Question 112 - In quantum computing, let the amplitude A = a | 0 > + b | 1 >, | a | | a | + | b | | b | = 1. Find the values of b if A = 0.8 | 0 > + b | 1 >.
Answer 112 - Let A = a | 0 > + b | 1 > = 0.8 | 0 > + b | 1 >, then a = 0.8. When | a | | a | + | b | | b | = 1, | b | | b | = 1 - | a | | a | = 1 - 0.8 x 0.8 = 1 - 0.64 = 0.36, | b | = 0.6. Finally b = +0.6 or -0.6. The answer is given by Kang Chuen Tat; PO Box 6263, Dandenong, Victoria VIC 3175, Australia; SMS +61405421706; chuentat@hotmail.com; http://kangchuentat.wordpress.com.
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QUANTUM COMPUTING - EXAMPLE 32.3 : A system of linear congruences consists of 3 equations : X ≡ 1 (mod 3), X ≡ 3 (mod 5), X ≡ 4 (mod 6). X has positive values. (a) List the values of these equations from 1 to 35. Then find the minimum value of X. (b)(i) Find the least common multiple (LCM) of b = 3, 5 and 6 where X ≡ a (mod b). (ii) If b - a has the same value of all equations above, then X + (b - a) is divisible by LCM. Find the value of minimum value of X via LCM division.
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COMPUTER PROGRAMMING FOR ENGINEERS - EXAMPLE 17.1 : By using Excel or other easiest programming package, explain how I, the integral of sin x dx from 0 to 3.142 could be approximated using random number. Find the exact value of I.
Question 64 – According to a heuristic of chemical engineering plant design, assume a pressure difference dP = 4 psi for each 10-ft rise in elevation. A pump is needed to pump liquid from a storage tank at a lower elevation to a heating tank at a higher elevation with the elevation difference of 60 ft. (a) Find the pressure loss due to such elevation. (b) If the required minimum inlet pressure to the heating tank is 9 psi, with 1 control valve is installed between pump and heating tank, what is the dP minimum required for the control valve and the entrance to the heating tank when the heuristic mentions that at least 10 psi is required for the control valve? (c) The pressure at the inlet of the pump is 8 psi and the flowrate of the liquid produces pressure head of 50 psi. What is the total pressure produced by the pump? (d) Assume a pipeline dP of 2 psi / 100 ft for liquid flow in a pipe according to heuristic, what is the approximate maximum length of the pipe in ft that can be installed between the pump and the heating tank?
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QUANTUM COMPUTING - EXAMPLE 32.4 : A system of linear congruences consists of 3 equations : X ≡ 1 (mod 2), X ≡ 3 (mod 3), X ≡ 4 (mod 5). X has positive values. (a)(i) List the values of these equations from 1 to approximately 40. (ii) Find the first smallest value and second smallest value of X. (iii) Guess the third smallest value of X. (b) Let X ≡ Aa (mod Ma), X ≡ Ab (mod Mb), X ≡ Ac (mod Mc). According to Chinese remainder theorem, X ≡ (Aa x Ya x Md + Ab x Yb x Me + Ac x Yc x Mf) [ mod (Ma x Mb x Mc) ]. (i) Show that Ma, Mb and Mc have the greatest common divisor of Ma x Mb x Mc. (ii) Find the values of Md, Me and Mf if Md = Mb x Mc, Me = Ma x Mc and Mf = Ma x Mb. (iii) Find the values of Ya, Yb and Yc if Ya = Remainder of (Md / Ma), Yb = Remainder of (Me / Mb) and Yc = Remainder of (Mf / Mc). (iv) Use Chinese remainder theorem to find X.
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FOOD ENGINEERING - QUESTION 23.2 : (a) A dryer reduces the moisture content of 100 kg of a potato product from 80 % to 10 % moisture. Find the mass of the water removed in such drying process. (b) During the drying process, the air is cooled from 80 °C to 71 °C in passing through the dryer. If the latent heat of vaporization corresponding to a saturation temperature of 71 °C is 2331 kJ / kg for water, find the heat energy required to evaporate the water only. (c) Assume potato enters at 24 °C, which is also the ambient air temperature, and leaves at the same temperature as the exit air. The specific heat of potato is 3.43 kJ / (kg °C). Find the minimum heat energy required to raise the temperature of the potatoes. (d) 250 kg of steam at 70 kPa gauge is used to heat 49,800 cubic metre of air to 80 °C, and the air is cooled to 71 °C in passing through the dryer. If the latent heat of steam at 70 kPa gauge is 2283 kJ / kg, find the heat energy in steam. (e) Calculate the efficiency of the dryer based heat input and output, in drying air. Use the formula (Ti - To) / (Ti - Ta) where Ti is the inlet (high) air temperature into the dryer, To is the outlet air temperature from the dryer, and Ta is the ambient air temperature.
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