On the modular Mckay graph of SL(p) with respect to its standard representation

2021 ◽  
Vol 574 ◽  
pp. 38-49
Author(s):  
Miriam G. Norris
2020 ◽  
Vol 32 (5) ◽  
pp. 1109-1129
Author(s):  
Dario Spirito

AbstractWe study decompositions of length functions on integral domains as sums of length functions constructed from overrings. We find a standard representation when the integral domain admits a Jaffard family, when it is Noetherian and when it is a Prüfer domains such that every ideal has only finitely many minimal primes. We also show that there is a natural bijective correspondence between singular length functions and localizing systems.


Author(s):  
Michael P. Brundage ◽  
Boonserm Kulvatunyou ◽  
Toyosi Ademujimi ◽  
Badarinath Rakshith

Various techniques are used to diagnose problems throughout all levels of the organization within the manufacturing industry. Often times, this root cause analysis is ad-hoc with no standard representation for artifacts or terminology (i.e., no standard representation for terms used in techniques such as fishbone diagrams, 5 why’s, etc.). Once a problem is diagnosed and alleviated, the results are discarded or stored locally as paper/digital text documents. When the same or similar problem reoccurs with different employees or in a different factory, the whole process has to be repeated without taking advantage of knowledge gained from previous problem(s) and corresponding solution(s). When discussing the diagnosis, personnel may miscommunicate over terms used in the root cause analysis leading to wasted time and errors. This paper presents a framework for a knowledge-based manufacturing diagnosis system that aims to alleviate these miscommunications. By learning from diagnosis methods used in manufacturing and in the medical community, this paper proposes a framework which integrates and formalizes root cause analysis by categorizing faults and failures that span multiple organizational levels. The proposed framework aims to enable manufacturing operations by leveraging machine learning and semantic technologies for the manufacturing system diagnosis. A use case for the manufacture of a bottle opener demonstrates the framework.


Author(s):  
Mohammad N. Abdulrahim ◽  
Nibal H. Kassem

We consider Wada's representation as a twisted version of the standard action of the braid group,Bn, on the free group withngenerators. Constructing a free group,Gnm, of ranknm, we compose Cohen's mapBn→Bnmand the embeddingBnm→Aut(Gnm)via Wada's map. We prove that the composition factors of the obtained representation are one copy of Burau representation andm−1copies of the standard representation after changing the parameterttotkin the definitions of the Burau and standard representations. This is a generalization of our previous result concerning the standard Artin representation of the braid group.


2020 ◽  
Vol 16 ◽  
pp. 2448-2468
Author(s):  
Kanhaya Lal ◽  
Rafael Bermeo ◽  
Serge Perez

Drawing and visualisation of molecular structures are some of the most common tasks carried out in structural glycobiology, typically using various software. In this perspective article, we outline developments in the computational tools for the sketching, visualisation and modelling of glycans. The article also provides details on the standard representation of glycans, and glycoconjugates, which helps the communication of structure details within the scientific community. We highlight the comparative analysis of the available tools which could help researchers to perform various tasks related to structure representation and model building of glycans. These tools can be useful for glycobiologists or any researcher looking for a ready to use, simple program for the sketching or building of glycans.


1998 ◽  
Vol 13 (19) ◽  
pp. 3347-3360
Author(s):  
LUIS J. BOYA ◽  
ERIC CHISOLM ◽  
S. M. MAHAJAN ◽  
E. C. G. SUDARSHAN

We contruct and study a continuous family of representations of the N-dimensional isotropic harmonic oscillator (N≥2) which are not unitarily equivalent to the standard one. We explain why such representations exist and we investigate their simpler properties: the spectrum of the Hamiltonian (which contains nonstandard values), the form of the energy eigenfunctions, and their behavior under the ladder operators. Various symmetry and dynamical groups (e.g. the rotation group) which are valid on the standard representation are not implemented on the new ones. We comment very briefly on the prospects of observing these representations experimentally.


Author(s):  
M.V. Pirogov ◽  
N.N. Pleshchev ◽  
V.V. Rozhkov

The paper considers the problem of generating a list of objects for space survey. To solve the problem it is proposed to use mathematical objects — schemes of radicals, aimed at eliminating critical weaknesses related to the use of mathematical models and corresponding software and hardware in the problem area of complex goal-oriented systems. Also mathematical standardization of complex goal-oriented systems based on the use of radical schemes seems to be necessary. The paper substantiates the need for using radical schemes for the standard representation of objects of observation and restrictions in the operation of the spacecraft target equipment for the task of designing its working program.


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