Eigenfunctions of Ordinary Differential Euler Operators

2020 ◽  
Vol 252 (2) ◽  
pp. 125-134
Author(s):  
Yu. Yu. Bagderina
Keyword(s):  
Euler Operators

Euler operators and conservation laws of the BBM equation

1979 ◽  
Vol 85 (1) ◽  
pp. 143-160 ◽  
Author(s):  
Peter J. Olver
Keyword(s):  
Wave Equation ◽  
Conservation Laws ◽  
Calculus Of Variations ◽  
Long Wave ◽  
Regularized Long Wave Equation ◽  
Formal Calculus ◽  
Euler Operators ◽  
Bbm Equation

AbstractThe BBM or Regularized Long Wave Equation is shown to possess only three non-trivial independent conservation laws. In order to prove this result, a new theory of Euler-type operators in the formal calculus of variations will be developed in detail.

Geometrical and Topological Issues in NMT-Based Modeling

1992 ◽  
Author(s):  
Mukul Saxena ◽  
Rajan Srivatsan ◽  
Jonathan E. Davis
Keyword(s):  
Data Structure ◽  
Geometric Modeling ◽  
Modeling Environment ◽  
Insertion Algorithm ◽  
The Face ◽  
Euler Operators ◽  
Application Specific ◽  
Model Topology

Abstract The Non-Manifold Topology (NMT) Radial Edge data structure, along with the supporting set of Euler operators, provides a versatile environment for modeling non-manifold domains. The operators provide the basic tools to construct and manipulate model topology. However, an implementation of the base functionality in a geometric modeling environment raises some geometry-related issues that need to be addressed to ensure the topological validity of the underlying model. This paper focuses on those issues and emphasizes the use of geometry in the implementation of topological operators. Enhancements to the topology manipulation operations are also discussed. Specifically, this paper describes (i) a geometry-based algorithm for face insertion within the Radial Edge data structure, (ii) a manifestation of the face-insertion algorithm to resolve topological ambiguities that arise in the design of topological glue operators, and (iii) enhancements to the topology deletion operators to meet application-specific requirements.

Higher Euler operators and some of their applications

1979 ◽  
Vol 20 (3) ◽  
pp. 522-531 ◽  
Author(s):  
S. J. Aldersley
Keyword(s):  
Euler Operators

scholarly journals Error Estimation of Functions by Fourier-Laguerre Polynomials Using Matrix-Euler Operators

2015 ◽  
Vol 2015 ◽  
pp. 1-4
Author(s):  
M. L. Mittal ◽  
Mradul Veer Singh
Keyword(s):  
Error Estimation ◽  
Laguerre Polynomials ◽  
Degree Of Approximation ◽  
Continuity Condition ◽  
Frontier Point ◽  
Laguerre Series ◽  
Summability Methods ◽  
The Individual ◽  
Euler Operators ◽  
Cesàro Matrix

Various investigators have studied the degree of approximation of a function using different summability (Cesáro means of order α: Cα, Euler Eq, and Nörlund Np) means of its Fourier-Laguerre series at the point x=0 after replacing the continuity condition in Szegö theorem by much lighter conditions. The product summability methods are more powerful than the individual summability methods and thus give an approximation for wider class of functions than the individual methods. This has motivated us to investigate the error estimation of a function by (T·Eq)-transform of its Fourier-Laguerre series at frontier point x=0, where T is a general lower triangular regular matrix. A particular case, when T is a Cesáro matrix of order 1, that is, C1, has also been discussed as a corollary of main result.

scholarly journals Converting CSG models into meshed B-Rep models using euler operators and propagation based marching cubes

2007 ◽  
Vol 29 (4) ◽  
pp. 337-344 ◽  
Author(s):  
Marcos de Sales G. Tsuzuki ◽  
Fabio K. Takase ◽  
Murilo Antônio S. Garcia ◽  
Thiago de Castro Martins
Keyword(s):  
Marching Cubes ◽  
Euler Operators

On the Topology of Sheet Metal Parts

1998 ◽  
Vol 120 (1) ◽  
pp. 10-16 ◽  
Author(s):  
H. Lipson ◽  
M. Shpitalni
Keyword(s):  
Sheet Metal ◽  
Conceptual Design ◽  
Topological Invariant ◽  
Manufacturing Processes ◽  
Qualitative Model ◽  
Topological Properties ◽  
Metal Parts ◽  
Sheet Metal Parts ◽  
Thin Walled ◽  
Euler Operators

This paper analyzes the topological properties of sheet metal parts represented schematically (zero thickness, zero bend radii). Although such parts are usually non-manifold objects, the paper establishes a general topological invariant f = s + b + e + w − v − gnm + m regarding the number of facets, components, bends, free edges, welds, vertices holes and volumes, respectively. Corresponding Euler operators are derived, providing a basis for a modeling system for sheet metal parts. With this invariant, it is possible to reason about manufacturing processes, such as number of components and arrangement of bend lines and weld lines, using only a single qualitative model of the product. This capability is particularly useful in the preliminary stage of conceptual design. A corresponding topological invariant v − e + f = s + m − gnm is also proposed for general sheet models and thin walled objects.

3D GIS spatial operation based on extended Euler operators

2008 ◽  
Author(s):  
Hongbo Xu ◽  
Guonian Lu ◽  
Yehua Sheng ◽  
Liangchen Zhou ◽  
Fei Guo ◽  
...  
Keyword(s):  
3D Gis ◽  
Euler Operators

scholarly journals Duality in Data Structures and Euler Operators of Solid Modelers.

1993 ◽  
Vol 59 (8) ◽  
pp. 1233-1238
Author(s):  
Masatoshi Niizeki ◽  
Fumikazu Konishi ◽  
Makoto Yoshida ◽  
Fujio Yamaguchi
Keyword(s):  
Data Structures ◽  
Euler Operators
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