scholarly journals H4(Co0; Z) = Z/24

2018 ◽  
Vol 2020 (21) ◽  
pp. 7873-7907 ◽  
Author(s):  
Theo Johnson-Freyd ◽  
David Treumann
Keyword(s):  
Cyclic Group ◽  
Dimensional Representation ◽  
Integral Cohomology ◽  
Pontryagin Class

Abstract We show that the 4th integral cohomology of Conway’s group $\mathrm{Co}_0$ is a cyclic group of order $24$, generated by the 1st fractional Pontryagin class of the $24$-dimensional representation.

A SAGBI Basis For 𝔽[V2 ⊕ V2 ⊕ V3]Cp

2009 ◽  
Vol 52 (1) ◽  
pp. 72-83 ◽  
Author(s):  
Alexander Duncan ◽  
Michael LeBlanc ◽  
David L.Wehlau
Keyword(s):  
Cyclic Group ◽  
Dimensional Representation

AbstractLet Cp denote the cyclic group of order p, where p ≥ 3 is prime. We denote by Vn the indecomposable n dimensional representation of Cp over a field of characteristic p. We compute a set of generators, in fact a SAGBI basis, for the ring of invariants [V2 ⊕ V2 ⊕ V3]Cp .

Reconstruction of Objects from their Projections Using Orthogonal Functions

1973 ◽  
Vol 31 ◽  
pp. 268-269
Author(s):  
Elrnar Zeitler
Keyword(s):  
Unit Area ◽  
Three Dimensional ◽  
One Dimension ◽  
Spatial Density ◽  
Dimensional Representation ◽  
Orthogonal Functions ◽  
Object A ◽  
Plane Normal ◽  
Dimensional Object ◽  
Spatial Density Distribution

Considering any finite three-dimensional object, a “projection” is here defined as a two-dimensional representation of the object's mass per unit area on a plane normal to a given projection axis, here taken as they-axis. Since the object can be seen as being built from parallel, thin slices, the relation between object structure and its projection can be reduced by one dimension. It is assumed that an electron microscope equipped with a tilting stage records the projectionWhere the object has a spatial density distribution p(r,ϕ) within a limiting radius taken to be unity, and the stage is tilted by an angle 9 with respect to the x-axis of the recording plane.

Revealing gross three-dimensional structure in the SEM

1987 ◽  
Vol 45 ◽  
pp. 656-657
Author(s):  
Sterling P. Newberry
Keyword(s):  
Freeze Drying ◽  
Three Dimensional ◽  
Dimensional Structure ◽  
Small Object ◽  
Final Solution ◽  
Dimensional Representation ◽  
X Ray ◽  
Three Dimensional Representation ◽  
Freeze Dried ◽  
Critical Point Drying

The beautiful three dimensional representation of small object surfaces by the SEM leads one to search for ways to open up the sample and look inside. Could this be the answer to a better microscopy for gross biological 3-D structure? We know from X-Ray microscope images that Freeze Drying and Critical Point Drying give promise of adequately preserving gross structure. Can we slice such preparations open for SEM inspection? In general these preparations crush more readily than they slice. Russell and Dagihlian got around the problem by “deembedding” a section before imaging. This some what defeats the advantages of direct dry preparation, thus we are reluctant to accept it as the final solution to our problem. Alternatively, consider fig 1 wherein a freeze dried onion root has a window cut in its surface by a micromanipulator during observation in the SEM.

scholarly journals Structured-light 3D scanning of exhibited historical clothing—a first-ever methodical trial and its results

2021 ◽  
Vol 9 (1) ◽  
Author(s):  
Jerzy Montusiewicz ◽  
Marek Miłosz ◽  
Jacek Kęsik ◽  
Kamil Żyła
Keyword(s):  
Cultural Heritage ◽  
Information Technologies ◽  
Structured Light ◽  
Three Dimensional ◽  
3D Models ◽  
3D Scanning ◽  
Dimensional Representation ◽  
3D Scanner ◽  
Three Dimensional Representation ◽  
3D Scanners

AbstractHistorical costumes are part of cultural heritage. Unlike architectural monuments, they are very fragile, which exacerbates the problems of their protection and popularisation. A big help in this can be the digitisation of their appearance, preferably using modern techniques of three-dimensional representation (3D). The article presents the results of the search for examples and methodologies of implementing 3D scanning of exhibited historical clothes as well as the attendant problems. From a review of scientific literature it turns out that so far practically no one in the world has made any methodical attempts at scanning historical clothes using structured-light 3D scanners (SLS) and developing an appropriate methodology. The vast majority of methods for creating 3D models of clothes used photogrammetry and 3D modelling software. Therefore, an innovative approach was proposed to the problem of creating 3D models of exhibited historical clothes through their digitalisation by means of a 3D scanner using structural light technology. A proposal for the methodology of this process and concrete examples of its implementation and results are presented. The problems related to the scanning of 3D historical clothes are also described, as well as a proposal how to solve them or minimise their impact. The implementation of the methodology is presented on the example of scanning elements of the Emir of Bukhara's costume (Uzbekistan) from the end of the nineteenth century, consisting of the gown, turban and shoes. Moreover, the way of using 3D models and information technologies to popularise cultural heritage in the space of digital resources is also discussed.

scholarly journals Commutative semigroups whose endomorphisms are power functions

2021 ◽  
Author(s):  
Ryszard Mazurek
Keyword(s):  
Positive Integer ◽  
Power Function ◽  
Cyclic Group ◽  
Commutative Semigroup ◽  
Commutative Monoid ◽  
Power Functions ◽  
Commutative Semigroups ◽  
Finite Cyclic Group

AbstractFor any commutative semigroup S and positive integer m the power function $$f: S \rightarrow S$$ f : S → S defined by $$f(x) = x^m$$ f ( x ) = x m is an endomorphism of S. We partly solve the Lesokhin–Oman problem of characterizing the commutative semigroups whose all endomorphisms are power functions. Namely, we prove that every endomorphism of a commutative monoid S is a power function if and only if S is a finite cyclic group, and that every endomorphism of a commutative ACCP-semigroup S with an idempotent is a power function if and only if S is a finite cyclic semigroup. Furthermore, we prove that every endomorphism of a nontrivial commutative atomic monoid S with 0, preserving 0 and 1, is a power function if and only if either S is a finite cyclic group with zero adjoined or S is a cyclic nilsemigroup with identity adjoined. We also prove that every endomorphism of a 2-generated commutative semigroup S without idempotents is a power function if and only if S is a subsemigroup of the infinite cyclic semigroup.

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