A partial plane of order 6 constructed from the icosahedron

2007 ◽  
Vol 44 (1-3) ◽  
pp. 287-292 ◽  
Author(s):  
Christoph Hering ◽  
Andreas Krebs
Keyword(s):  
Partial Plane

A New Kind of Free Extension for Projective Planes

1962 ◽  
Vol 5 (2) ◽  
pp. 167-170 ◽  
Author(s):  
Seymour Ditor
Keyword(s):  
General Structure ◽  
Projective Planes ◽  
Line Incident ◽  
Free Extension ◽  
Extensive Class ◽  
Partial Plane ◽  
Set Of Points

Marshall Hall [l] shows how projective planes of very general structure may be constructed and at the same time exhibits an extensive class which are non-Desarguesian. Here we shall indicate how his method of free extension can be generalized to yield a class of planes which seem to be distinct from those which he obtains.A partial plane is a system consisting of two distinct sets of elements, a set of "points" P, Q,… and a set of "lines" l, m,…, and a relation between these two sets, called "incidence", such that for any two distinct points, there is at most one line incident with both (or, equivalently, for any two distinct lines, there is at most one point incident with both). A partial plane is complete if every two distinct points are joined by a line and every two distinct lines intersect in a point.

Optical Reflection from a Monolayer of Embedded Nano-Objects Covered by a Thick Capping Layer

2007 ◽  
Vol 31 ◽  
pp. 52-55
Author(s):  
C.M.J. Wijers ◽  
O. Voskoboynikov
Keyword(s):  
Plane Waves ◽  
Optical Response ◽  
Reflection Coefficients ◽  
Dipole Strength ◽  
Reflection And Transmission ◽  
Capping Layer ◽  
Optical Reflection ◽  
Continuum Description ◽  
Partial Plane ◽  
Analytical Expressions

In a hybrid discrete-continuum description the optical response of a capped monolayer of nano-objects has been determined. The monolayer emits a summation of partial plane waves obeying traditional reflection and transmission, enabling solution of the monolayer dipole strength. For thick capping layers the resulting reflection coefficients could be approximated by analytical expressions. These results have been used to investigate the feasibility of experimental detection of the optical response of nano-object monolayers.

Three-Dimension Finite Element Analysis for the Concrete Canoe

2014 ◽  
Vol 501-504 ◽  
pp. 659-669
Author(s):  
Chu Yang Lou ◽  
Yu Xuan Wang ◽  
Zhe Ming Liu
Keyword(s):  
Finite Element Analysis ◽  
Cross Section ◽  
Foundation Engineering ◽  
Three Dimension ◽  
Element Analysis ◽  
Engineering Theory ◽  
Fea Model ◽  
Support Conditions ◽  
Partial Plane ◽  
Tongji University

This paper focuses on the structural analysis of concrete canoes. It firstly introduces the background of the concrete canoe competition and some typical FEA methods for concrete canoes. Then the paper establishes and analyzes an FEA model with SAP2000. Considering the similarity between concrete canoes and strip foundations under column, the paper uses the foundation engineering theory of strip foundations under column to determine the support conditions, and the applied loads of concrete canoes under 2 key loading cases. The result is proved to be accurate according to the experience of Tongji University Concrete Canoe Team. Finally, a conjecture of partial plane cross-section assumption of concrete canoe is proposed according to the result of FEA.

scholarly journals Orientation to polarized light in tethered flying honeybees

2020 ◽  
Vol 223 (23) ◽  
pp. jeb228254
Author(s):  
Norihiro Kobayashi ◽  
Ryuichi Okada ◽  
Midori Sakura
Keyword(s):  
Light Stimulus ◽  
Polarized Light ◽  
Rotation Frequency ◽  
Compass Orientation ◽  
Black Paint ◽  
Flight Direction ◽  
Periodic Movement ◽  
Vector Information ◽  
Vector Orientation ◽  
Partial Plane

ABSTRACTMany insects exploit the partial plane polarization of skylight for visual compass orientation and/or navigation. In the present study, using a tethering system, we investigated how flying bees respond to polarized light stimuli. The behavioral responses of honeybees (Apis mellifera) to a zenithal polarized light stimulus were observed using a tethered animal in a flight simulator. Flight direction of the bee was recorded by monitoring the horizontal movement of its abdomen, which was strongly anti-correlated with its torque. When the e-vector orientation of the polarized light was rotated clockwise or counterclockwise, the bee responded with periodic right-and-left abdominal movements; however, the bee did not show any clear periodic movement under the static e-vector or depolarized stimulus. The steering frequency of the bee was well coordinated with the e-vector rotation frequency of the stimulus, indicating that the flying bee oriented itself to a certain e-vector orientation, i.e. exhibited polarotaxis. The percentage of bees exhibiting clear polarotaxis was much smaller under the fast stimulus (3.6 deg s−1) compared with that under a slow stimulus (0.9 or 1.8 deg s−1). Bees did not demonstrate any polarotactic behavior after the dorsal rim area of the eyes, which mediates insect polarization vision in general, was bilaterally covered with black paint. Preferred e-vector orientations under the clockwise stimulus varied among individuals and distributed throughout −90 to 90 deg. Some bees showed similar preferred e-vector orientations for clockwise and counterclockwise stimuli whereas others did not. Our results strongly suggest that flying honeybees utilize the e-vector information from the skylight to deduce their heading orientation for navigation.

Partial plane level of terrace and its test

2000 ◽  
Author(s):  
Yanan Liu ◽  
JianKang Zeng ◽  
Jun-Qi Liu ◽  
Tong S. Wu
Keyword(s):  
Partial Plane

scholarly journals The Largest Pure Partial Planes of Order 6 Have Size 25

10.37236/6473 ◽  
2018 ◽  
Vol 25 (4) ◽  
Author(s):  
Yibo Gao
Keyword(s):  
Search Space ◽  
Computer Search ◽  
Partial Plane ◽  
Rule Out

In this paper, we prove that the largest pure partial plane of order 6 has size 25. At the same time, we classify all pure partial planes of order 6 and size 25 up to isomorphism. Our major approach is computer search. The search space is very large so we use combinatorial arguments to rule out some of the cases. For the remaining cases, we subdivide each search by phases and use multiple checks to reduce search space via symmetry.

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