scholarly journals Generating a topological drawing of the flat part of a nonplanar graph

2020 ◽  
Vol 12 (1) ◽  
Author(s):  
S.V. Kurapov ◽  
M.V. Davidovsky ◽  
A.V. Tolok
Keyword(s):  
Flat Part ◽  
Nonplanar Graph ◽  
Topological Drawing

scholarly journals KNOT-INEVITABLE PROJECTIONS OF PLANAR GRAPHS

1996 ◽  
Vol 05 (06) ◽  
pp. 877-883 ◽  
Author(s):  
KOUKI TANIYAMA ◽  
TATSUYA TSUKAMOTO
Keyword(s):  
Planar Graph ◽  
Planar Graphs ◽  
Spatial Graph ◽  
Torus Knot ◽  
Nonplanar Graph

For each odd number n, we describe a regular projection of a planar graph such that every spatial graph obtained by giving it over/under information of crossing points contains a (2, n)-torus knot. We also show that for any spatial graph H, there is a regular projection of a (possibly nonplanar) graph such that every spatial graph obtained from it contains a subgraph that is ambient isotopic to H.

scholarly journals Archery by the Apaches – implications of using the bow and arrow in hunter-gatherer communities

2016 ◽  
Vol 43 ◽  
pp. 515-525
Author(s):  
Žiga Šmit
Keyword(s):  
Native American ◽  
Model Calculation ◽  
Air Drag ◽  
Old World ◽  
Regression Procedure ◽  
Flat Part ◽  
Bow And Arrow ◽  
Medium Strength ◽  
Close Range ◽  
Ballistic Trajectory

This review focuses on the technical and social details of production, training, and use of archery equipment by a Native American tribe, the Apaches. The study aims to understand the use of the bow in the Mesolithic and Early and Middle Neolithic societies of the Old World. The paper further describes arrow ballistics. An arrow and bow with similar dimensions and materials to those used by the Apaches was reconstructed and used in ballistic experiments. Shooting and the subsequent model calculation showed that the effective range of arrows made of reed and projected by a bow of medium strength (16–18kg) was not more than approx. 20m. Due to the initial flat part of the ballistic trajectory, such arrows were quite efficient in close-range contests. Within the model calculation, a regression procedure was introduced to determine the arrow air-drag parameters from an ensemble of shots.

scholarly journals Making a Graph Crossing-Critical by Multiplying its Edges

10.37236/2712 ◽  
2013 ◽  
Vol 20 (1) ◽  
Author(s):  
Laurent Beaudou ◽  
César Hernández-Vélez ◽  
Gelasio Salazar
Keyword(s):  
Crossing Number ◽  
Polyhedral Graph ◽  
Nonplanar Graph

A graph is crossing-critical if the removal of any of its edges decreases its crossing number. This work is motivated by the following question: to what extent is crossing-criticality a property that is inherent to the structure of a graph, and to what extent can it be induced on a noncritical graph by multiplying (all or some of) its edges? It is shown that if a nonplanar graph $G$ is obtained by adding an edge to a cubic polyhedral graph, and $G$ is sufficiently connected, then $G$ can be made crossing-critical by a suitable multiplication of edges.

A Standardised Method of Representing Fatigue Test Results

1958 ◽  
Vol 62 (570) ◽  
pp. 456-457 ◽  
Author(s):  
M. Fine
Keyword(s):  
Fatigue Life ◽  
Fatigue Test ◽  
Test Results ◽  
Flat Part

Figure 1 is a set of S-N curves for DTD. 150, taken from Rotol Structures Department Report No. 337. It is difficult to estimate N accurately on the flat part of the curve, and estimates of fatigue life by different people can be very different. Fig. 1, although based on scanty test results, is typical of S-N curves.

scholarly journals FUJITA DECOMPOSITION AND HODGE LOCI

2018 ◽  
Vol 19 (4) ◽  
pp. 1389-1408 ◽  
Author(s):  
Paola Frediani ◽  
Alessandro Ghigi ◽  
Gian Pietro Pirola
Keyword(s):  
Totally Geodesic ◽  
Exterior Power ◽  
Period Map ◽  
Flat Part ◽  
Torelli Theorem

