Lower bound of extremal Pompeiu radius for half of cone

Researches in Mathematics ◽

10.15421/240910 ◽

2021 ◽

Vol 17 ◽

pp. 73

Author(s):

L.V. Elets

Keyword(s):

Lower Bound ◽

Circular Cone

Lower estimates are established for the smallest radius of a ball, in which a given set is the Pompeiu set. As the set, the half of the straight circular cone with radius of base 1 and attitude $h > 1$ is considered. For $h > 3$ the exact value of extreme Pompeiu radius is obtained.

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New results and applications for the Ideal Extended Kalman Filter asa Cramer-Rao lower bound estimator

10.2514/6.1992-4596 ◽

1992 ◽

Cited By ~ 2

Author(s):

MARTIN MOORMAN ◽

THOMAS BULLOCK

Keyword(s):

Kalman Filter ◽

Lower Bound ◽

Extended Kalman Filter ◽

Cramer Rao Lower Bound ◽

The Ideal

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Lower bound for the lifespan of solutions to the generalized KdV equation with low-degree of nonlinearity

The Role of Metrics in the Theory of Partial Differential Equations ◽

10.2969/aspm/08510303 ◽

2020 ◽

Author(s):

Hayato Miyazaki

Keyword(s):

Lower Bound ◽

Kdv Equation ◽

Generalized Kdv Equation ◽

Low Degree

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

Доклады Академии наук ◽

10.31857/s0869-56524852142-144 ◽

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.

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A Lower Bound for Schur Numbers and Multicolor Ramsey Numbers

The Electronic Journal of Combinatorics ◽

10.37236/1188 ◽

1994 ◽

Vol 1 (1) ◽

Cited By ~ 8

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

The Electronic Journal of Combinatorics ◽

10.37236/1748 ◽

2003 ◽

Vol 10 (1) ◽

Cited By ~ 4

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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