scholarly journals The Geometry of Frequency Squares

2001 ◽  
Vol 96 (2) ◽  
pp. 376-387 ◽  
Author(s):  
Dieter Jungnickel ◽  
V.C. Mavron ◽  
T.P. McDonough
Keyword(s):  
Frequency Squares

Free Vibration of the Triple-Walled Carbon Nanotubes

2009 ◽  
Author(s):  
Demetris Pentaras ◽  
Isaac Elishakoff
Keyword(s):  
Carbon Nanotubes ◽  
Natural Frequencies ◽  
Polynomial Equation ◽  
Galerkin Methods ◽  
Frequency Spectra ◽  
Closed Form Solutions ◽  
Simply Supported ◽  
Cubic Polynomial ◽  
Walled Carbon Nanotubes ◽  
Frequency Squares

Natural frequencies of the triple-walled carbon nanotubes (TWCNTs) are determined both exactly and approximately. For the case of TWCNT which is simply supported at it ends closed-form solutions are obtained. It is shown that there are three series of natural frequencies corresponding to the cubic polynomial equation for natural frequency squares. For the TWCNT that has other boundary conditions approximate Bubnov-Galerkin and Petrov-Galerkin methods are applied. Simple polynomial coordinate functions are utilized. Each of these methods yields three natural frequencies corresponding to the lower and of each frequency spectra.

scholarly journals Balanced diagonals in frequency squares

2018 ◽  
Vol 341 (8) ◽  
pp. 2293-2301
Author(s):  
Nicholas J. Cavenagh ◽  
Adam Mammoliti
Keyword(s):  
Frequency Squares

scholarly journals Maximal sets of mutually orthogonal frequency squares

2021 ◽  
Vol 89 (3) ◽  
pp. 525-558
Author(s):  
Nicholas J. Cavenagh ◽  
Adam Mammoliti ◽  
Ian M. Wanless
Keyword(s):  
Frequency Squares

scholarly journals Frequency Squares and Affine Designs

10.37236/1534 ◽  
2000 ◽  
Vol 7 (1) ◽  
Author(s):  
V C Mavron
Keyword(s):  
Design Theory ◽  
Theory Construction ◽  
Basic Design ◽  
Complete Sets ◽  
Almost All ◽  
Two Parameter ◽  
Frequency Squares

The known methods for constructing complete sets of mutually orthogonal frequency squares all yield one of two parameter sets. We show that almost all these constructions can be derived from one basic design theory construction.

Sets of mutually orthogonal Sudoku frequency squares

2018 ◽  
Vol 87 (1) ◽  
pp. 57-65
Author(s):  
John T. Ethier ◽  
Gary L. Mullen
Keyword(s):  
Frequency Squares

scholarly journals Some new results on mutually orthogonal frequency squares

2014 ◽  
Vol 331 ◽  
pp. 175-187 ◽  
Author(s):  
Mingchao Li ◽  
Yan Zhang ◽  
Beiliang Du
Keyword(s):  
Frequency Squares

scholarly journals Enumeration formulas for latin and frequency squares

1993 ◽  
Vol 111 (1-3) ◽  
pp. 157-163 ◽  
Author(s):  
József Dénes ◽  
Gary L. Mullen
Keyword(s):  
Frequency Squares
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