scholarly journals On the Graphs of Hoffman-Singleton and Higman-Sims

10.37236/1830 ◽  
2004 ◽  
Vol 11 (1) ◽  
Author(s):  
Paul R. Hafner
Keyword(s):  
Simple Group ◽  
Steiner System ◽  
Transitive Action ◽  
Quadratic Equations ◽  
New Construction ◽  
Definition Of ◽  
Sims Graph

We propose a new elementary definition of the Higman-Sims graph in which the 100 vertices are parametrised with ${\Bbb Z}_4\times{\Bbb Z}_5\times{\Bbb Z}_5$ and adjacencies are described by linear and quadratic equations. This definition extends Robertson's pentagon-pentagram definition of the Hoffman-Singleton graph and is obtained by studying maximum cocliques of the Hoffman-Singleton graph in Robertson's parametrisation. The new description is used to count the 704 Hoffman-Singleton subgraphs in the Higman-Sims graph, and to describe the two orbits of the simple group HS on them, including a description of the doubly transitive action of HS within the Higman-Sims graph. Numerous geometric connections are pointed out. As a by-product we also have a new construction of the Steiner system $S(3,6,22)$.

scholarly journals Models and scales for quality control: toward the definition of specifications (GOA-LOG) for the generation and re-use of HBIM object libraries in a Common Data Environment

2021 ◽  
Author(s):  
Raffaella Brumana ◽  
Chiara Stanga ◽  
Fabrizio Banfi
Keyword(s):  
Model Generation ◽  
Model Concept ◽  
Generative Process ◽  
New Construction ◽  
Phases Of Development ◽  
Data Environment ◽  
Definition Of ◽  
Object Models ◽  
Geometric Content ◽  
New Buildings

AbstractThe paper focuses on new opportunities of knowledge sharing, and comparison, thanks to the circulation and re-use of heritage HBIM models by means of Object Libraries within a Common Data Environment (CDE) and remotely-accessible Geospatial Virtual Hubs (GVH). HBIM requires a transparent controlled quality process in the model generation and its management to avoid misuses of such models once available in the cloud, freeing themselves from object libraries oriented to new buildings. The model concept in the BIM construction process is intended to be progressively enriched with details defined by the Level of Geometry (LOG) while crossing the different phases of development (LOD), from the pre-design to the scheduled maintenance during the long life cycle of buildings and management (LLCM). In this context, the digitization process—from the data acquisition until the informative models (scan-to-HBIM method)—requires adapting the definition of LOGs to the different phases characterizing the heritage preservation and management, reversing the new construction logic based on simple-to-complex informative models. Accordingly, a deeper understanding of the geometry and state of the art (as-found) should take into account the complexity and uniqueness of the elements composing the architectural heritage since the starting phases of the analysis, adopting coherent object modeling that can be simplified for different purposes as in the construction site and management over time. For those reasons, the study intends (i) to apply the well-known concept of scale to the object model generation, defining different Grades of Accuracy (GOA) related to the scales (ii) to start fixing sustainable roles to guarantee a free choice by the operators in the generation of object models, and (iii) to validate the model generative process with a transparent communication of indicators to describe the richness in terms of precision and accuracy of the geometric content here declined for masonry walls and vaults, and (iv) to identifies requirements for reliable Object Libraries.

A New Construction of the Injective Hull

1968 ◽  
Vol 11 (1) ◽  
pp. 19-21 ◽  
Author(s):  
Isidore Fleischer
Keyword(s):  
Essential Extension ◽  
Injective Hull ◽  
Minimal Cardinality ◽  
New Construction ◽  
Definition Of

The definition of injectivity, and the proof that every module has an injective extension which is a subextension of every other injective extension, are due to R. Baer [B]. An independent proof using the notion of essential extension was given by Eckmann-Schopf [ES]. Both proofs require the p reliminary construction of some injective overmodule. In [F] I showed how the latter proof could be freed from this requirement by exhibiting a set F in which every essential extension could be embedded. Subsequently J. M. Maranda pointed out that F has minimal cardinality. It follows that F is equipotent with the injective hull. Below Icon struct the injective hull by equipping Fit self with a module strucure.

