scholarly journals Euler Transformation of Polyhedral Complexes

2021 ◽  
pp. 1-29
Author(s):  
Prashant Gupta ◽  
Bala Krishnamoorthy
Keyword(s):  
Geometric Realization ◽  
Edge Length ◽  
Aspect Ratios ◽  
Degree Of A Vertex ◽  
Maximum Angle ◽  
Euler Transformation ◽  
Geometric Quality ◽  
Coverage Problems ◽  
New Formula ◽  
Eulerian Tour

We propose an Euler transformation that transforms a given [Formula: see text]-dimensional cell complex [Formula: see text] for [Formula: see text] into a new [Formula: see text]-complex [Formula: see text] in which every vertex is part of the same even number of edges. Hence every vertex in the graph [Formula: see text] that is the [Formula: see text]-skeleton of [Formula: see text] has an even degree, which makes [Formula: see text] Eulerian, i.e., it is guaranteed to contain an Eulerian tour. Meshes whose edges admit Eulerian tours are crucial in coverage problems arising in several applications including 3D printing and robotics. For [Formula: see text]-complexes in [Formula: see text] ([Formula: see text]) under mild assumptions (that no two adjacent edges of a [Formula: see text]-cell in [Formula: see text] are boundary edges), we show that the Euler transformed [Formula: see text]-complex [Formula: see text] has a geometric realization in [Formula: see text], and that each vertex in its [Formula: see text]-skeleton has degree [Formula: see text]. We bound the numbers of vertices, edges, and [Formula: see text]-cells in [Formula: see text] as small scalar multiples of the corresponding numbers in [Formula: see text]. We prove corresponding results for [Formula: see text]-complexes in [Formula: see text] under an additional assumption that the degree of a vertex in each [Formula: see text]-cell containing it is [Formula: see text]. In this setting, every vertex in [Formula: see text] is shown to have a degree of [Formula: see text]. We also present bounds on parameters measuring geometric quality (aspect ratios, minimum edge length, and maximum angle of cells) of [Formula: see text] in terms of the corresponding parameters of [Formula: see text] for [Formula: see text]. Finally, we illustrate a direct application of the proposed Euler transformation in additive manufacturing.

MOAA and Topology Judgment for Mesh Construction

2004 ◽  
Author(s):  
Wen-Jie Cheng ◽  
Arzu Gonenc Sorguc ◽  
Junichi Shinoda ◽  
Ichiro Hagiwara
Keyword(s):  
Topology Optimization ◽  
Data Set ◽  
Basic Principles ◽  
Intersection Problem ◽  
Line Segments ◽  
Original Surface ◽  
Aspect Ratios ◽  
And Topology ◽  
Maximum Angle ◽  
Data Points

In this paper, the Maximum Opposite Angulation Approach (MOAA) for 3-D including the topology optimization is discussed. The MOAA algorithm is developed to generate meshes in 2-D and 3-D. The basic principles of the algorithm both in 2-D applications and in 3-D applications, is to pre-set uniformity to the initial data set to form point pairs yielding possible shortest line segments. These line segments are connected with the points providing the maximum angle for the vertex of the triangular mesh to be constructed. Thus, the algorithm provides triangular meshes having well balanced interior angles and good aspect ratios. The MOAA algorithm can be proved similar to the Delaunay’s approach in 2-D from the principle and with the quickest speed. In 3-D, it was also shown that it is much more efficient than many Delaunay class algorithms with mesh architectures preserving the topology, for uniformly organized data points. In this study, the topology optimization together with the MOAA algorithm is presented to improve the precision of reconstruction of the original surface. In this context, topology judgment for intersection problem in 3-D, distortion phenomenon, the possibility of loosing some characteristics of the original surface is thoroughly investigated.

scholarly journals Sharp geometric requirements in the Wachspress interpolation error estimate

2018 ◽  
Vol 9 (1) ◽  
pp. 29-36
Author(s):  
Gabriel Monzón
Keyword(s):  
Aspect Ratio ◽  
Error Estimate ◽  
Edge Length ◽  
Interpolation Error ◽  
Barycentric Coordinates ◽  
Geometric Conditions ◽  
Angle Condition ◽  
Maximum Angle ◽  
Interpolation Error Estimate ◽  
Generalized Barycentric Coordinates

