Sunlet Decomposition of Certain Equipartite Graphs

International Journal of Combinatorics ◽

10.1155/2013/907249 ◽

2013 ◽

Vol 2013 ◽

pp. 1-4 ◽

Cited By ~ 1

Author(s):

Abolape D. Akwu ◽

Deborah O. A. Ajayi

Keyword(s):

Graph Theory ◽

Necessary Condition ◽

Equipartite Graphs

Let L2n stand for the sunlet graph which is a graph that consists of a cycle and an edge terminating in a vertex of degree one attached to each vertex of cycle Cn. The necessary condition for the equipartite graph Kn+I*K̅m to be decomposed into L2n for n≥2 is that the order of L2n must divide n2m2/2, the order of Kn+I*K̅m. In this work, we show that this condition is sufficient for the decomposition. The proofs are constructive using graph theory techniques.

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Configuration synthesis of electric-drive transmissions for tracked vehicles

Advances in Mechanical Engineering ◽

10.1177/1687814017749665 ◽

2018 ◽

Vol 10 (1) ◽

pp. 168781401774966

Author(s):

Ming-Fei Gao ◽

Ji-Bin Hu ◽

Zeng-Xiong Peng

Keyword(s):

Graph Theory ◽

Electric Drive ◽

Synthesis Method ◽

Theory Model ◽

Degree Of Freedom ◽

Transmission Mechanism ◽

Necessary Condition ◽

Tracked Vehicles ◽

Configuration Synthesis ◽

Complex Transmission

This article focus on the configuration synthesis of electric-drive transmissions for tracked vehicles. First, a new graph theory model is proposed to represent the transmission mechanism, which makes the complex transmission system easier to understand. Second, a configuration synthesis method is proposed based on kinematics and statics, in which the speed degree of freedom and torque degree of freedom are considered as the constraints of configuration synthesis. Also, the expressions for speed degree of freedom and torque degree of freedom are derived. Third, based on the graph theory model, the necessary condition to achieve skid steering in the transmission of tracked vehicles is obtained. The results of this article can provides a theoretical basis for the design and analysis of transmission mechanism of tracked vehicles.

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The Infancy of Solar-Type Stars and its Relevance for the Origin of Life

International Astronomical Union Colloquium ◽

10.1017/s0252921100014780 ◽

1997 ◽

Vol 161 ◽

pp. 267-282 ◽

Cited By ~ 1

Author(s):

Thierry Montmerle

Keyword(s):

Main Sequence ◽

Solar Nebula ◽

Circumstellar Disks ◽

T Tauri Stars ◽

Necessary Condition ◽

Sequence Evolution ◽

T Tauri ◽

Solar Type ◽

Optical Domain ◽

The Origin Of Life

AbstractFor life to develop, planets are a necessary condition. Likewise, for planets to form, stars must be surrounded by circumstellar disks, at least some time during their pre-main sequence evolution. Much progress has been made recently in the study of young solar-like stars. In the optical domain, these stars are known as «T Tauri stars». A significant number show IR excess, and other phenomena indirectly suggesting the presence of circumstellar disks. The current wisdom is that there is an evolutionary sequence from protostars to T Tauri stars. This sequence is characterized by the initial presence of disks, with lifetimes ~ 1-10 Myr after the intial collapse of a dense envelope having given birth to a star. While they are present, about 30% of the disks have masses larger than the minimum solar nebula. Their disappearance may correspond to the growth of dust grains, followed by planetesimal and planet formation, but this is not yet demonstrated.

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Universal ESEM

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100149763 ◽

1993 ◽

Vol 51 ◽

pp. 786-787

Author(s):

G.D. Danilatos

Keyword(s):

Electron Microscope ◽

Scanning Electron Microscope ◽

High Vacuum ◽

Natural Extension ◽

Necessary Condition ◽

Environmental Scanning ◽

Detection Systems ◽

Small Gain ◽

Detection Medium ◽

Scanning Electron

The environmental scanning electron microscope (ESEM) has evolved as the natural extension of the scanning electron microscope (SEM), both historically and technologically. ESEM allows the introduction of a gaseous environment in the specimen chamber, whereas SEM operates in vacuum. One of the detection systems in ESEM, namely, the gaseous detection device (GDD) is based on the presence of gas as a detection medium. This might be interpreted as a necessary condition for the ESEM to remain operational and, hence, one might have to change instruments for operation at low or high vacuum. Initially, we may maintain the presence of a conventional secondary electron (E-T) detector in a "stand-by" position to switch on when the vacuum becomes satisfactory for its operation. However, the "rough" or "low vacuum" range of pressure may still be considered as inaccessible by both the GDD and the E-T detector, because the former has presumably very small gain and the latter still breaks down.

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