Group-schemes and formal group-schemes

Expanding on the notion of “keeping intention,” introduced in Chapter 2, Chapter 5 shows how contemplative Christians refine their capacity to “keep attention” and cultivate “contemplative senses” through formal group rituals, body awareness techniques, and the construction of aesthetic environments. It notes the contemplative Christian concept of the Body of Christ in which individual bodies and the collective body are perceived as interconnected entities with expandable and contractible boundaries. The chapter describes the monastic Daily Office and how non-monastic contemplatives adapt monastic rites to their lives outside monasteries. Introducing the important relationship between agency and habitus in contemplative practice, the chapter also develops a model that explicates the process of changing perception, called “contemplative transformation,” as an ever-moving ritualization between “posture” (intentional cataphatic ritual action and positive knowledge) and “flow” (apophatic, ambiguous “inner gestures” and “unknowing”).

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Polycyclic-by-Finite Affine Group Schemes

Proceedings of the London Mathematical Society ◽

10.1112/plms/s3-52.3.495 ◽

1986 ◽

Vol s3-52 (3) ◽

pp. 495-516 ◽

Cited By ~ 1

Author(s):

W. W. Crawley-Boevey

Keyword(s):

Affine Group ◽

Group Schemes ◽

Finite Affine

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Stable cohomotopy and cobordism of abelian groups

Mathematical Proceedings of the Cambridge Philosophical Society ◽

10.1017/s0305004100058734 ◽

1981 ◽

Vol 90 (2) ◽

pp. 273-278 ◽

Cited By ~ 2

Author(s):

C. T. Stretch

Keyword(s):

Abelian Group ◽

Abelian Groups ◽

Finite Abelian Group ◽

Formal Group ◽

Characteristic Class ◽

Burnside Ring ◽

Classifying Space ◽

Formal Group Law ◽

Stable Cohomotopy ◽

Group Law

The object of this paper is to prove that for a finite abelian group G the natural map is injective, where Â(G) is the completion of the Burnside ring of G and σ0(BG) is the stable cohomotopy of the classifying space BG of G. The map â is detected by means of an M U* exponential characteristic class for permutation representations constructed in (11). The result is a generalization of a theorem of Laitinen (4) which treats elementary abelian groups using ordinary cohomology. One interesting feature of the present proof is that it makes explicit use of the universality of the formal group law of M U*. It also involves a computation of M U*(BG) in terms of the formal group law. This may be of independent interest. Since writing the paper the author has discovered that M U*(BG) has previously been calculated by Land-weber(5).

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Astrobiology in Brazil: early history and perspectives

International Journal of Astrobiology ◽

10.1017/s1473550412000250 ◽

2012 ◽

Vol 11 (4) ◽

pp. 189-202 ◽

Cited By ~ 4

Author(s):

Fabio Rodrigues ◽

Douglas Galante ◽

Ivan G. Paulino-Lima ◽

Rubens T.D. Duarte ◽

Amancio C.S. Friaça ◽

...

Keyword(s):

Formal Group ◽

Scientific Production ◽

Funding Agencies ◽

First Occurrence ◽

History Of ◽

The Subject ◽

Review Reports ◽

Number Of Publications ◽

Brazilian History ◽

The University

AbstractThis review reports the Brazilian history in astrobiology, as well as the first delineation of a vision of the future development of the field in the country, exploring its abundant biodiversity, highly capable human resources and state-of-the-art facilities, reflecting the last few years of stable governmental investments in science, technology and education, all conditions providing good perspectives on continued and steadily growing funding for astrobiology-related research. Brazil is growing steadily and fast in terms of its worldwide economic power, an effect being reflected in different areas of the Brazilian society, including industry, technology, education, social care and scientific production. In the field of astrobiology, the country has had some important landmarks, more intensely after the First Brazilian Workshop on Astrobiology in 2006. The history of astrobiology in Brazil, however, is not so recent and had its first occurrence in 1958. Since then, researchers carried out many individual initiatives across the country in astrobiology-related fields, resulting in an ever growing and expressive scientific production. The number of publications, including articles and theses, has particularly increased in the last decade, but still counting with the effort of researchers working individually. That scenario started to change in 2009, when a formal group of Brazilian researchers working with astrobiology was organized, aiming at congregating the scientific community interested in the subject and to promote the necessary interactions to achieve a multidisciplinary work, receiving facilities and funding from the University de Sao Paulo and other funding agencies.

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Formal groups and Z -entropies

Proceedings of The Royal Society A Mathematical Physical and Engineering Sciences ◽

10.1098/rspa.2016.0143 ◽

2016 ◽

Vol 472 (2195) ◽

pp. 20160143 ◽

Cited By ~ 13

Author(s):

Piergiulio Tempesta

Keyword(s):

Algebraic Topology ◽

Formal Group ◽

Point Of View ◽

Trace Form ◽

Formal Groups ◽

Form Class ◽

New Family ◽

Mathematical Properties ◽

Composition Process ◽

Group Law

We shall prove that the celebrated Rényi entropy is the first example of a new family of infinitely many multi-parametric entropies. We shall call them the Z-entropies . Each of them, under suitable hypotheses, generalizes the celebrated entropies of Boltzmann and Rényi. A crucial aspect is that every Z -entropy is composable (Tempesta 2016 Ann. Phys. 365 , 180–197. ( doi:10.1016/j.aop.2015.08.013 )). This property means that the entropy of a system which is composed of two or more independent systems depends, in all the associated probability space, on the choice of the two systems only. Further properties are also required to describe the composition process in terms of a group law. The composability axiom, introduced as a generalization of the fourth Shannon–Khinchin axiom (postulating additivity), is a highly non-trivial requirement. Indeed, in the trace-form class, the Boltzmann entropy and Tsallis entropy are the only known composable cases. However, in the non-trace form class, the Z -entropies arise as new entropic functions possessing the mathematical properties necessary for information-theoretical applications, in both classical and quantum contexts. From a mathematical point of view, composability is intimately related to formal group theory of algebraic topology. The underlying group-theoretical structure determines crucially the statistical properties of the corresponding entropies.

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