Operator Norm and Lower Bound of Four-Dimensional Generalized Hausdorff Matrices

2021 ◽  
Author(s):  
Gholamreza Talebi
Keyword(s):  
Lower Bound ◽  
Operator Norm ◽  
Hausdorff Matrices

scholarly journals Operator norm and lower bound of four-dimensional matrices

2017 ◽  
Vol 28 (6) ◽  
pp. 1134-1143 ◽  
Author(s):  
Gholamreza Talebi
Keyword(s):  
Lower Bound ◽  
Operator Norm

The Fröhlich Hamiltonian: mathematical results. I. Hamiltonian with cut-off

1976 ◽  
Vol 54 (15) ◽  
pp. 1613-1620 ◽  
Author(s):  
Bernard M. de Dormale ◽  
Georges Bader
Keyword(s):  
Lower Bound ◽  
Coulomb Interaction ◽  
Fock Space ◽  
Perturbation Series ◽  
Operator Norm

We study the Fröhlich Hamiltonian with cut-off. We show that this Hamiltonian is self-adjoint in the Fock space and semibounded when the number of electrons is kept constant. The lower bound we give generalizes the bound obtained for one electron by Lee and Pines to the case of several electrons. We also give a domain where the perturbation series for the resolvent of the Hamiltonian does converge in the operator norm. Finally, we study the influence of the Coulomb interaction.

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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