Erratum for “Lower-Bound Optimal Design of Concrete Structures”

AbstractWe prove that, for any small $\varepsilon > 0$, the number of irrationals among the following odd zeta values: $\zeta (3),\zeta (5),\zeta (7),\ldots ,\zeta (s)$ is at least $( c_0 - \varepsilon )({s^{1/2}}/{(\log s)^{1/2}})$, provided $s$ is a sufficiently large odd integer with respect to $\varepsilon$. The constant $c_0 = 1.192507\ldots$ can be expressed in closed form. Our work improves the lower bound $2^{(1-\varepsilon )({\log s}/{\log \log s})}$ of the previous work of Fischler, Sprang and Zudilin. We follow the same strategy of Fischler, Sprang and Zudilin. The main new ingredient is an asymptotically optimal design for the zeros of the auxiliary rational functions, which relates to the inverse totient problem.

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Automatic Generation of Truss Model for Optimal Design of Reinforced Concrete Structures

ACI Structural Journal ◽

10.14359/10286 ◽

2001 ◽

Vol 98 (4) ◽

Keyword(s):

Reinforced Concrete ◽

Optimal Design ◽

Concrete Structures ◽

Automatic Generation ◽

Reinforced Concrete Structures ◽

Truss Model

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Computational platform for non‐linear analysis/ optimal design of reinforced concrete structures

Engineering Computations ◽

10.1108/eum0000000005785 ◽

2001 ◽

Vol 18 (5/6) ◽

pp. 726-743 ◽

Cited By ~ 10

Author(s):

S.M.R. Tabatabai ◽

K.M. Mosalam

Keyword(s):

Reinforced Concrete ◽

Optimal Design ◽

Concrete Structures ◽

Linear Analysis ◽

Reinforced Concrete Structures ◽

Non Linear ◽

Computational Platform

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Bayesian Input Design for Linear Dynamical Model Discrimination

Entropy ◽

10.3390/e21040351 ◽

2019 ◽

Vol 21 (4) ◽

pp. 351

Author(s):

Piotr Bania

Keyword(s):

Optimal Design ◽

Lower Bound ◽

High Energy ◽

Dynamical Model ◽

Model Discrimination ◽

Energy Limit ◽

Bayesian Design ◽

Input Design ◽

Almost All ◽

Constraint Selection

A Bayesian design of the input signal for linear dynamical model discrimination has been proposed. The discrimination task is formulated as an estimation problem, where the estimated parameter indexes particular models. As the mutual information between the parameter and model output is difficult to calculate, its lower bound has been used as a utility function. The lower bound is then maximized under the signal energy constraint. Selection between two models and the small energy limit are analyzed first. The solution of these tasks is given by the eigenvector of a certain Hermitian matrix. Next, the large energy limit is discussed. It is proved that almost all (in the sense of the Lebesgue measure) high energy signals generate the maximum available information, provided that the impulse responses of the models are different. The first illustrative example shows that the optimal signal can significantly reduce error probability, compared to the commonly-used step or square signals. In the second example, Bayesian design is compared with classical average D-optimal design. It is shown that the Bayesian design is superior to D-optimal design, at least in this example. Some extensions of the method beyond linear and Gaussian models are briefly discussed.

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