Rawlsian governments and the race to the bottom

This paper argues that there is no race to the bottom when the social planner adopts a Rawlsian criterion, only the poor are mobile and they do not work at the optimal tax outcome. This argument is developed within a two skill-model of optimal income taxation.Income taxation

Manifolds and Forms on Manifolds

In this chapter we reintroduce manifolds in a somewhat more mathematically rigorous manor while simultaneously trying not to overwhelm you with details. As always we will still place an emphasis on conceptual understanding and the big picture. Manifold theory is a vast and rich subject and there are numerous books that present manifolds in a completely rigorous manor with all the gory technical details made explicit. When you understand this chapter you will be prepared to tackle these texts

Impacts from above-ground activities in the Eagle Ford Shale play on landscapes and hydrologic flows, La Salle County, Texas

textExpanded production of hydrocarbons by means of horizontal drilling and hydraulic fracturing of shale formations has become one of the most important changes in the North American petroleum industry in decades, and the Eagle Ford (EF) Shale play in South Texas is currently one of the largest producers of oil and gas in the United States. Since 2008, more than 5000 wells have been drilled in the EF. To date, little research has focused on landscape impacts (e.g., fragmentation and soil erosion) from the construction of drilling pads, roads, pipelines, and other infrastructure. The goal of this study was to assess the spatial fragmentation from the recent EF shale boom, focusing on La Salle County, Texas. To achieve this goal, a database of wells and pipelines was overlain onto base maps of land cover, soil type, vegetation assemblages, and hydrologic units. Changes to the continuity of different ecoregions and supporting landscapes were then assessed using the Landscape Fragmentation Tool as quantified by land area and continuity of core landscape areas (those degraded by “edge effects”). Results show an increase in ecosystem fragmentation with a reduction in core areas of 8.7% (~333 km²) and an increase in landscape patches (0.2%; 6.4 km²), edges (1.8%; ~69 km²), and perforated areas (4.2%; ~162 km²) within the county. Pipeline construction dominates sources of landscape disturbance, followed by drilling and injection pads (85%, 15%, and 0.03% of disturbed area, respectively). This analysis indicates an increase in the potential for soil loss, with 51% (~58 km²) of all disturbance regimes occurring on soils with low water-transmission rates and a high runoff potential (hydrologic soil group D). Additionally, 88% (~100 km²) of all disturbances occurred on soils with a wind erodibility index of approximately 19 kt/km²/yr or higher, resulting in an estimated potential of 2 million tonnes of soil loss per year. Depending on the placement of infrastructure relative to surface drainage patterns and erodible soil, these results show that small changes in placement may significantly reduce ecological and hydrological impacts as they relate to surface runoff. Furthermore, rapid site reclamation of drilling pads and pipeline right-of-ways could substantially mitigate potential impacts.Energy and Earth Resource

Basis independence of implicitly defined hamiltonian circuit dynamics

© Springer International Publishing Switzerland 2017. The Bloch-Crouch formulation of LC-circuit dynamics is seen to be an implicitly defined Hamiltonian system on a particular manifold. A particular basis independent Dirac structure is shown to be equivalent to the hybrid input-output representation of the Dirac structure used by Bloch and Crouch thereby allowing circuit dynamics to be written in a basis independent fashion

Changes of Variables and Integration of Forms

Integration is one of the most a fundamental concepts in mathematics. In calculus you began by learning how to integrate one-variable functions on $\mathbb {R}$. Then, you learned how to integrate two- and three-variable functions on $\mathbb {R}^2$ and $\mathbb {R}^3$. After this you learned how to integrate a function after a change-of-variables, and finally in vector calculus you learned how to integrate vector fields along curves and over surfaces. It turns out that differential forms are actually very nice things to integrate. Indeed, there is an intimate relationship between the integration of differential forms and the change-of-variables formulas you learned in calculus. In section one we define the integral of a two-form on $\mathbb {R}^2$ in terms of Riemann sums. Integrals of n-forms on $\mathbb {R}^n$ can be defined analogously. We then use the ideas from Chap. 6 along with the Riemann sum procedure to derive the change of coordinates formula from first principles. In section two we look carefully at a simple change of coordinates example. Section three continues by looking at changes from Cartesian coordinates to polar, cylindrical, and spherical coordinates. Finally in section four we consider a more general setting where we see how we can integrate arbitrary one- and two-forms on parameterized one- and two-dimensional surfaces

Push-Forwards and Pull-Backs

In this chapter we introduce two extremely important concepts, the push-forward of a vector and the pull-back of a differential form. In section one we take a close look at a simple change of coordinates and see what affect this change of coordinates has on the volume of the unit square. This allows us to motivate the push-forward of a vector in section two. Push-forwards of vectors allow us to move, or push-forward, a vector from one manifold to another. In the case of coordinate changes the two manifolds are actually the same manifold, only equipped with different coordinate systems

An Example: Electromagnetism

Electromagnetism is probably the first truly elegant and exciting application of differential forms in physics. Electromagnetism deals with both electrical fields and magnetic fields and Maxwell\u27s equations are the four equations that describe how these fields act and how they are related to each other. Maxwell\u27s complicated equations are rendered stunningly simple and beautiful when written in differential forms notation instead of the usual vector calculus notation

Generalized Stokes\u27 Theorem

The generalized version of Stokes\u27 theorem, henceforth simply called Stokes\u27 theorem, is an extraordinarily powerful and useful tool in mathematics. We have already encountered it in Sect. 9.5 where we found a common way of writing the fundamental theorem of line integrals, the vector calculus version of Stokes\u27 theorem, and the divergence theorem as ∫M dα =∫∂M α. More precisely Stokes\u27 theorem can be stated as follows

Designating market maker behaviour in Limit Order Book markets

Financial exchanges provide incentives for limit order book (LOB) liquidity provision to certain market participants, termed designated market makers or designated sponsors. While quoting requirements typically enforce the activity of these participants for a certain portion of the day, we argue that liquidity demand throughout the trading day is far from uniformly distributed, and thus this liquidity provision may not be calibrated to the demand. We propose that quoting obligations also include requirements about the speed of liquidity replenishment, and we recommend use of the Threshold Exceedance Duration (TED) for this purpose. We present a comprehensive regression modelling approach using GLM and GAMLSS models to relate the TED to the state of the LOB and identify the regression structures that are best suited to modelling the TED. Such an approach can be used by exchanges to set target levels of liquidity replenishment for designated market makers