منابع مشابه
The tallest column — optimality revisited
The problem of the optimal design of the tallest unloaded column under selfweight is revisited with a view towards clarifying the optimality of the design proposed by Keller and Niordson (The Tallest Column, J. Math. Mech. 16 (1966), pp. 433–446). The height of the tallest column is related to the rst eigenvalue of a Sturm–Liouville operator. Since the operator associated with the Keller–Niords...
متن کاملThe Shape of the Tallest Column∗
The height at which an unloaded column will buckle under its own weight is the fourth root of the least eigenvalue of a certain Sturm–Liouville operator. We show that the operator associated with the column proposed by Keller and Niordson [J. Math. Mech., 16 (1966), pp. 433– 446] does not possess a discrete spectrum. This calls into question their formal use of perturbation theory, so we consid...
متن کاملThe Shape of the Tallest Column: Corrected
Our summary of the work of Keller and Niordson (J. Math. Mech. 16, pp. 433–446, 1966) was inaccurate. We offer a correction.
متن کاملThe Tallest Column — A Dynamical System Approach Using a Symmetry Solution
A classic problem, the design of the tallest column, is solved again using a different method. By the use of a similarity solution the equations are transformed and the difficult singularity at the endpoint is peeled away. The resulting autonomous system has a critical point and the solution must be on its stable manifold. The solution is found by starting near the critical point in the directi...
متن کاملWeak linkage between the heaviest rainfall and tallest storms
Conventionally, the heaviest rainfall has been linked to the tallest, most intense convective storms. However, the global picture of the linkage between extreme rainfall and convection remains unclear. Here we analyse an 11-year record of spaceborne precipitation radar observations and establish that a relatively small fraction of extreme convective events produces extreme rainfall rates in any...
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ژورنال
عنوان ژورنال: Indiana University Mathematics Journal
سال: 1966
ISSN: 0022-2518
DOI: 10.1512/iumj.1967.16.16029