scholarly journals On rectifiable measures in Carnot groups: representation

2021 ◽  
Vol 61 (1) ◽  
Author(s):  
Gioacchino Antonelli ◽  
Andrea Merlo
Keyword(s):  
Large Class ◽  
Hausdorff Measure ◽  
Carnot Group ◽  
Lipschitz Functions ◽  
Carnot Groups ◽  
Geodesic Sphere ◽  
Area Formula ◽  
Definition Of ◽  
Lipschitz Graphs ◽  
Almost All

AbstractThis paper deals with the theory of rectifiability in arbitrary Carnot groups, and in particular with the study of the notion of $$\mathscr {P}$$ P -rectifiable measure. First, we show that in arbitrary Carnot groups the natural infinitesimal definition of rectifiabile measure, i.e., the definition given in terms of the existence of flat tangent measures, is equivalent to the global definition given in terms of coverings with intrinsically differentiable graphs, i.e., graphs with flat Hausdorff tangents. In general we do not have the latter equivalence if we ask the covering to be made of intrinsically Lipschitz graphs. Second, we show a geometric area formula for the centered Hausdorff measure restricted to intrinsically differentiable graphs in arbitrary Carnot groups. The latter formula extends and strengthens other area formulae obtained in the literature in the context of Carnot groups. As an application, our analysis allows us to prove the intrinsic $$C^1$$ C 1 -rectifiability of almost all the preimages of a large class of Lipschitz functions between Carnot groups. In particular, from the latter result, we obtain that any geodesic sphere in a Carnot group equipped with an arbitrary left-invariant homogeneous distance is intrinsic $$C^1$$ C 1 -rectifiable.

scholarly journals Hausdorff measure of the singular set of quasiregular maps on Carnot groups

2003 ◽  
Vol 2003 (35) ◽  
pp. 2203-2220 ◽  
Author(s):  
Irina Markina
Keyword(s):  
Vector Space ◽  
Hausdorff Measure ◽  
Carnot Group ◽  
Quasiregular Mapping ◽  
Carnot Groups ◽  
Singular Set ◽  
Quasiregular Mappings ◽  
Local Index ◽  
Dimensional Hausdorff Measure ◽  
Homogeneous Dimension

Recently, the theory of quasiregular mappings on Carnot groups has been developed intensively. Letνstand for the homogeneous dimension of a Carnot group and letmbe the index of the last vector space of the corresponding Lie algebra. We prove that the(ν−m−1)-dimensional Hausdorff measure of the image of the branch set of a quasiregular mapping on the Carnot group is positive. Some estimates of the local index of quasiregular mappings are also obtained.

scholarly journals Frege’s puzzle and the ex ante Pareto principle

2020 ◽  
Author(s):  
Anna Mahtani
Keyword(s):  
Policy Choice ◽  
Choice Situation ◽  
Pareto Principle ◽  
Social Situations ◽  
Central Importance ◽  
Ex Ante ◽  
Definition Of ◽  
Almost All ◽  
Rational Behaviour ◽  
Fixed Population

Abstract The ex ante Pareto principle has an intuitive pull, and it has been a principle of central importance since Harsanyi’s defence of utilitarianism (to be found in e.g. Harsanyi, Rational behaviour and bargaining equilibrium in games and social situations. CUP, Cambridge, 1977). The principle has been used to criticize and refine a range of positions in welfare economics, including egalitarianism and prioritarianism. But this principle faces a serious problem. I have argued elsewhere (Mahtani, J Philos 114(6):303-323 2017) that the concept of ex ante Pareto superiority is not well defined, because its application in a choice situation concerning a fixed population can depend on how the members of that population are designated. I show in this paper that in almost all cases of policy choice, there will be numerous sets of rival designators for the same fixed population. I explore two ways that we might complete the definition of ex ante Pareto superiority. I call these the ‘supervaluationist’ reading and the ‘subvaluationist’ reading. I reject the subvaluationist reading as uncharitable, and argue that the supervaluationist reading is the most promising interpretation of the ex ante Pareto principle. I end by exploring some of the implications of this principle for prioritarianism and egalitarianism.

scholarly journals Pseudoinversion of degenerate metrics

2003 ◽  
Vol 2003 (55) ◽  
pp. 3479-3501 ◽  
Author(s):  
C. Atindogbe ◽  
J.-P. Ezin ◽  
Joël Tossa
Keyword(s):  
Differential Geometry ◽  
Large Class ◽  
Smooth Manifold ◽  
Differential Operators ◽  
Type Operator ◽  
Lorentzian Space ◽  
Lightlike Hypersurface ◽  
Definition Of ◽  
Lightlike Hypersurfaces ◽  
Theoretical Results

Let(M,g)be a smooth manifoldMendowed with a metricg. A large class of differential operators in differential geometry is intrinsically defined by means of the dual metricg∗on the dual bundleTM∗of 1-forms onM. If the metricgis (semi)-Riemannian, the metricg∗is just the inverse ofg. This paper studies the definition of the above-mentioned geometric differential operators in the case of manifolds endowed with degenerate metrics for whichg∗is not defined. We apply the theoretical results to Laplacian-type operator on a lightlike hypersurface to deduce a Takahashi-like theorem (Takahashi (1966)) for lightlike hypersurfaces in Lorentzian spaceℝ1n+2.

