The Nonlinear Bending of Thin Rods

1959 ◽  
Vol 26 (1) ◽  
pp. 40-43 ◽  
Author(s):  
T. P. Mitchell
Keyword(s):  
Closed Form ◽  
Normal Load ◽  
Unified Approach ◽  
Nonlinear Bending ◽  
Circular Arc ◽  
Closed Form Solutions

Abstract The nonlinear bending of straight and circular-arc cantilevers under vertical and horizontal point loads is analyzed from a unified approach. Formulas for determining the deflected shape of the cantilevers are presented. Closed-form solutions are obtained for bending under two types of distributed loads. In particular, the problem of bending under a uniformly distributed normal load is solved.

IT'S YOUR CHOICE: A UNIFIED APPROACH TO CHOOSER OPTIONS

2010 ◽  
Vol 13 (01) ◽  
pp. 139-161 ◽  
Author(s):  
KLAUS SANDMANN ◽  
MANUEL WITTKE
Keyword(s):  
Interest Rates ◽  
Closed Form ◽  
International Economy ◽  
Multidimensional Model ◽  
Unified Approach ◽  
Unified Framework ◽  
Stochastic Interest Rates ◽  
Closed Form Solutions ◽  
Inflation Rates ◽  
Stochastic Interest

We propose a unified framework for the pricing and hedging of chooser options on lognormal assets. This includes e.g. exchange or inflation rates under stochastic interest rates or equities under stochastic interest rates and dividend yields. This extends and includes chooser options under deterministic interest rates by a multidimensional model of an international economy with correlated stochastic processes. In this framework we derive closed form solutions of the arbitrage price for different specifications of chooser options. Also different hedge strategies are derived and their properties compared.

Closed Form Solutions of Joint Water-Filling for Coordinated Transmission

2010 ◽  
Vol E93-B (12) ◽  
pp. 3461-3468 ◽  
Author(s):  
Bing LUO ◽  
Qimei CUI ◽  
Hui WANG ◽  
Xiaofeng TAO ◽  
Ping ZHANG
Keyword(s):  
Closed Form ◽  
Closed Form Solutions ◽  
Water Filling
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