AbstractGeometric conditions on general polygons are given in [9] in order to guarantee the error estimate for interpolants built from generalized barycentric coordinates, and the question about identifying sharp geometric restrictions in this setting is proposed. In this work, we address the question when the construction is made by using Wachspress coordinates. We basically show that the imposed conditionsbounded aspect ratio property(barp),maximum angle condition(MAC) andminimum edge length property(melp) are actually equivalent to (MAC, melp), and if any of these conditions is not satisfied, then there is no guarantee that the error estimate is valid. In this sense, (MAC) and (melp) can be regarded as sharp geometric requirements in the Wachspress interpolation error estimate.

A new formula for using the audiogram to predict hearing loss for speech. (Rep. No. 273).

1956 ◽  
Author(s):  
J. Donald Harris ◽  
Henry L. Haines ◽  
Cecil K. Myers
Keyword(s):  
Hearing Loss ◽  
New Formula

Macrosomia – a new formula for optimized fetal weight estimation

2008 ◽  
Vol 68 (S 01) ◽  
Author(s):  
NC Hart ◽  
J Siemer ◽  
B Meurer ◽  
TW Goecke ◽  
RL Schild
Keyword(s):  
Fetal Weight ◽  
Weight Estimation ◽  
Fetal Weight Estimation ◽  
New Formula

Avalanche Stratification - Experimental Tests of the “Metastable Wedge” and “Continuous Flow” Models

2000 ◽  
Vol 627 ◽  
Author(s):  
M. E. Swanson ◽  
M. Landreman ◽  
J. Michel ◽  
J. Kakalios
Keyword(s):  
Continuous Flow ◽  
Granular Media ◽  
Experimental Tests ◽  
Coarse Sand ◽  
Angle Of Repose ◽  
Flow Models ◽  
Maximum Angle ◽  
Stratification Effect ◽  
Upward Moving ◽  
Moving Layer

ABSTRACTWhen an initially homogeneous binary mixture of granular media such as fine and coarse sand is poured near the closed edge of a “quasi-two-dimensional” Hele-Shaw cell consisting of two vertical transparent plates held a narrow distance apart, the mixture spontaneously forms alternating segregated layers. Experimental measurements of this stratification effect are reported in order to determine which model, one which suggests that segregation only occurs when the granular material contained within a metastable heap between the critical and maximum angle of repose avalanches down the free surface, or one for which the segregation results from smaller particles becoming trapped in the top surface and being removed from the moving layer during continuous flow. The result reported here indicate that the Metastable Wedge model provides a natural explanation for the initial mixed zone which precedes the formation of the layers, while the Continuous Flow model explains the observed upward moving kink of segregated material for higher granular flux rates, and that both mechansims are necessary in order to understand the observed pairing of segregated layersfor intermediate flow rates and cell separations.

Tire Treadwear — A Comprehensive Evaluation of the Factors: Generic Type, Aspect Ratio, Tread Pattern, and Tread Composition Part III: Results of Supplementary and UTQG Treadwear Test Series

1986 ◽  
Vol 14 (4) ◽  
pp. 235-263
Author(s):  
A. G. Veith
Keyword(s):  
Carbon Black ◽  
Comprehensive Evaluation ◽  
Work Intensity ◽  
Generic Type ◽  
Aspect Ratios ◽  
Index Variation ◽  
Primary Determinant ◽  
Severity Levels ◽  
High Test ◽  
Better Than

Abstract The effect of tread compound variation on tire treadwear was studied using bias and radial tires of two aspect ratios. Compound variations included types of rubber and carbon black as well as the levels of carbon black, process oil, and curatives. At low to moderate test severity, SBR and an SBR/BR blend performed better than NR while at high test severity NR and SBR were better than the SBR/BR blend. The SBR/BR blend was the best at low severity testing. Higher structure and higher surface area carbon black gave improved treadwear at all severity levels. The concept of a “frictional work intensity” as the primary determinant of treadwear index variation with test severity is proposed. Some factors which influence frictional work intensity are discussed.