scholarly journals Legal status of cryptocurrency in Asian countries

2021 ◽  
Vol 66 ◽  
pp. 96-102
Author(s):  
V.M. Logoida
Keyword(s):  
Civil Rights ◽  
Government Regulation ◽  
Legal Status ◽  
Legal Regulation ◽  
Intangible Asset ◽  
Asian Countries ◽  
Legal Nature ◽  
Liberal Approach ◽  
Definition Of ◽  
Almost All

The article is devoted to the study of the experience of legal regulation of the legal status of cryptocurrencies and transactions with them in Asian countries (except for the People's Republic of China and Asian countries - members of the Commonwealth of Independent States, as the author examined them in separate publications). In the article the author, based on the study of regulations, administrative and judicial practice of all major countries in this part of the world, emphasizes the divergent trends in cryptocurrency transactions regulation in the region, when some countries move from a liberal approach to the use of cryptocurrencies to their total ban and vice versa. It is noted that almost all countries in the region give a legal assessment of the payment function of cryptocurrencies, using regulatory or prohibitive approaches, depending on the chosen policy, which indirectly confirms their understanding of the legal nature of cryptocurrencies primarily as a means of payment. At the same time, these countries not only categorically distinguish cryptocurrencies from fiat money issued by central banks, but also mostly avoid the official definition of cryptocurrency as private (decentralized) cash, preferring to qualify them as an intangible asset, virtual asset, digital asset, financial value and even a good or service, which is currently a kind of compromise between political expediency and economic realities. The author also notes that the Asian region is characterized by very active attempts to resolve the legal status of cryptocurrencies at the legislative level, and not just administrative or judicial response to the actual legal relationship, although the progress of different countries in this matter is different. As a result, the author concludes that in the Asian countries considered in the article, there is no same view on the legal nature of cryptocurrency, its qualification as an object of civil rights, and ways to regulate transactions with it (libertarian approach, positive-cryptocurrency approach but with detailed government regulation and control or a completely restrictive policy in relation to the cryptocurrency market).

scholarly journals The Tax Cuts and Jobs Act and the Middle Class

2019 ◽  
Vol 26 (01) ◽  
pp. 53
Author(s):  
Deborah Combs ◽  
Brian Nichols
Keyword(s):  
Middle Class ◽  
The United States ◽  
Census Bureau ◽  
Tax Rates ◽  
United States Census ◽  
United States Census Bureau ◽  
Definition Of ◽  
Almost All ◽  
Jobs Act ◽  
Tax Cuts

This paper explores how the tax cuts and jobs act of 2017 impacts middle-class taxpayers by calculating the tax liability at different levels of income and deductions in 2017 versus 2018. The results confirm the statements supporting the positive effect of the tax change for the middle class. The tax cut and jobs act eliminates personal exemptions, changes the standard deductions at various incomes and family sizes, and lowers marginal tax rates. After providing details of the act, this research examines the definition of the U.S. middle class by using prior research from the Pew Research Center, the United States Census Bureau, and the federal reserve to determine which income levels are attributable to the middle class. Then the tax liability for these income classes is calculated for single and married filing jointly taxpayers in both 2017 and 2018 to determine if the tax cuts and jobs act reduces the tax liability for the middle class. The results show that in almost all scenarios the tax liability in 2018 will be lower than in 2017, regardless of whether standard or itemized deductions are taken. The marriage penalty is no longer applicable, and the new tax act provides a substantial benefit to large families

Historical Account or Discourse on Identity? A Reexamination of Fulbe Hegemony and Autochthonous Submission in Banyo

1998 ◽  
Vol 25 ◽  
pp. 93-110 ◽  
Author(s):  
Quentin Gausset
Keyword(s):  
Nineteenth Century ◽  
The Other ◽  
Islamic State ◽  
Local Populations ◽  
Northern Cameroon ◽  
Definition Of ◽  
Historical Accounts ◽  
In The Beginning ◽  
Almost All ◽  
The Military

Traditional accounts of the nineteenth-century Fulbe conquest in northern Cameroon tell roughly the same story: following the example of Usman Dan Fodio in Nigeria, the Fulbe of Cameroon organized in the beginning of the nineteenth century a “jihad” or a “holy war” against the local pagan populations to convert them to Islam and create an Islamic state. The divisions among the local populations and the military superiority of the Fulbe allowed them to conquer almost all northern Cameroon. They forced those who submitted to give an annual tribute of goods and servants, and they raided the other groups. In these traditional accounts the Fulbe are presented as unchallenged masters, while the local populations are depicted as slaves who were powerless over their fate; their role in the conquest of the region and in the administration of the new political order is supposed to have been insignificant.I will show that, on the contrary, in the area of Banyo the Wawa and Bute played a crucial role in the conquest of the sultanate and in its administration. I will then re-examine the cliche that all members of the local populations were the slaves of the Fulbe by distinguishing the fate of the Wawa and Bute on one side from that of the Kwanja and Mambila on the other, and by showing the importance of the Fulbe's identity in shaping the definition of slavery. Finally I will argue that, if the historical accounts found in the scientific literature invariably insist on Fulbe hegemony and minimize the role played by the local populations, it is because those accounts are often based on Fulbe traditions, and because these traditions are remodeled by the Fulbe in order to correspond to their discourse on identity.

