A lower bound for \tau(n) of any k-perfect numbers

2015 ◽  
Vol 4 ◽  
pp. 99-103
Author(s):  
Keneth Adrian P. Dagal
Keyword(s):  
Lower Bound ◽  
Perfect Numbers

Odd Perfect Numbers: A Search Procedure, and a New Lower Bound of 10 36

1973 ◽  
Vol 27 (124) ◽  
pp. 1004
Author(s):  
D. S. ◽  
Bryant Tuckerman
Keyword(s):  
Lower Bound ◽  
Search Procedure ◽  
Perfect Numbers

scholarly journals A new lower bound for odd perfect numbers

1989 ◽  
Vol 53 (187) ◽  
pp. 431 ◽  
Author(s):  
Richard P. Brent ◽  
Graeme L. Cohen
Keyword(s):  
Lower Bound ◽  
Perfect Numbers

Supplement to A New Lower Bound for Odd Perfect Numbers

1989 ◽  
Vol 53 (187) ◽  
pp. S7
Author(s):  
Richard P. Brent ◽  
Graeme L. Cohen
Keyword(s):  
Lower Bound ◽  
Perfect Numbers

The least distance between extremums and minimal period of solutions to autonomous vector differential equations

2019 ◽  
Vol 485 (2) ◽  
pp. 142-144
Author(s):  
A. A. Zevin
Keyword(s):  
Lower Bound ◽  
Differential Equations ◽  
Periodic Solutions ◽  
Lipschitz Constant ◽  
Minimal Period ◽  
Arbitrary Vector ◽  
Vector Norm ◽  
Sharp Lower Bound

Solutions x(t) of the Lipschitz equation x = f(x) with an arbitrary vector norm are considered. It is proved that the sharp lower bound for the distances between successive extremums of xk(t) equals π/L where L is the Lipschitz constant. For non-constant periodic solutions, the lower bound for the periods is 2π/L. These estimates are achieved for norms that are invariant with respect to permutation of the indices.

A Lower Bound for Schur Numbers and Multicolor Ramsey Numbers

10.37236/1188 ◽  
1994 ◽  
Vol 1 (1) ◽  
Author(s):  
Geoffrey Exoo
Keyword(s):  
Lower Bound ◽  
Lower Bounds ◽  
Ramsey Numbers

For $k \geq 5$, we establish new lower bounds on the Schur numbers $S(k)$ and on the k-color Ramsey numbers of $K_3$.

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