scholarly journals A Cheeger-type exponential bound for the number of triangulated manifolds

2020 ◽  
Vol 7 (2) ◽  
pp. 233-247
Author(s):  
Karim Adiprasito ◽  
Bruno Benedetti
Keyword(s):  
Exponential Bound

scholarly journals EXPLICIT INTERPOLATION BOUNDS BETWEEN HARDY SPACE AND

2013 ◽  
Vol 95 (2) ◽  
pp. 158-168
Author(s):  
H.-Q. BUI ◽  
R. S. LAUGESEN
Keyword(s):  
Growth Rate ◽  
Linear Operator ◽  
Bounded Linear Operator ◽  
Bounded Mean Oscillation ◽  
Complex Interpolation ◽  
Bounded Linear ◽  
Exponential Bound ◽  
Mean Oscillation ◽  
Good Lambda Inequality ◽  
Interpolation Result

AbstractEvery bounded linear operator that maps ${H}^{1} $ to ${L}^{1} $ and ${L}^{2} $ to ${L}^{2} $ is bounded from ${L}^{p} $ to ${L}^{p} $ for each $p\in (1, 2)$, by a famous interpolation result of Fefferman and Stein. We prove ${L}^{p} $-norm bounds that grow like $O(1/ (p- 1))$ as $p\downarrow 1$. This growth rate is optimal, and improves significantly on the previously known exponential bound $O({2}^{1/ (p- 1)} )$. For $p\in (2, \infty )$, we prove explicit ${L}^{p} $ estimates on each bounded linear operator mapping ${L}^{\infty } $ to bounded mean oscillation ($\mathit{BMO}$) and ${L}^{2} $ to ${L}^{2} $. This $\mathit{BMO}$ interpolation result implies the ${H}^{1} $ result above, by duality. In addition, we obtain stronger results by working with dyadic ${H}^{1} $ and dyadic $\mathit{BMO}$. The proofs proceed by complex interpolation, after we develop an optimal dyadic ‘good lambda’ inequality for the dyadic $\sharp $-maximal operator.

scholarly journals On the exponential bound in four dimensional simplical gravity

1994 ◽  
Vol 335 (3-4) ◽  
pp. 355-358 ◽  
Author(s):  
J. Ambjørn ◽  
J. Jurkiewicz
Keyword(s):  
Exponential Bound

An Upper Bound on the Failure Probability for Linear Structures

1973 ◽  
Vol 40 (1) ◽  
pp. 181-185 ◽  
Author(s):  
L. H. Koopmans ◽  
C. Qualls ◽  
J. T. P. Yao
Keyword(s):  
Stochastic Process ◽  
Failure Probability ◽  
Upper Bound ◽  
Impulse Response Function ◽  
Linear Structures ◽  
Stochastic Response ◽  
Gaussian Stochastic Process ◽  
Exponential Bound ◽  
Mean And Variance ◽  
The Mean

This paper establishes a new upper bound on the failure probability of linear structures excited by an earthquake. From Drenick’s inequality max|y(t)| ≤ MN, where N2 = ∫h2, M2, = ∫x2, x(t) is a nonstationary Gaussian stochastic process representing the excitation of the earthquake, and y(t) is the stochastic response of the structure with impulse response function h(τ), we obtain an exponential bound computable in terms of the mean and variance of the energy M2. A numerical example is given.

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