Root data with group actions

Suppose $k$ is a field, $G$ is a connected reductive algebraic $k$-group, $T$ is a maximal $k$-torus in $G$, and $\Gamma$ is a finite group that acts on $(G,T)$. From the above, one obtains a root datum $\Psi$ on which $\text{Gal}(k)\times\Gamma$ acts. Provided that $\Gamma$ preserves a positive system in $\Psi$, not necessarily invariant under $\text{Gal}(k)$, we construct an inverse to this process. That is, given a root datum on which $\text{Gal}(k)\times\Gamma$ acts appropriately, we show how to construct a pair $(G,T)$, on which $\Gamma$ acts as above. Although the pair $(G,T)$ and the action of $\Gamma$ are canonical only up to an equivalence relation, we construct a particular pair for which $G$ is $k$-quasisplit and $\Gamma$ fixes a $\text{Gal}(k)$-stable pinning of $G$. Using these choices, we can define a notion of taking "$\Gamma$-fixed points" at the level of equivalence classes, and this process is compatible with a general "restriction" process for root data with $\Gamma$-action.Comment: v2: one word inserted, one citation inserted, one reference updated, one misspelling correcte

Benchmarking Image Processing Algorithms for Unmanned Aerial System-Assisted Crack Detection in Concrete Structures

This paper summarizes the results of traditional image processing algorithms for detection of defects in concrete using images taken by Unmanned Aerial Systems (UASs). Such algorithms are useful for improving the accuracy of crack detection during autonomous inspection of bridges and other structures, and they have yet to be compared and evaluated on a dataset of concrete images taken by UAS. The authors created a generic image processing algorithm for crack detection, which included the major steps of filter design, edge detection, image enhancement, and segmentation, designed to uniformly compare dierent edge detectors. Edge detection was carried out by six filters in the spatial (Roberts, Prewitt, Sobel, and Laplacian of Gaussian) and frequency (Butterworth and Gaussian) domains. These algorithms were applied to fifty images each of defected and sound concrete. Performances of the six filters were compared in terms of accuracy, precision, minimum detectable crack width, computational time, and noise-to-signal ratio. In general, frequency domain techniques were slower than spatial domain methods because of the computational intensity of the Fourier and inverse Fourier transformations used to move between spatial and frequency domains. Frequency domain methods also produced noisier images than spatial domain methods. Crack detection in the spatial domain using the Laplacian of Gaussian filter proved to be the fastest, most accurate, and most precise method, and it resulted in the finest detectable crack width. The Laplacian of Gaussian filter in spatial domain is recommended for future applications of real-time crack detection using UAS

From Packet to Power Switching: Digital Direct Load Scheduling

At present, the power grid has tight control over its dispatchable generation capacity but a very coarse control on the demand. Energy consumers are shielded from making price-aware decisions, which degrades the efficiency of the market. This state of affairs tends to favor fossil fuel generation over renewable sources. Because of the technological difficulties of storing electric energy, the quest for mechanisms that would make the demand for electricity controllable on a day-to-day basis is gaining prominence. The goal of this paper is to provide one such mechanisms, which we call Digital Direct Load Scheduling (DDLS). DDLS is a direct load control mechanism in which we unbundle individual requests for energy and digitize them so that they can be automatically scheduled in a cellular architecture. Specifically, rather than storing energy or interrupting the job of appliances, we choose to hold requests for energy in queues and optimize the service time of individual appliances belonging to a broad class which we refer to as "deferrable loads". The function of each neighborhood scheduler is to optimize the time at which these appliances start to function. This process is intended to shape the aggregate load profile of the neighborhood so as to optimize an objective function which incorporates the spot price of energy, and also allows distributed energy resources to supply part of the generation dynamically.Comment: Accepted by the IEEE journal of Selected Areas in Communications (JSAC): Smart Grid Communications series, to appea

Multinational Corporations, Transfer Prices, and Taxes: Evidence from the U.S. Petroleum Industry

Economic research on transfer-pricing behavior by multinational corporadons has emphasized theoretical modeling and institutional description. This paper presents the fiit systematic empirical analysis of transfer prices, using data from the petroleum industry. On the basis of oil imported into the United States over the period 1973 - 1984, we test two propositions: i) Are prices set by integrated companies for their internal transfers different from those prevailing in arm 's-length (i.e., inter-company) trade, when other variables, such as oil quality, are controlled for? ii) Do average effective corporate income tar rates explain observed patterns of transfer pricing? Regression analysis leads to the following conclusions: i) Transfer and arm's-length prices differ significantly for oil origznating in some countries but not all. When multiplied by the relevant import volumes, these differences are relatively smalL The revenue transferred through deviations from arm's-length prices represents two percent or less of the value of the crude oil imported by multinational companies each year. ii) The observed differences between arm's-length and transfer prices are not easily explained by average effective tax rates in exporting countries. Our results provide little support for the claim that multinational petroleum companies set their transfer prices to evade taxes. We offer several hypotheses to explain our findings.

Reliability analysis of continuous fiber composite laminates

A composite lamina may be viewed as a homogeneous solid whose directional strengths are random variables. Calculation of the lamina reliability under a multi-axial stress state can be approached by either assuming that the strengths act separately (modal or independent action), or that they interact through a quadratic interaction criterion. The independent action reliability may be calculated in closed form, while interactive criteria require simulations; there is currently insufficient data to make a final determination of preference between them. Using independent action for illustration purposes, the lamina reliability may be plotted in either stress space or in a non-dimensional representation. For the typical laminated plate structure, the individual lamina reliabilities may be combined in order to produce formal upper and lower bounds of reliability for the laminate, similar in nature to the bounds on properties produced from variational elastic methods. These bounds are illustrated for a (0/plus or minus 15)sub s Graphite/Epoxy (GR/EP) laminate. And addition, simple physically plausible phenomenological rules are proposed for redistribution of load after a lamina has failed. These rules are illustrated by application to (0/plus or minus 15)sub s and (90/plus or minus 45/0)sub s GR/EP laminates and results are compared with respect to the proposed bounds