Compactness of derivations from commutative Banach algebras

We consider the compactness of derivations from commutative Banach algebras into their dual modules. We show that if there are no compact derivations from a commutative Banach algebra, $A$, into its dual module, then there are no compact derivations from $A$ into any symmetric $A$-bimodule; we also prove analogous results for weakly compact derivations and for bounded derivations of finite rank. We then characterise the compact derivations from the convolution algebra $\ell^1(\Z_+)$ to its dual. Finally, we give an example (due to J. F. Feinstein) of a non-compact, bounded derivation from a uniform algebra $A$ into a symmetric $A$-bimodule

Trade and Security Among the Ruins

The collision of trade and security interests is taking place today in an increasingly fragmented landscape. Governments’ conceptions of their own vital interests are undergoing a rapid transformation as the concept of “national security” expands to encompass issues such as national industrial policy, cybersecurity, and responses to climate change and pandemic disease. At the same time, the system for settling trade disputes is being pulled apart by competing tendencies toward legalism and deformalization. Last year, a landmark decision suggested that international adjudicators could oversee this clash between security and trade, deciding which security interests can override trade rules and which ones cannot. Then the collapse of the WTO Appellate Body threw into doubt the future of a legalized trade regime, suggesting a partial return to a system driven by politics. I argue that this fragmented landscape provides an opportunity to experiment with different ways of resolving the clash between trade and security. After introducing the expansion of state security interests with reference to recent policy developments, I identify three emerging models for reconciling expanded security interests with trade obligations: structured politics, trade legalism, and judicial managerialism. Each of these models brings tradeoffs in terms of oversight and flexibility, and each is associated with an ideal institutional setting. Rather than attempting to vindicate one model for all settings and all purposes, we should embrace plurality, especially at a moment where the relationship between trade and security appears to be undergoing a historic transformation

A search method for thin positions of links

We give a method for searching for thin positions of a given link.Comment: Published by Algebraic and Geometric Topology at http://www.maths.warwick.ac.uk/agt/AGTVol5/agt-5-42.abs.htm

Behavioral Economics and Workforce Development: A Review of the Literature from Labor Economics and the Broader Field

Literature Reviewhere is mutual benefit for employers and workers when workers improve their skills beyond the minimum requirements for their position—a fact not lost on employers, many of who are willing to provide education and training opportunities to staff, including frontline workers. These opportunities typically include on-the-job-training, tuition reimbursement for postsecondary courses, and paid leave to attend classes. Despite often generous budgets for these activities, relatively few workers take advantage of these opportunities, potentially limiting increases in productivity, wages and longer-term career advancement (Tompson, Benz, Agiesta, & Junius, 2013). This dilemma raises an interesting research question: Can emerging lessons from behavioral science experiments be applied to cutting the Gordian Knot of worker participation in education and training programs? This review of current literature on the topic is intended to explore the strengths and limitations of applying tools of behavioral sciences to increase the participation and completion rate of training for lower-wage, frontline incumbent workers in ways that benefit both workers and sponsoring firms.The Hitachi FoundationRay Marshall Center for the Study of Human Resource

The structure of the C4 cluster radical

The first infrared spectrum of gas phase, jet-cooled C4 has been measured by high resolution diode laser absorption spectroscopy. Twelve rovibrational transitions are assigned to the nu3(sigmau) antisymmetric stretch of linear 3Sigma - g C4. No evidence is observed for the bent structure of triplet C4 recently observed in a matrix study by Cheung and Graham [J. Chem. Phys. 91, 6664 (1989)]. Indeed, the measured band origin (1548.9368(21) cm^–1) and effective ground state C–C bond length [1.304 31(21)A] are consistent with several ab initio predictions of a rigid, linear, cumulenic structure for this cluster radical

The C9 cluster: Structure and infrared frequencies

The high resolution infrared spectrum of the C9 cluster has been measured in direct absorption by infrared diode laser spectroscopy of a pulsed supersonic carbon cluster jet. Fifty-one rovibrational transitions have been assigned to the nu6 (sigmau ) antisymmetric stretch fundamental of the 1Sigma + 9 linear ground state of C9. The measured rotational constant [429.30(50) MHz] is in good agreement with ab initio calculations and indicates an effective bond length of 1.278 68(75) Å, consistent with cumulenic bonding in this cluster. Several perturbations are observed in the upper state, and the upper- and lower-state centrifugal distortion constants are observed to be anomolously large, evidencing a high degree of Coriolis mixing of the normal modes