Wyniki wyszukiwania - BazTech

Ograniczanie wyników

Znaleziono wyników: 2

Liczba wyników na stronie

Wyniki wyszukiwania

Wyszukiwano:
w słowach kluczowych: lower and upper bounds

Sortuj według:

Ogranicz wyniki do:

The saint-venant torsion of a cartesian orthotropic bar with an isosceles right-angled triangle cross-section

Ecsedi István, Baksa Attila

Engineering Transactions

2024

Vol. 72, iss. 1

81--94

The Saint-Venant torsion of the Cartesian orthotropic homogeneous linearly elastic bar is considered. The cross-section of the prismatic bar is an isosceles right-angled triangular plane domain. An approximate analytical method is presented to obtain Prandtl’s stress function, shearing stresses, and torsional rigidity. Upper and lower bounds for the torsional rigidity are provided. The obtained results for shearing stresses are verified through FEM computation.

Inequalities for quantiles of the chi-square distribution

Inglot T.

Probability and Mathematical Statistics

2010

Vol. 30, Fasc. 2

339--351

We obtain a new sharp lower estimate for tails of the central chi-square distribution. Using it we prove quite accurate lower bounds for the chi-square quantiles covering the case of increasing number of degrees of freedom and simultaneously tending to zero tail probabilities. In the case of small tail probabilities we also provide upper bounds for these quantiles which are close enough to the lower ones. As a byproduct we propose a simple approximation formula which is easy to calculate for the chi-square quantiles. It is expressed explicitly in terms of tail probabilities and a number of degrees of freedom.