scholarly journals The stresses on centrally symmetric complexes and the lower bound theorems

2021 ◽  
Vol 4 (3) ◽  
pp. 541-549
Author(s):  
Isabella Novik ◽  
Hailun Zheng
Keyword(s):  
Lower Bound ◽  
Centrally Symmetric

scholarly journals Norms of weighted sums of log-concave random vectors

2019 ◽  
Vol 22 (04) ◽  
pp. 1950036
Author(s):  
Giorgos Chasapis ◽  
Apostolos Giannopoulos ◽  
Nikos Skarmogiannis
Keyword(s):  
Lower Bound ◽  
Convex Bodies ◽  
Upper Bounds ◽  
Alternative Proof ◽  
Weighted Sums ◽  
Symmetric Convex ◽  
Random Vectors ◽  
Integral Expression ◽  
Centrally Symmetric ◽  
Sharp Lower Bound

Let [Formula: see text] and [Formula: see text] be centrally symmetric convex bodies of volume 1 in [Formula: see text]. We provide upper bounds for the multi-integral expression [Formula: see text] in the case where [Formula: see text] is isotropic. Our approach provides an alternative proof of the sharp lower bound, due to Gluskin and Milman, for this quantity. We also present some applications to “randomized” vector balancing problems.

scholarly journals A Lower Bound Theorem for Centrally Symmetric Simplicial Polytopes

2018 ◽  
Vol 61 (3) ◽  
pp. 541-561 ◽  
Author(s):  
Steven Klee ◽  
Eran Nevo ◽  
Isabella Novik ◽  
Hailun Zheng
Keyword(s):  
Lower Bound ◽  
Simplicial Polytopes ◽  
Centrally Symmetric ◽  
Bound Theorem

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 $K_3$.

On the Crossing Number of $K_{m,n}$

10.37236/1748 ◽  
2003 ◽  
Vol 10 (1) ◽  
Author(s):  
Nagi H. Nahas
Keyword(s):  
Lower Bound ◽  
Bipartite Graph ◽  
Complete Bipartite Graph ◽  
Crossing Number

The best lower bound known on the crossing number of the complete bipartite graph is : $$cr(K_{m,n}) \geq (1/5)(m)(m-1)\lfloor n/2 \rfloor \lfloor(n-1)/2\rfloor$$ In this paper we prove that: $$cr(K_{m,n}) \geq (1/5)m(m-1)\lfloor n/2 \rfloor \lfloor (n-1)/2 \rfloor + 9.9 \times 10^{-6} m^2n^2$$ for sufficiently large $m$ and $n$.

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