scholarly journals Non-arithmetic lattices and the Klein quartic

2019 ◽  
Vol 2019 (754) ◽  
pp. 253-279 ◽  
Author(s):  
Martin Deraux
Keyword(s):  
Automorphism Group ◽  
Geometric Construction ◽  
Fundamental Groups ◽  
Ball Quotients ◽  
New Construction

Abstract We give an algebro-geometric construction of some of the non-arithmetic ball quotients constructed by the author, Parker and Paupert. The new construction reveals a relationship between the corresponding orbifold fundamental groups and the automorphism group of the Klein quartic, and also with groups constructed by Barthel–Hirzebruch–Höfer and Couwenberg–Heckman–Looijenga.

Residue: A Geometric Construction

2002 ◽  
Vol 45 (2) ◽  
pp. 284-293 ◽  
Author(s):  
Fernando Sancho de Salas
Keyword(s):  
Geometric Structure ◽  
Differential Forms ◽  
Geometric Construction ◽  
Residue Theorem ◽  
Cohomology Groups ◽  
Local Coordinates ◽  
New Construction

AbstractA new construction of the ordinary residue of differential forms is given. This construction is intrinsic, i.e., it is defined without local coordinates, and it is geometric: it is constructed out of the geometric structure of the local and global cohomology groups of the differentials. The Residue Theorem and the local calculation then follow from geometric reasons.

scholarly journals Geometric Construction-Based Realization of Planar Elastic Behaviors With Parallel and Serial Manipulators

2017 ◽  
Vol 9 (5) ◽  
Author(s):  
Shuguang Huang ◽  
Joseph M. Schimmels
Keyword(s):  
Elastic Properties ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Geometric Construction ◽  
Elastic Component ◽  
Elastic Behavior ◽  
Serial Manipulators ◽  
New Construction ◽  
Necessary And Sufficient ◽  
Serial Mechanism

This paper addresses the passive realization of any selected planar elastic behavior with a parallel or a serial manipulator. Sets of necessary and sufficient conditions for a mechanism to passively realize an elastic behavior are presented. These conditions completely decouple the requirements on component elastic properties from the requirements on mechanism kinematics. The restrictions on the set of elastic behaviors that can be realized with a mechanism are described in terms of acceptable locations of realizable elastic behavior centers. Parallel–serial mechanism pairs that realize identical elastic behaviors (dual elastic mechanisms) are described. New construction-based synthesis procedures for planar elastic behaviors are developed. Using these procedures, one can select the geometry of each elastic component from a restricted space of kinematically allowable candidates. With each selection, the space is further restricted until the desired elastic behavior is achieved.

scholarly journals Ultra regular covering space and its automorphism group

2010 ◽  
Vol 20 (4) ◽  
pp. 699-710 ◽  
Author(s):  
Sang-Eon Han
Keyword(s):  
Automorphism Group ◽  
Transformation Group ◽  
Covering Space ◽  
Fundamental Groups ◽  
Discrete Transformation ◽  
Local Isomorphism ◽  
Digital Space ◽  
Regular Covering ◽  
Digital Covering ◽  
Digital Spaces

Ultra regular covering space and its automorphism groupIn order to classify digital spaces in terms of digital-homotopic theoretical tools, a recent paper by Han (2006b) (see also the works of Boxer and Karaca (2008) as well as Han (2007b)) established the notion of regular covering space from the viewpoint of digital covering theory and studied an automorphism group (or Deck's discrete transformation group) of a digital covering. By using these tools, we can calculate digital fundamental groups of some digital spaces and classify digital covering spaces satisfying a radius 2 local isomorphism (Boxer and Karaca, 2008; Han, 2006b; 2008b; 2008d; 2009b). However, for a digital covering which does not satisfy a radius 2 local isomorphism, the study of a digital fundamental group of a digital space and its automorphism group remains open. In order to examine this problem, the present paper establishes the notion of an ultra regular covering space, studies its various properties and calculates an automorphism group of the ultra regular covering space. In particular, the paper develops the notion of compatible adjacency of a digital wedge. By comparing an ultra regular covering space with a regular covering space, we can propose strong merits of the former.

Main Provisions Of The Concept Of Technology Of Diamond Cutting And Drilling Of Building Structures

2019 ◽  
pp. 59-63
Keyword(s):  
Combustion Engine ◽  
Front Surface ◽  
The Body ◽  
Building Structures ◽  
Diamond Cutting ◽  
Variable Diameter ◽  
Diamond Drilling ◽  
Single Structure ◽  
New Construction ◽  
Non Destructive

The main provisions of the concept of technology of diamond cutting and drilling of building structures are considered. The innovativeness of the technology, its main possibilities and advantages are presented. Carrying out works with the help of this technology in underwater conditions expands its use when constructing and reconstructing hydraulic structure. The use of diamond drilling equipment with motors equipped with an internal combustion engine is considered. Drilling holes with a variable diameter during the reconstruction of the runways of airfields makes it possible to combine the landing mats into a single structure. The ability to cut inside the concrete mass, parallel to the front surface, has no analogues among the methods of concrete treatment. The use of this technology for producing blind openings in the body of concrete without weakening the structure is also unique. Work with precision quality in cutting and diamond drilling of concrete and reinforced concrete was noted by architects and began to be implemented in the manufacture of inter-room and inter-floor openings. Non-destructive approach to the fragmentation of building structures allows them to be reused. The technology of diamond cutting and drilling is located at the junction of new construction, repair, reconstruction of buildings and structures, and dismantling of structures. Attention is paid to the complexity and combinatorial application of diamond technology. Economic efficiency and ecological safety of diamond technology are presented. The main directions of further research for the development of technology are indicated.

Filling words in fundamental groups of Riemann surfaces

2013 ◽  
Vol 50 (1) ◽  
pp. 31-50
Author(s):  
C. Zhang
Keyword(s):  
Riemann Surface ◽  
Fundamental Group ◽  
Riemann Surfaces ◽  
Fundamental Groups ◽  
Closed Geodesics ◽  
New Words

The purpose of this article is to utilize some exiting words in the fundamental group of a Riemann surface to acquire new words that are represented by filling closed geodesics.

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