scholarly journals Polynomial Invariants of the Euclidean Group Action on Multiple Screws

2021 ◽  
Author(s):  
◽  
Deborah Crook

<p>In this work, we examine the polynomial invariants of the special Euclidean group in three dimensions, SE(3), in its action on multiple screw systems. We look at the problem of finding generating sets for these invariant subalgebras, and also briefly describe the invariants for the standard actions on R^n of both SE(3) and SO(3). The problem of the screw system action is then approached using SAGBI basis techniques, which are used to find invariants for the translational subaction of SE(3), including a full basis in the one and two-screw cases. These are then compared to the known invariants of the rotational subaction. In the one and two-screw cases, we successfully derive a full basis for the SE(3) invariants, while in the three-screw case, we suggest some possible lines of approach.</p>

2021 ◽  
Author(s):  
◽  
Deborah Crook

<p>In this work, we examine the polynomial invariants of the special Euclidean group in three dimensions, SE(3), in its action on multiple screw systems. We look at the problem of finding generating sets for these invariant subalgebras, and also briefly describe the invariants for the standard actions on R^n of both SE(3) and SO(3). The problem of the screw system action is then approached using SAGBI basis techniques, which are used to find invariants for the translational subaction of SE(3), including a full basis in the one and two-screw cases. These are then compared to the known invariants of the rotational subaction. In the one and two-screw cases, we successfully derive a full basis for the SE(3) invariants, while in the three-screw case, we suggest some possible lines of approach.</p>


2015 ◽  
Vol 16 (5) ◽  
pp. 1073-1098 ◽  
Author(s):  
Mattias Derlén ◽  
Johan Lindholm

AbstractThe case law of the Court of Justice of the European Union (CJEU) is one of the most important sources of European Union law. However, case law's role in EU law is not uniform. By empirically studying how the Court uses its own case law as a source of law, we explore the correlation between, on the one hand, the characteristics of a CJEU case—type of action, actors involved, and area of law—and, on the other hand, the judgment's “embeddedness” in previous case law and value as a precedent in subsequent cases. Using this approach, we test, confirm, and debunk existing scholarship concerning the role of CJEU case law as a source of EU law. We offer the following conclusions: that CJEU case law cannot be treated as a single entity; that only a limited number of factors reliably affect a judgment's persuasive or precedential power; that the Court's use of its own case law as a source of law is particularly limited in successful infringement proceedings; that case law is particularly important in preliminary references—especially those concerning fundamental freedoms and competition law; and that initiating Member State and the number of observations affects the behavior of the Court.


2019 ◽  
Vol 5 (1) ◽  
pp. 488-495
Author(s):  
Cláudia Martins ◽  
Sérgio Ferreira

AbstractThe linguistic rights of Mirandese were enshrined in Portugal in 1999, though its “discovery” dates back to the very end of the 19th century at the hands of Leite de Vasconcellos. For centuries, it was the first or only language spoken by people living in the northeast of Portugal, particularly the district of Miranda do Douro. As a minority language, it has always moved among three dimensions. On the one hand, the need to assert and defend this language and have it acknowledged by the country, which proudly believe(d) in their monolingual history. Unavoidably, this has ensued the action of translation, especially active from the mid of the 20th century onwards, with an emphasis on the translation of the Bible and Portuguese canonical literature, as well as other renowned literary forms (e.g. The Adventures of Asterix). Finally, the third axis lies in migration, either within Portugal or abroad. Between the 1950s and the 1960s, Mirandese people were forced to leave Miranda do Douro and villages in the outskirts in the thousands. They fled not only due to the deeply entrenched poverty, but also the almost complete absence of future prospects, enhanced by the fact that they were regarded as not speaking “good” Portuguese, but rather a “charra” language, and as ignorant backward people. This period coincided with the building of dams on the river Douro and the cultural and linguistic shock that stemmed from this forceful contact, which exacerbated their sense of not belonging and of social shame. Bearing all this in mind, we seek to approach the role that migration played not only in the assertion of Mirandese as a language in its own right, but also in the empowerment of new generations of Mirandese people, highly qualified and politically engaged in the defence of this minority language, some of whom were former migrants. Thus, we aim to depict Mirandese’s political situation before and after the endorsement of the Portuguese Law no. 7/99.


1971 ◽  
Vol 26 (1) ◽  
pp. 10-17 ◽  
Author(s):  
A. R. Allnatt

AbstractA kinetic equation is derived for the singlet distribution function for a heavy impurity in a lattice of lighter atoms in a temperature gradient. In the one dimensional case the equation can be solved to find formal expressions for the jump probability and hence the heat of transport, q*. for a single vacancy jump of the impurity, q* is the sum of the enthalpy of activation, a term involving only averaging in an equilibrium ensemble, and two non-equilibrium terms in­volving time correlation functions. The most important non-equilibrium term concerns the cor­relation between the force on the impurity and a microscopic heat flux. A plausible extension to three dimensions is suggested and the relation to earlier isothermal and non-isothermal theories is indicated


2021 ◽  
Vol 10 (8) ◽  
pp. 2999-3012
Author(s):  
K. Atchonouglo ◽  
G. de Saxcé ◽  
M. Ban

In this paper, we constructed relationships with the differents 2D elasticity tensor invariants. Indeed, let ${\bf A}$ be a 2D elasticity tensor. Rotation group action leads to a pair of Lax in linear elasticity. This pair of Lax leads to five independent invariants chosen among six. The definite positive criteria are established with the determined invariants. We believe that this approach finds interesting applications, as in the one of elastic material classification or approaches in orbit space description.


