Suppose that s(t) is a real-valued signal. We have a set of orthonormal basis functions {ϕi(t)}N i=1 with which we wish to approximate s(t) as s ˆ(t) = N∑ i =1 siϕi(t) such that the energy in the error signal e(t) = s(t) − s ˆ(t) E e = ∫−[infinity] [infinity] e2(t)dt = ∫−[infinity] [infinity] (s(t) − s ˆ(t))2dt is minimized. Calculate the optimum coefficients {si}N i=1 that minimize Ee.

Amass of m 1.5 kg of steam is contained in a closed rigid container. initially the pressure and temperature of the steam are: p 1.5 mpa and t 240°c (superheated state), respectively. then the temperature drops to t2= 100°c as the result of heat transfer to the surroundings. determine: a) quality of the steam at the end of the process, b) heat transfer with the surroundings. for: p1.5 mpa and t 240°c: enthalpy of superheated vapour is 2900 kj/kg, specific volume of superheated vapour is 0. 1483 m/kg, while for t 100°c: enthalpy of saturated liquid water is 419kj/kg, specific volume of saturated liquid water is 0.001043m/kg, enthalpy of saturated vapour is 2676 kj/kg, specific volume of saturated vapour is 1.672 m/kg and pressure is 0.1 mpa.

A-mn has a cubic structure with a0 0.8931 nm and a density of 7.47 g/cm3. b-mn has a different cubic structure, with a0 0.6326 nm and a density of 7.26 g/cm3. the atomic weight of manganese is 54.938 g/mol and the atomic radius is 0.112 nm. determine the percent volume change that would occur if a-mn transforms to b-mn.

What is creep? what is stress relaxation?