The zoom-on-possessee construction in Kam (Dong): the anatomy of a new construction type

2005 ◽  
Vol 41 (2) ◽  
pp. 307-352 ◽  
Author(s):  
MATTHIAS GERNER
Keyword(s):  
Word Order ◽  
Body Part ◽  
Guizhou Province ◽  
General Definition ◽  
Republic Of China ◽  
Noun Incorporation ◽  
New Construction ◽  
Construction Type ◽  
Definition Of ◽  
Asian Languages

Kam, a Kadai language spoken in Guizhou province (People's Republic of China), has a family of intransitive possessive constructions with the word order ‘Possessor–Verb–Possessee’. (The basic word order in Kam is SV and AVO.) While two recent papers have featured this unique construction type for an array of other Southeast Asian languages, they fail to acknowledge its distinct semantic value in contrast to the related construction type ‘Possessee–Possessor–Verb’. The former construction type displays a so-called ‘zoom-effect’: the possessor is predicated IN, AT or THROUGH his/her/its possessee; the predication zooms from the possessor on his/her/its possessee. The latter construction, in contrast, views the possessee as an entity separated from its possessor, and the predicate as applying solely to the possessee. After illustrating the ‘zoom-effect’ for a representative sample of Kam constructions, I demonstrate that ‘zoom-effects’ do not merely exist when the possessee–possessor compound has the zero-role (=intransitive subject) as above, but also when it assumes other semantic roles (e.g. patient, force, etc.). A general definition of this construction type, called ‘zoom-on-possessee construction’, is proposed; it enables us to unify and account for an array of hitherto disparate construction types that run in the literature under labels such as ‘proprioceptive state expressions’, ‘body part locative constructions’, ‘dative of affect’, etc. Furthermore, I discuss in some detail whether zoom-on-possessee constructions are better accounted for within a multi-stratal or a mono-stratal framework and, finally, whether the concept of noun-incorporation has any relevance.

Use of BIM in rehabilitation and assessment of the built heritage: from the visible to the intangible

2019 ◽  
Author(s):  
Hélder S. Sousa ◽  
Carmen Sguazzo ◽  
Manuel Cabaleiro
Keyword(s):  
Relevant Information ◽  
Destructive Testing ◽  
Building Information Modelling ◽  
Information Modelling ◽  
Traditional Assessment ◽  
Existing Structures ◽  
Built Heritage ◽  
Building Information ◽  
New Construction ◽  
Definition Of

<p>Building Information Modelling (BIM) has been increasingly expanding its application to different fields of civil engineering and Historic building information modelling (HBIM) is an example of that. Although, the concept has already drawn the attention of several researchers, there are still many limitations to a full and holistic process that may take HBIM to the same level of applicability that BIM used for new construction has.</p><p>Traditionally, assessment of existing structures, specially heritage structures, begin with the documentation of all important information dealing with the history, characteristics, type, material, uses and applied techniques, among other relevant information that may be retrieved by different sources. Further on, a geometrical survey accompanied with visual inspection and non or semi destructive testing leads to the geometry definition of the structure and to its condition (damage/defects) mapping. All of this information, must be analysed for consequent structural assessment and after stored in a proper database in order to monitor the condition change of the structure along time.</p><p>This paper, presents a framework for use of BIM in rehabilitation and assessment of the built heritage, based on the review of recent works, as to allow a better understanding of the potential for the management of important and significant structures. The paper deals with the dilemma of bringing what a “traditional” assessment can see to how intangible information may be applied.</p>

scholarly journals Usage of Interface Management System in Adaptive Reuse of Buildings

Buildings ◽  
2019 ◽  
Vol 9 (5) ◽  
pp. 105 ◽  
Author(s):  
Ekin Eray ◽  
Benjamin Sanchez ◽  
Carl Haas
Keyword(s):  
Construction Projects ◽  
Adaptive Reuse ◽  
Project Delivery ◽  
Interface Management ◽  
Building Projects ◽  
Planning Methods ◽  
New Construction ◽  
Definition Of ◽  
Building Project

Adaptive reuse of buildings is considered a superior alternative for new construction in terms of sustainability and a disruptive practice in the current capital project delivery model for the renewal of today’s built environment. In comparison to green-field construction projects, adaptive reuse projects require distinct stages, definition of interfaces, decision gates, and planning methods in order to secure the success of the building project. Unfortunately, little research has been done regarding establishing feasible systems for the planning, assessment, and management of adaptive reuse projects, leading to underperforming building projects outcomes. Interface management (IM) can improve renovation projects outcomes by defining appropriate ways to identify, record, monitor, and track project interfaces. IM has the potential of bringing cost and time benefits during adaptive reuse projects execution. The aim of this study is to develop a reference framework for implementing IM for adaptive reuse projects. First, the inefficiencies of redevelopment projects are explained inside of a circular economy (CE) context. Second, an ontology of IM for adaptive reuse projects is defined based on the current barriers to adaptive reuse and the most common interface problems in construction projects. Third, the defined ontology is expanded through a case study by showing examples of adaptive reuse barriers on a case project, and how IM could have been part of the solution for these problems. Finally, this study concludes with the suggestions on interface management systems (IMS) implementation for future adaptive reuse projects.

