Results 11 to 20 of about 69,132 (324)
An inequality for regular near polygons [PDF]
European Journal of Combinatorics, 2003 Let $G$ denote a near-polygon distance-regular graph with diameter $d\geq 3$, valency $k$ and intersection numbers $a_1>0$, $c_2>1$. Let $ _1$ denote the second largest eigenvalue for the adjacency matrix of $G$. We show $ _1$ is at most $(k-a_1-c_2)/(c_2-1)$. We show the following are equivalent: (i) Equality is attained above; (ii) $G$ is $Q$-
Paul Terwilliger, Chih-wen Weng
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Regular ternary polygonal forms [PDF]
The Ramanujan Journal, 2020 Inspired by Dickson's classification of regular ternary quadratic forms, we prove that there are no primitive regular $m$-gonal forms when $m$ is sufficiently large. In order to do so, we construct sequences of primes that are inert in a certain quadratic field and show that they satisfy a certain inequality bounding the next prime by the product of ...
Zilong He, Ben Kane
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Circle packing in regular polygons
Physics of Fluids, 2022 We study the packing of a large number of congruent and non-overlapping circles inside a regular polygon. We have devised efficient algorithms that allow one to generate configurations of N densely packed circles inside a regular polygon, and we have carried out intensive numerical experiments spanning several polygons (the largest number of sides ...
Paolo Amore
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Kink-free deformations of polygons [PDF]
, 1989 We consider a discrete version of the Whitney-Graustein theorem concerning regular equivalence of closed curves. Two regular polygons P and P’, i.e. polygons without overlapping adjacent edges, are called regularly equivalent if there is a continuous one-
Vegter, Gert
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Spin-orbit induced interference in polygon-structures [PDF]
, 2004 We investigate the spin-orbit induced spin-interference pattern of ballistic electrons travelling along any regular polygon. It is found that the spin-interference depends strongly on the Rashba and Dresselhaus spin-orbit constants as well as on the ...
B. L. Al’tshuler +8 more
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Distance Distributions in Regular Polygons [PDF]
IEEE Transactions on Vehicular Technology, 2013 This paper derives the exact cumulative density function of the distance between a randomly located node and any arbitrary reference point inside a regular $\el$-sided polygon. Using this result, we obtain the closed-form probability density function (PDF) of the Euclidean distance between any arbitrary reference point and its $n$-th neighbour node ...
Khalid, Zubair, Durrani, Salman
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Free vibration frequencies of prismatic thin shells [PDF]
Известия Саратовского университета. Новая серия: Математика. Механика. ИнформатикаThe paper examines the natural frequencies of prismatic thin shells, the cross-section of which is the regular polygon. Spectra of free vibration frequencies of such shells are analyzed as the number of cross-section sides increases, provided that the ...
Dzebisashvili, Georgii Tamazovich +2 more
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Calculations of Dihedral Groups Using Circular Indexation [PDF]
Mathematics Interdisciplinary Research, 2019 In this work, a regular polygon with n sides is described by a periodic (circular) sequence with period n. Each element of the sequence represents a vertex of the polygon.
Reza Dianat, Mojgan Mogharrab
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Journal of Water and Climate Change, 2021 The effects of climate change caused by global warming can be seen in changes of climate variables such as precipitation, humidity, and temperatures.
Gokmen Ceribasi, Ahmet Iyad Ceyhunlu
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In search for a perfect shape of polyhedra: Buffon transformation [PDF]
, 2014 For an arbitrary polygon consider a new one by joining the centres of consecutive edges. Iteration of this procedure leads to a shape which is affine equivalent to a regular polygon.
Schreiber, V. +2 more
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