Characteristic of basic tools of mobile learning in informatics

2021 ◽  
pp. 9-13
Author(s):  
I. V. Izhdeneva
Keyword(s):  
Mobile Devices ◽  
Mobile Learning ◽  
Cognitive Activity ◽  
Point Of View ◽  
Learning Tools ◽  
Difficult Situation ◽  
Characteristic Features ◽  
Definition Of ◽  
Almost All ◽  
Educational Potential

The article actualizes the possibilities of mobile learning based on the use of mobile devices and technologies available to almost all students. Various approaches to the definition of the concept of "mobile learning" are analyzed, including techno-centric and information-centric approaches. The concept of mobility as one of the attributes of learning tools is revealed. The importance of mobile learning in the current difficult situation of distance learning during the pandemic is substantiated. The characteristic features of mobile learning are highlighted, affecting its main functions, learning tools and independence from the time and place of learning. Possible directions for the implementation of mobile learning are characterized, from simple transfer of educational content to compliance with basic educational theories. From the point of view of the functioning and directions of development of mobile learning, its basic principles in teaching informatics are formulated. The types of students' activities are briefly characterized; some advantages of mobile learning are highlighted and its features as visualization, interactivity, efficiency of use in teaching children with disabilities are characterized. Some popular educational apps for mobile devices are considered, their characteristics are given, and their educational potential is revealed. Examples of mobile applications are given, the use of which in informatics lessons will help to activate the educational and cognitive activity of students and stimulate them to engage in informatics, coding and robotics.

STRATEGIC PLANNING AND MANAGEMENT OF PROFIT ENTERPRISES IN THE DIGITAL ECONOMY

2018 ◽  
Author(s):  
Daria Bukreieva ◽  
◽  
Karina Tupitsyna ◽  
Anna Bolsha ◽  
◽  
...  
Keyword(s):  
Strategic Planning ◽  
Human Factor ◽  
Statistical Data ◽  
Digital Technologies ◽  
Digital Economy ◽  
Strategic Development ◽  
Definition Of ◽  
Management Functions ◽  
Almost All ◽  
Financial Result

The article is devoted to the topical issue of the strategic development of the enterprise in the digital economy. The advantages of enterprises that use the results of the digital economy in their activities have been established. The main characteristics of the digital economy are determined, approaches to the definition of terms are investigated. The state of profitability of Ukrainian enterprises by industry is analyzed on the basis of statistical data. Based on the results of the analysis of statistical data, it was determined that in the conditions of the pandemic and quarantine of the last two years, most sectors of the economy suffered losses. Only those industries that were vital and those that use modern information and digital technologies had a positive financial result of their activities. These calculations showed that it is fundamentally important to introduce digital technologies at enterprises in various sectors of the economy. The article lists the main seven stages of introducing digital technologies into the management activities of enterprises. The above stages of introducing digital technologies into the activities of enterprises are used both for general strategic transformations at enterprises, and for individual management functions. It also reflects the main benefits of introducing digital technologies into strategic planning and profit management in enterprises. The main obstacles that may arise during the implementation of digital technologies are highlighted, among which the main one is associated with the human factor. It is also indicated in the article that almost all enterprises in their activities can start with the introduction of technologies for working with big data, which allow to efficiently process large volumes of information, analyze it and make management decisions based on the results. An analysis of modern research in the field of digital technologies implementation showed that digital technologies are necessary not only in the current activities of an enterprise, but also in strategic and management functions, especially in planning and managing the company's profit.

A Remark on Disintegrations With Almost All Components Non -Additive

1979 ◽  
Vol 31 (4) ◽  
pp. 786-788 ◽  
Author(s):  
Nghiem Dang-Ngoc
Keyword(s):  
Real Function ◽  
Measure Space ◽  
Gibbs States ◽  
List Type ◽  
Additive Measure ◽  
Finitely Additive Measure ◽  
Coin Tossing ◽  
Definition Of ◽  
Almost All

We extend a theorem of L. E. Dubins on “purely finitely additive disintegrations” of measures (cf. [4]) and apply this result to the disintegrations of extremal Gibbs states with respect to the asymptotic algebra enlarging another result of L. E. Dubins on the symmetric coin tossing game.We recall the following definition of L. E. Dubins (cf. [3], [4]): Let (X , , μ) be a measure space, a sub σ-algebra of . A real function σx (A), is called a measurable-disintegration of μ if:(i) ∀x ∊ X , σx(.) is a finitely additive measure .(ii) ∀A ∊ , σ. (A) is constant on each -atom.(iii) For each A ∊ , σ. (A) is measurable with respect to the completion of by μ and (iv)σx(B) = 1 if x ∊ B ∊ .

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