scholarly journals On the Codes Related to the Higman-Sims Graph

10.37236/4267 ◽  
2015 ◽  
Vol 22 (1) ◽  
Author(s):  
Wolfgang Knapp ◽  
Hans-Jörg Schaeffer
Keyword(s):  
Simple Group ◽  
Linear Codes ◽  
Maximal Subgroups ◽  
Dual Codes ◽  
Golay Code ◽  
Weight Enumerators ◽  
Low Weight ◽  
Vertex Set ◽  
Almost All ◽  
Sims Graph

All linear codes of length $100$ over a field $F$ which admit the Higman-Sims simple group HS in its rank $3$ representation are determined. By group representation theory it is proved that they can all be understood as submodules of the permutation module $F\Omega$ where $\Omega$ denotes the vertex set of the Higman-Sims graph. This module is semisimple if $\mathrm{char} F\neq 2,5$ and absolutely indecomposable otherwise. Also if $\mathrm{char} F \in \{2, 5\}$ the submodule lattice is determined explicitly. The binary case $F = \mathbb{F}_2$ is studied in detail under coding theoretic aspects. The HS-orbits in the subcodes of dimension $\leq 23$ are computed explicitly and so also the weight enumerators are obtained. The weight enumerators of the dual codes are determined by MacWilliams transformation. Two fundamental methods are used: Let $v$ be the endomorphism determined by an adjacency matrix. Then in $H_{22} = \mathrm{Im} v $ the HS-orbits are determined as $v$-images of certain low weight vectors in $F\Omega$ which carry some special graph configurations. The second method consists in using the fact that $H_{23}/H_{21}$ is a Klein four group under addition, if $H_{23}$ denotes the code generated by $H_{22}$ and a "Higman vector" $x(m)$ of weight 50 associated to a heptad $m$ in the shortened Golay code $G_{22}$, and $H_{21}$ denotes the doubly even subcode of $H_{22}\leq H_{78} = {H_{22}}^\perp$. Using the mentioned observation about $H_{23}/H_{21}$ and the results on the HS-orbits in $H_{23}$ a model of G. Higman's geometry is constructed, which leads to a direct geometric proof that G. Higman's simple group is isomorphic to HS. Finally, it is shown that almost all maximal subgroups of the Higman-Sims group can be understood as stabilizers in HS of codewords in $H_{23}$.

scholarly journals RESPONSIBILITY IN CONSTRUCTION LAW OF LATVIA

2019 ◽  
Vol 3 (84) ◽  
pp. 72
Author(s):  
Inara Ziemele
Keyword(s):  
Comparative Analysis ◽  
General Construction ◽  
Actual Process ◽  
New Construction ◽  
Legislative Amendments ◽  
Construction Law ◽  
Definition Of ◽  
Administrative Responsibility

The new Construction Law and others Construction Regulations come into force more than four years ago, but there is still actual process of definition of responsibility in construction.The aim of paper is to summarize and analyse information about how responsibility in construction has changed and are going to change to define it distinctly.There are used methods of historical, teleological, systematic text condensation, analysis and comparative analysis for research, analyse and summarize information about how responsibility in construction has changed and are going to change to define it in normative acts.The main conclusion shows that now there is not clearness about responsibility of every person in construction, but there are made legislative amendments of Construction Law and General Construction Regulations to define responsibility more distinctly. From 01.01.2020. there will be in force new Law of administrative responsibility what will allow to inflict penalty for longer time.

scholarly journals Features of monitoring bearing structures in the scientific and technical support of construction

2021 ◽  
Vol 258 ◽  
pp. 09058
Author(s):  
Sergey Muzychenko ◽  
Dmitry Topchiy
Keyword(s):  
Survey Design ◽  
Technical Support ◽  
Maximum Efficiency ◽  
Labor Costs ◽  
Load Bearing ◽  
Expert Control ◽  
Construction Methods ◽  
Standard Design ◽  
New Construction ◽  
Definition Of

