 figures; improved exposition, added illustrations, corrected minor errors, added reference

The Supreme Court’s Theory of Private Law

In this Article, we revisit the clash between private law and the First Amendment in the Supreme Court\u27s recent case, Snyder v. Phelps, using a private-law lens. We are scholars who write about private law as individual justice, a perspective that has been lost in recent years but is currently enjoying something of a revival. Our argument is that the Supreme Court\u27s theory of private law has led it down a path that has distorted its doctrine in several areas, including the First Amendment–tort clash in Snyder. In areas that range from punitive damages to preemption, the Supreme Court has adopted a particular and dominant, but highly contested, theory of private law. It is the theory that private law is not private at all; it is part and parcel of government regulation, or public law in disguise. Part I is a brief overview of how that jurisprudential view came to be, as well as a sketch of a competing view of private law as individual justice. In Part II, we briefly trace the development of the doctrine surrounding the tension between the First Amendment and private law, particularly tort law, and how it helps lead to the view of private law as government regulation displayed in Snyder. We also point out how the intentional infliction of emotional distress tort, the main claim at issue in Snyder, is a particularly poor vehicle for the Court\u27s theory of private law. A relatively recent tort, it was developed by scholars and judges as a means of redress for plaintiffs who had been wronged, but were left without a remedy. Part III presents the central claims of the Article. We argue that the conception of private law as government regulation in Snyder arises from a combination of (1) the doctrinal tools that judges use in First Amendment cases, (2) the unitary nature of the state-action doctrine, and (3) the influence of instrumentalism, specifically in obscuring the plaintiff\u27s agency and the state interest in redress, and in privileging a particular view of compensation. In Part IV, we present some normative or prescriptive implications of our analysis, and then conclude

The Supreme Court’s Theory of Private Law

In this Article, we revisit the clash between private law and the First Amendment in the Supreme Court\u27s recent case, Snyder v. Phelps, using a private-law lens. We are scholars who write about private law as individual justice, a perspective that has been lost in recent years but is currently enjoying something of a revival. Our argument is that the Supreme Court\u27s theory of private law has led it down a path that has distorted its doctrine in several areas, including the First Amendment–tort clash in Snyder. In areas that range from punitive damages to preemption, the Supreme Court has adopted a particular and dominant, but highly contested, theory of private law. It is the theory that private law is not private at all; it is part and parcel of government regulation, or public law in disguise. Part I is a brief overview of how that jurisprudential view came to be, as well as a sketch of a competing view of private law as individual justice. In Part II, we briefly trace the development of the doctrine surrounding the tension between the First Amendment and private law, particularly tort law, and how it helps lead to the view of private law as government regulation displayed in Snyder. We also point out how the intentional infliction of emotional distress tort, the main claim at issue in Snyder, is a particularly poor vehicle for the Court\u27s theory of private law. A relatively recent tort, it was developed by scholars and judges as a means of redress for plaintiffs who had been wronged, but were left without a remedy. Part III presents the central claims of the Article. We argue that the conception of private law as government regulation in Snyder arises from a combination of (1) the doctrinal tools that judges use in First Amendment cases, (2) the unitary nature of the state-action doctrine, and (3) the influence of instrumentalism, specifically in obscuring the plaintiff\u27s agency and the state interest in redress, and in privileging a particular view of compensation. In Part IV, we present some normative or prescriptive implications of our analysis, and then conclude

Mass Loss by Hot Stars

Mechanism explaining mass loss for luminous hot stars using ultraviolet line spectra of some ion

Associations Between Physical Activity and Obesity in a Multi-Ethnic Sample of Adolescent Girls

Purpose: The increasing prevalence of obesity and low participation in physical activity among young racial/ethnic minorities constitute serious public health issues. Research has shown that overweight and obese individuals have increased risks for the following conditions: coronary heart disease, Type 2 diabetes, cancers (endometrial, breast, and colon), hypertension, dyslipidemia, stroke, liver and gallbladder disease, sleep apnea and respiratory problems, osteoarthritis (a degeneration of cartilage and its underlying bone within a joint), and gynecological problems (abnormal menses, infertility). Because chronic diseases disproportionately impact ethnic and racial minorities, this study examined the association between physical activity and body mass index (BMI) in a multi-ethnic group of adolescent girls. Methods: In this cross-sectional study of 188 adolescent girls ages 14-17 years, BMI was calculated as body weight in kilograms divided by height in meters squared. Energy expenditure of activity was measured using a 24-hour recall self-administered activity checklist (SAPAC). Results: Analysis of variance showed a significant inverse association between BMI and vigorous physical activity (p = 0.02), no significant associations with light (p 0.84), and moderate (p = 0.68) physical activity. There was an 11% difference between obese and normal weight, and 4% difference between overweight and normal weight groups in weighted vigorous physical activity participation. Ethnic differences indicated that non-Hispanic white girls participated more in vigorous physical activity than both Mexican American and African American girls. Conclusion: Physical activity programs should focus on promoting moderate to vigorous activities among adolescent girls taking into consideration sociocultural and economic factors that appear to influence levels and types of activity in this population. In addition, supportive social networks consistent with physical activity contexts of this age group should be promoted