scholarly journals On the maximal length of arithmetic progressions

2013 ◽  
Vol 18 (0) ◽  
Author(s):  
Minzhi Zhao ◽  
Huizeng Zhang
Keyword(s):  
Arithmetic Progressions ◽  
Maximal Length

On the maximal length of two sequences of integers in arithmetic progressions with the same prime divisors

1996 ◽  
Vol 121 (4) ◽  
pp. 295-307 ◽  
Author(s):  
R. Balasubramanian ◽  
M. Langevin ◽  
T. N. Shorey ◽  
M. Waldschmidt
Keyword(s):  
Arithmetic Progressions ◽  
Maximal Length ◽  
Prime Divisors

scholarly journals Colorings with only rainbow arithmetic progressions

2020 ◽  
Vol 161 (2) ◽  
pp. 507-515
Author(s):  
J. Pach ◽  
I. Tomon
Keyword(s):  
Arithmetic Progressions

Load Distribution of Parallel Springs With Random Length and Stiffness

1987 ◽  
Vol 109 (4) ◽  
pp. 402-406 ◽  
Author(s):  
Go¨ran Gerbert ◽  
Jacques de Mare´
Keyword(s):  
Uniform Distribution ◽  
Load Distribution ◽  
Simple Formula ◽  
Mechanical Design ◽  
Numerical Results ◽  
Maximal Length ◽  
Major Influence ◽  
Length Variation ◽  
Spring Stiffness ◽  
Failure Risk

There are many applications in mechanical design where load distribution is modelled with parallel springs. Here random variation in spring length and spring stiffness is considered. Length variation is assumed to be the major influence and the case with uniform distribution is analyzed in detail. Small variations in spring stiffness are included. Numerical results are given. A simple formula is presented which gives the maximal length deviation as a function of the number of springs. The formula is based on a 10 percent failure risk which is a common number in practical mechanical design.

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