The purpose of this article is to analyze the possibility and feasibility of using forms and methods of scientific and technical support to increase the efficiency of monitoring the properties and states of load-bearing structures. The task is to substantiate and develop an algorithm for assessing and predicting the states of load-bearing structures while monitoring the parameters of the effects on external and internal environment of construction production. Research methods are systematic approach to the analysis of the conditions for obtaining relevant and reliable information data on the states of bearing structures being erected. Research hypothesis - expanding the scope of scientific and technical support in the format of predicting possible changes in properties and states will significantly increase the efficiency in monitoring carried out during the construction of load-bearing structures and suitable for assessing the subsequent operational suitability of construction facilities. The result of this research is a mathematical model for predicting (assessing) changes in properties and states during the construction of load-bearing structures. In recent years, due to increasing volume of construction of high-rise buildings, the relevance of such a line of activity as scientific and technical support of construction is growing. In comparison with technical supervision, which has the task of monitoring the activities of contractors, scientific and technical support of construction (STSC) has both an applied and a scientific approach, specifically, it develops and implements new construction methods, as well as modern materials, in order to obtain maximum efficiency and saving money and labor costs during construction and installation work. The very definition of scientific and technical support sounds like this - a set of works of scientific and analytical, methodological, informational, expert control and organizational nature carried out by specialized organizations in the process of survey, design and erection of construction facilities in order to ensure the quality of construction, reliability (safety, functional suitability and durability) of buildings and structures, taking into account the applied non-standard design and technical solutions, materials and structures.

HNN Extensions of Inverse Semigroups and Applications

1997 ◽  
Vol 07 (05) ◽  
pp. 605-624 ◽  
Author(s):  
Akihiro Yamamura
Keyword(s):  
Inverse Semigroups ◽  
General Definition ◽  
Hnn Extensions ◽  
Hnn Extension ◽  
Algorithmic Problems ◽  
New Construction ◽  
Definition Of ◽  
Inverse Subsemigroups ◽  
Finitely Presented ◽  
Markov Properties

Originally the concept of an HNN extension of a group was introduced by Higman, Neumann and Neumann in their study of embeddability of groups. Howie introduced the concept of HNN extensions of semigroups and showed embeddability in the case that the associated subsemigroups are unitary. On the other hand, T. E. Hall showed the embeddability of HNN extensions of inverse semigroups of a special type in his survey article on amalgamation of inverse semigroups. We introduce a more general definition of an HNN extension and show that free inverse semigroups and the bicyclic semigroup are HNN extensions of semilattices as examples of our new construction. We discuss weak HNN embeddability in several classes of semigroups and strong HNN embeddability in the class of inverse semigroups. One of our main purposes in the study of HNN extensions of inverse semigroups is to employ HNN extensions to examine some algorithmic problems. We prove the undecidability of Markov properties of finitely presented inverse semigroups using HNN extensions. This result was announced by Vazhenin in 1978, but no proof of it has been published to date. We also show undecidability of several non-Markov properties and discuss some undecidable problems on finitely generated inverse subsemigroups of finitely presented inverse semigroups.

scholarly journals Algebraic and combinatorial structures on Baxter permutations

2011 ◽  
Vol DMTCS Proceedings vol. AO,... (Proceedings) ◽  
Author(s):  
Samuele Giraudo
Keyword(s):  
Hopf Algebra ◽  
Hopf Algebras ◽  
Symmetric Functions ◽  
Combinatorial Theory ◽  
Combinatorial Structures ◽  
Plactic Monoid ◽  
Insertion Algorithm ◽  
New Construction ◽  
Definition Of ◽  
Theory Series

International audience We give a new construction of a Hopf subalgebra of the Hopf algebra of Free quasi-symmetric functions whose bases are indexed by objects belonging to the Baxter combinatorial family (\emphi.e. Baxter permutations, pairs of twin binary trees, \emphetc.). This construction relies on the definition of the Baxter monoid, analog of the plactic monoid and the sylvester monoid, and on a Robinson-Schensted-like insertion algorithm. The algebraic properties of this Hopf algebra are studied. This Hopf algebra appeared for the first time in the work of Reading [Lattice congruences, fans and Hopf algebras, \textitJournal of Combinatorial Theory Series A, 110:237–273, 2005]. Nous proposons une nouvelle construction d'une sous-algèbre de Hopf de l'algèbre de Hopf des fonctions quasi-symétriques libres dont les bases sont indexées par les objets de la famille combinatoire de Baxter (\emphi.e. permutations de Baxter, couples d'arbres binaires jumeaux, \emphetc.). Cette construction repose sur la définition du mono\"ıde de Baxter, analogue du mono\"ıde plaxique et du mono\"ıde sylvestre, et d'un algorithme d'insertion analogue à l'algorithme de Robinson-Schensted. Les propriétés algébriques de cette algèbre de Hopf sont étudiées. Cette algèbre de Hopf est apparue pour la première fois dans le travail de Reading [Lattice congruences, fans and Hopf algebras, \textitJournal of Combinatorial Theory Series A, 110:237–273, 2005].

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