S-Shaped Transition Curves as an Element of Reverse Curves in Road Design

Aesthetics Vase Design with Transition Curves

Transition curves with monotone curvature profile are widely applied in fair curve design. Advantage of using transition curve is that it can avoid the undesirable curvature extrema. Demonstration of transition curve in designing surface of revolution, particular of vase design can be often seen in literature. For these demonstrations, authors mainly focused on the curvature control of the vase...

INEXTENSIBLE FLOWS OF CURVES IN LIE GROUPS

In this paper, we study inextensible ows in three dimensional Lie groups with a bi-invariant metric. The necessary and sucient conditions for inextensible curve ow are expressed as a partial dierential equation involving the curvatures. Also, we give some results for special cases of Lie groups.

J-Shaped Curves and Public Health.

Interventions that alter population-level risk exposure haveyieldedanumberof improvements inpublichealth. Tobaccotaxesareanexampleofsuchpopulation-basedapproachestodiseaseprevention. Inthecaseoftobacco,the harmsofshiftingtotalpopulationexposurethroughtaxationareminimal,becausethereisnosafelevelofconsumption. However, other risk factors do not exhibit the same linear relationshipbetweenexposurea...

Decomposition of s ― Concentration Curves

For any given order of stochastic dominance, standard concentration curves are decomposed into contribution curves corresponding to within-group inequalities, between-group inequalities, and transvariational inequalities. We prove, for all orders, that contribution curve dominance implies systematically welfare-improving tax reforms and conversely. Accordingly, we point out some undesirable fis...

Principal Curves : Learning , Design