Mathematical Lens: 8

2014 ◽  
Vol 108 (3) ◽  
pp. 172-175
Keyword(s):  
Circular Segment

The number 8 often appears as two overlapping circles, as shown in photographs 1 and 2. This design can be made by starting with two circles, removing a circle and a circular segment from each circle, and then joining the regions that remain (see fig. 1).

scholarly journals Genome organization of the Chelonus inanitus polydnavirus: excision sites, spacers and abundance of proviral and excised segments

2007 ◽  
Vol 88 (2) ◽  
pp. 450-457 ◽  
Author(s):  
Marc Annaheim ◽  
Beatrice Lanzrein
Keyword(s):  
Symbiotic Association ◽  
Opposite Orientation ◽  
Double Stranded Dna ◽  
Circular Segment ◽  
Multiple Copies ◽  
Flanking Sequences ◽  
Terminal Repeats ◽  
First Time ◽  
Segmented Genome ◽  
Combined Data

Polydnaviruses are only found in symbiotic association with parasitic wasps within the families Ichneumonidae and Braconidae (ichnoviruses and bracoviruses). They have a segmented genome consisting of circular double-stranded DNA. In the proviral linear form they are integrated in the wasp's genome; in two bracoviruses, segments were found to be clustered. Proviral segments have direct terminal repeats. Segment excision has been proposed to occur through juxtaposition of these repeats by formation of a loop and recombination; one copy of the repeat then ends up in the circular segment and one in the rejoined DNA. Here we analysed the excision/circularization site of four segments of the Chelonus inanitus bracovirus (CiV) and found that they are similar to the two already known sites; on the basis of the combined data an extended excision site motif was found. Analyses of segment flanking sequences led to the first identification of one complete and several partial spacers between proviral segments in a polydnavirus. The spacer between the proviral segments CiV14 and CiV22.5 has a length of 2065 bp; the terminal repeats of CiV14 and CiV22.5 were seen to have an opposite orientation and from this a model on the spacial organization of the loops of the proviral cluster is proposed. Through various approaches it was shown that spacers are not excised or injected into the host. Measurement of relative abundances of various segments in proviral and excised form indicates for the first time that abundant segments are present in multiple copies in the proviral form.

Flow and Heat Transfer in Ducts of Arbitrary Shape With Arbitrary Thermal Boundary Conditions

1966 ◽  
Vol 88 (4) ◽  
pp. 351-357 ◽  
Author(s):  
E. M. Sparrow ◽  
A. Haji-Sheikh
Keyword(s):  
Heat Transfer ◽  
Boundary Conditions ◽  
Cross Section ◽  
Arbitrary Cross Section ◽  
Space Technology ◽  
Closed Form Solutions ◽  
Thermal Boundary Conditions ◽  
Flow And Heat Transfer ◽  
Temperature Distributions ◽  
Circular Segment

A computation-oriented method of analysis is presented for determining closed-form solutions for fully developed laminar flow and heat transfer in ducts of arbitrary cross section. The analytical method can accommodate both uniform and circumferentially varying thermal boundary conditions. The solutions provide information for local quantities such as the velocity and the temperature distributions as well as for overall quantities such as the friction factor and the Nusselt number. As an application of the method, solutions are presented for flow and for heat transfer in ducts of circular-segment cross section, a configuration that is of current interest in space technology.

Heat treatment of disks of circular segment saws

1975 ◽  
Vol 17 (5) ◽  
pp. 438-438
Author(s):  
A. F. Volovik ◽  
D. P. Troyanov
Keyword(s):  
Heat Treatment ◽  
Circular Segment

Free vibration of circular‐segment‐shaped membranes and plates of rectangular orthotropy

1983 ◽  
Vol 73 (6) ◽  
pp. 2034-2040 ◽  
Author(s):  
Toshihiro Irie ◽  
Gen Yamada ◽  
Yukinori Kobayashi
Keyword(s):  
Free Vibration ◽  
Circular Segment

Inclined Flat Punch of Arbitrary Shape on an Elastic Half-Space

1986 ◽  
Vol 53 (4) ◽  
pp. 798-806 ◽  
Author(s):  
V. I. Fabrikant
Keyword(s):  
Integral Representation ◽  
Half Space ◽  
Arbitrary Shape ◽  
Contact Problems ◽  
Elastic Half Space ◽  
Elastic Contact ◽  
Circular Sector ◽  
Flat Punch ◽  
Circular Segment ◽  
Arbitrary Planform

A new method is proposed for the analysis of elastic contact problems for a flat inclined punch of arbitrary planform under the action of a normal noncentrally applied force. The method is based on an integral representation for the reciprocal distance between two points obtained by the author earlier. Some simple yet accurate relationships are established between the tilting moments and the angles of inclination of an arbitrary flat punch. Specific formulae are derived for a punch whose planform has a shape of a polygon, a triangle, a rectangle, a rhombus, a circular sector and a circular segment. All the formulae are checked against the solutions known in the literature, and their accuracy is confirmed.

scholarly journals The synthesis of a segmented stair-climbing wheel

2018 ◽  
Vol 15 (1) ◽  
pp. 172988141774947 ◽  
Author(s):  
Vladimir Mostyn ◽  
Vaclav Krys ◽  
Tomas Kot ◽  
Zdenko Bobovsky ◽  
Petr Novak
Keyword(s):  
Rotation Angle ◽  
Stair Climbing ◽  
Circular Segment ◽  
Circular Profile ◽  
Bidirectional Movement ◽  
Centre Of Rotation ◽  
Flat Ground

The article describes the process of development of an essentially new wheel suitable both for moving on flat ground and for travelling on stairs. The stair-climbing wheel is composed of rotary circular segments arranged around a shared carrier with arms to form a complete circular profile of the wheel adapted for moving on flat ground; for travelling on stairs, individual segments are rotated by an appropriate angle to touch down tangentially on the stepping surface of the stairs. The dimensions of individual segments, the centre of rotation of individual segments and the angle of their partial turn have been chosen so that the length of the arc along which the circular segment rolls is equal to the length of the stepping surface of an average stair, and, at the same time, the circular segment touches down tangentially on the stepping surface while the wheel turns around the edge of the previous segment. Using the rotation angle of the turnable segments, the wheel can be adapted to the height of non-standard stairs. The segments can be inclined in both directions for bidirectional movement of the wheel up and down the stairs. An undercarriage equipped with these wheels can be used in the field of exploratory robots and for the transportation of persons and materials on stairs.

Amplification of a circular segment of SV40 DNA

Nature ◽  
1974 ◽  
Vol 251 (5471) ◽  
pp. 153-155 ◽  
Author(s):  
DANA DAVOLI ◽  
GEORGE C. FAREED
Keyword(s):  
Circular Segment ◽  
Sv40 Dna
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