ANALYSIS OF THE INFLUENCE OF DIMENSIONS OF THE ROPE MIDWATER TRAWLS ON THEIR PERFORMANCE SUBJECT TO GEOMETRIC PROPERTIES OF CONE SHELLS

2017 ◽  
pp. 25-33
Author(s):  
Alexander Vasilievich Dvernik
Keyword(s):  
Surface Properties ◽  
Conical Shell ◽  
Side Surface ◽  
Theoretic Analysis ◽  
Good Convergence ◽  
Large Size ◽  
Quality Coefficient ◽  
Geometric Quality ◽  
The Relationship ◽  
Parameters Calculation

The article studies different shell constructions of mid-water trawls and their properties. The problem settled is suggested to be solved taking into account real geometric interrelations between spacious and surface properties of cone shells. The author suggests to accept a so-called geometric quality coefficient as a criterion of the properties of a conical shell, which represents the ratio of the shell to the area of its side surface and by analogy to use it to the shell of the trawl. The relationship between the trawl dimensions and geometric quality coefficient have been studied. Comparing these figures with the actual characteristics of trawls showed good convergence. According to the results of theoretic analysis and parameters calculation, trawl large-size shells will always have advantages in geometric characteristics over mid-size and, especially, small-size shells. The results of the analysis can be used for approximate calculations of the parameters of the trawl and justification of ways to improve the performance of existing mid-water trawls.

Analysis of the influence of the hole depth on the geometric quality of the machined part, when the cutting fluid and the machining parameters are varied

2017 ◽  
Author(s):  
Eder Silva Costa ◽  
Pedro Henrique Pires França ◽  
Leonardo Rosa Ribeiro da Silva ◽  
Wisley Sales ◽  
Álisson Rocha Machado ◽  
...  
Keyword(s):  
Cutting Fluid ◽  
Machining Parameters ◽  
Hole Depth ◽  
Geometric Quality

Topology knots and hierarchy problem

2019 ◽  
Author(s):  
Vitaly Kuyukov
Keyword(s):  
Quantum Theory ◽  
String Theory ◽  
Quantum Gravity ◽  
Dimensional Space ◽  
Space Time ◽  
Elementary Particles ◽  
Hierarchy Problem ◽  
Topological Quantum ◽  
Dimensional Space Time ◽  
New Formula

Many approaches to quantum gravity consider the revision of the space-time geometry and the structure of elementary particles. One of the main candidates is string theory. It is possible that this theory will be able to describe the problem of hierarchy, provided that there is an appropriate Calabi-Yau geometry. In this paper we will proceed from the traditional view on the structure of elementary particles in the usual four-dimensional space-time. The only condition is that quarks and leptons should have a common emerging structure. When a new formula for the mass of the hierarchy is obtained, this structure arises from topological quantum theory and a suitable choice of dimensional units.

The analysis

2019 ◽  
Author(s):  
Fariha Azalea
Keyword(s):  
Secondary School ◽  
Direct Observation ◽  
Test Score ◽  
Learning Experience ◽  
Descriptive Study ◽  
Cognitive Test ◽  
21St Century Skill ◽  
Maximum Angle ◽  
Post Test ◽  
Collaboration And Communication

This article exposes how STEM-based learning is applied in science class to give students meaningful learning experience in the topic of Pascal Law. This study is motivated by the demand of 21st century skill which expect people to have 4C skills; critical thinking, creativity, collaboration, and communication. In this study, STEM-based learning is conducted at a private secondary school located in Bandung with 28 students of grade 8 as the subjects. Students are provided a problem related to the application of Pascal Law namely hydraulic bridge. They are challenged to design their own hydraulic bridge which can be lifted with maximum angle but in minimum time. A descriptive study is taken where all the data is obtained through direct observation and students’ interview. Based on cognitive test, there is difference on pre-test and post-test score that resulting in the number of gain. Based on direct observation, none of students just sitting on their seat without activities and all are on collaboration to reach their goal. Students’ interview indicates they enjoy learning process as it is their first experience accomplishing a project and it makes them more understand the concept through the real application. Overall of the study, STEM-based learning through hydraulic bridge project stimulates students to be able to think critically, to be creative, to collaborate, and to communicate.

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