This paper contains two results on Hodge loci in $\mathsf{M}_{g}$. The first concerns fibrations over curves with a non-trivial flat part in the Fujita decomposition. If local Torelli theorem holds for the fibers and the fibration is non-trivial, an appropriate exterior power of the cohomology of the fiber admits a Hodge substructure. In the case of curves it follows that the moduli image of the fiber is contained in a proper Hodge locus. The second result deals with divisors in $\mathsf{M}_{g}$. It is proved that the image under the period map of a divisor in $\mathsf{M}_{g}$ is not contained in a proper totally geodesic subvariety of $\mathsf{A}_{g}$. It follows that a Hodge locus in $\mathsf{M}_{g}$ has codimension at least 2.

scholarly journals The maximum size of an independent set in a nonplanar graph

1975 ◽  
Vol 81 (3) ◽  
pp. 554-556 ◽  
Author(s):  
Michael O. Albertson ◽  
Joan P. Hutchinson
Keyword(s):  
Independent Set ◽  
Maximum Size ◽  
Nonplanar Graph

Stress Distribution of Strip at the Parts in Contact with Roll in Continuous Annealing Furnace

2011 ◽  
Vol 383-390 ◽  
pp. 379-384
Author(s):  
Yi Ding Xing ◽  
Zhi Wen ◽  
Rui Feng Dou ◽  
Xiao Hong Feng ◽  
Zhi Li ◽  
...  
Keyword(s):  
Stress Distribution ◽  
Axial Direction ◽  
Circumferential Direction ◽  
Strip Width ◽  
Continuous Annealing ◽  
Centripetal Force ◽  
Uniform Stress ◽  
Annealing Furnace ◽  
Flat Part ◽  
Continuous Annealing Furnace

The phenomenon of buckling is attributed to the non-uniform stress imposed on strip. This paper investigates the occurrence of this non-uniform by calculating the stress distribution in circumferential and axial direction. The results indicate that stress distribution is even in circumferential direction, and the non-uniform happens in the axial direction. Furthermore, this non-uniform is quiet related to the proportion of strip width and the roll flat part length. Meanwhile, the roll flat part length should as long as it could be in the context of insuring the enough centripetal force to prevent the snaking.

scholarly journals Mode Coupling at around M-Point in PZT

Materials ◽  
2021 ◽  
Vol 15 (1) ◽  
pp. 79
Author(s):  
Sergey Vakhrushev ◽  
Alexey Filimonov ◽  
Konstantin Petroukhno ◽  
Andrey Rudskoy ◽  
Stanislav Udovenko ◽  
...  
Keyword(s):  
Phase Transition ◽  
Lead Zirconate Titanate ◽  
Phonon Dispersion ◽  
Lead Zirconate ◽  
Incommensurate Phase ◽  
Flat Part ◽  
Dispersion Surface ◽  
Phonon Spectra ◽  
Scattering Study ◽  
Antiphase Domains

The question of the microscopic origin of the M-superstructure and additional satellite peaks in the Zr-rich lead zirconate-titanate is discussed for nearly 50 years. Clear contradiction between the selection rules of the critical scattering and the superstructure was found preventing unambiguous attributing of the observed superstructure either to the rotation of the oxygen octahedra or to the antiparallel displacements of the lead cations. Detailed analysis of the satellite pattern explained it as the result of the incommensurate phase transition rather than antiphase domains. Critical dynamics is the key point for the formulated problems. Recently, the oxygen tilt soft mode in the PbZr0.976Ti0.024O3 (PZT2.4) was found. But this does not resolve the extinction rules contradiction. The results of the inelastic X-ray scattering study of the phonon spectra of PZT2.4 around M-point are reported. Strong coupling between the lead and oxygen modes resulting in mode anticrossing and creation of the wide flat part in the lowest phonon dispersion curves is identified. This flat part corresponds to the mixture of the displacements of the lead and oxygen ions and can be an explanation of the extinction rules contradiction. Moreover, a flat dispersion surface is a typical prerequisite for the incommensurate phase transition.

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