Write down a PDE and final time/boundary conditions for the value of a butterfly spread, as described in Exercise 1.3. Exercise 1.3. ⋆⋆ Suppose that for the same asset and expiry date, you hold a European call option with exercise price E1 and another with exercise price E3, where E3 > E1 and also write two calls with exercise price E2 := (E1 + E3)/2. This is an example of a butterfly spread.

Apump is used to circulate hot water in a home heating system. water enters the well-insulated pump operating at steady state at a rate of 0.42 gal/min. the inlet pressure and temperature are 14.7 lbf/in.2, and 180°f, respectively; at the exit the pressure is 60 lbf/in.2 the pump requires 1/15 hp of power input. water can be modeled as an incompressible substance with constant density of 60.58 lb/ft3 and constant specific heat of 1 btu/lb or. neglecting kinetic and potential energy effects, determine the temperature change, in °r, as the water flows through the pump.

Afull journal bearing has a journal diameter of 27 mm, with a unilateral tolerance of -0.028 mm. the bushing bore has a diameter of 27.028 mm and a unilateral tolerance of 0.04 mm. the l/d ratio is 0.5. the load is 1.3 kn and the journal runs at 1200 rev/min. if the average viscosity is 50 mpa-s, find the minimum film thickness, the power loss, and the side flow for the minimum clearance assembly.

Agas mixture consists of 8 kmol of h2 and 2 kmol of n2. determine the mass of each gas and the apparent gas constant of the mixture.