2013 ◽  
Vol 4 (2) ◽  
pp. 31-50 ◽  
Author(s):  
Alexander Brem ◽  
Björn Ivens

The fields of frugal and reverse innovation as well as sustainability and its management have received tremendous interest in recent times. However, there is little literature on how both fields are related to each other. Hence, this paper gives an overview of research in both areas and provides a view of the relationship between frugal and reverse innovation, sustainability management and performance constructs. The link between frugal and reverse innovation on the one hand and sustainability performance on the other hand is established through a differentiated perspective on dimensions representing different fields of sustainability management, i.e. the sustainability of resources used in value creation, the sustainability of the actual value creation processes, and the sustainability of the outcomes of value creation processes. Moreover, we also argue for a positive link between the three dimensions of sustainability management and a company’s market performance.


2014 ◽  
Vol 31 (10) ◽  
pp. 2078-2087 ◽  
Author(s):  
Michael L. Larsen ◽  
Clarissa A. Briner ◽  
Philip Boehner

Abstract The spatial positions of individual aerosol particles, cloud droplets, or raindrops can be modeled as a point processes in three dimensions. Characterization of three-dimensional point processes often involves the calculation or estimation of the radial distribution function (RDF) and/or the pair-correlation function (PCF) for the system. Sampling these three-dimensional systems is often impractical, however, and, consequently, these three-dimensional systems are directly measured by probing the system along a one-dimensional transect through the volume (e.g., an aircraft-mounted cloud probe measuring a thin horizontal “skewer” through a cloud). The measured RDF and PCF of these one-dimensional transects are related to (but not, in general, equal to) the RDF/PCF of the intrinsic three-dimensional systems from which the sample was taken. Previous work examined the formal mathematical relationship between the statistics of the intrinsic three-dimensional system and the one-dimensional transect; this study extends the previous work within the context of realistic sampling variability. Natural sampling variability is found to constrain substantially the usefulness of applying previous theoretical relationships. Implications for future sampling strategies are discussed.


2013 ◽  
Vol 749 ◽  
pp. 180-186
Author(s):  
Sheng Lu ◽  
Dai Li Yang ◽  
Shi Yu Xiao ◽  
Ali Lu

Friction stir welding (FSW) experiments were carried out on AZ31 magnesium alloy under the optimized welding parameters. The temperature distribution, macrostructure and microstructure, mechanical properties of the joint were studied along three dimensions (transverse direction, longitudinal direction, thickness direction). Temperature distribution, joint appearance and microstructure demonstrate asymmetric gradient in three dimensions. The peak temperature of featured points at the welding beginning stage was lower, and the one in the ending stage was higher. The temperature of advancing side was higher than that of the retreating side. More in detail, the dynamically recrystallized microstructure in weld nugget zone (WNZ) was uniform and small. The thermomechanically affected zones (TMAZ) closed to the WNZ, which were characterized with bended and elongated grains. At advancing side, the interface between TMAZ and WNZ was very distinct. The microhardness distribution showed a typical W shape. The profile showed a slightly lower hardness in the WNZ than in the base metal,HAZ, and TMAZ correspond to the lowest one. The FSW joints were observed to fail mostly at the boundary between WNZ and TMAZ at the advancing side.


Geophysics ◽  
2018 ◽  
Vol 83 (2) ◽  
pp. U9-U22 ◽  
Author(s):  
Jide Nosakare Ogunbo ◽  
Guy Marquis ◽  
Jie Zhang ◽  
Weizhong Wang

Geophysical joint inversion requires the setting of a few parameters for optimum performance of the process. However, there are yet no known detailed procedures for selecting the various parameters for performing the joint inversion. Previous works on the joint inversion of electromagnetic (EM) and seismic data have reported parameter applications for data sets acquired from the same dimensional geometry (either in two dimensions or three dimensions) and few on variant geometry. But none has discussed the parameter selections for the joint inversion of methods from variant geometry (for example, a 2D seismic travel and pseudo-2D frequency-domain EM data). With the advantage of affordable computational cost and the sufficient approximation of a 1D EM model in a horizontally layered sedimentary environment, we are able to set optimum joint inversion parameters to perform structurally constrained joint 2D seismic traveltime and pseudo-2D EM data for hydrocarbon exploration. From the synthetic experiments, even in the presence of noise, we are able to prescribe the rules for optimum parameter setting for the joint inversion, including the choice of initial model and the cross-gradient weighting. We apply these rules on field data to reconstruct a more reliable subsurface velocity model than the one obtained by the traveltime inversions alone. We expect that this approach will be useful for performing joint inversion of the seismic traveltime and frequency-domain EM data for the production of hydrocarbon.


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