Interested to Buy Any Domain ? << Click Here >> for more details...
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.
- 1 Answers
- 2300 Views
- I also Faced
- E-Mail Answers
QUANTUM COMPUTING - ANSWER 32.4 : (a)(i) 1 (mod 2) = 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39. 3 (mod 3) = 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39. 4 (mod 5) = 4, 9, 14, 19, 24, 29, 34, 39. (ii) By observation on X, 3 equations have common values of 9 and 39. First smallest value = 9, second smallest value = 39. (iii) Third smallest value = second smallest value + (second smallest value - first smallest value) = 39 + (39 - 9) = 69. (b)(i) Let Ma = 2, Mb = 3, Mc = 5 where they are prime numbers. Their greatest common divisor is 2 x 3 x 5 = Ma x Mb x Mc (shown). (ii) Md = Mb x Mc = 3 x 5 = 15, Me = Ma x Mc = 2 x 5 = 10, Mf = Ma x Mb = 2 x 3 = 6. (iii) Ma = 2, Mb = 3, Mc = 5, Md = 15, Me = 10, Mf = 6. Md / Ma = 15 / 2 = 7 remain 1, Ya = 1. Me / Mb = 10 / 3 = 3 remain 1, Yb = 1. Mf / Mc = 6 / 5 = 1 remain 1, Yc = 1. (iv) Let Aa = 1, Ab = 3, Ac = 4, Ya = 1, Yb = 1, Yc = 1, Ma = 2, Mb = 3, Mc = 5, Md = 15, Me = 10, Mf = 6. X ≡ (Aa x Ya x Md + Ab x Yb x Me + Ac x Yc x Mf) [ mod (Ma x Mb x Mc) ] = (1 x 1 x 15 + 3 x 1 x 10 + 4 x 1 x 6) [ mod (2 x 3 x 5) ] = 69 mod 30 = 39 mod 30 = 9 mod 30. 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.
| Is This Answer Correct ? | 0 Yes | 0 No |
What are advantages using hollow shaft impeller?
What is the difference between horizontal and vertical heat exchanger?
What is vapour flooding and liquid floodin in distillation?
In gas and water who's density is greater and why?
ENGINEERING MATERIAL - EXAMPLE 12.3 : Let a ^ 2 = a x a and a ^ 3 = a x a x a where ^ is power function. Niobium is a metal with a body-centered cubic structure. The length of the unit cell structure is b = 0.3349 nm. (a) Find the volume for a unit cell structure for niobium. (b) There are 2 atoms per unit cell structure of niobium. The metal has a molar mass of 92.9 g / mol. One mole of the metal consists of 6.02 x 10 ^ 23 atoms. Find the mass of niobium per unit cell and the density of niobium.
Question 63 – Autocad computer program is used to draw a pipe that is used to transport natural gases for processing. Actual length of the pipe is 10 metres. The pipe has cross sectional area of circle in shape with measured circumference of s = 3 metres. (a) If 10 units are used to represent the actual length of the pipe in computerised engineering drawing, find the diameter of the pipe, d that will be shown in the engineering drawing. (b) If one unit in the program equals to 1 centimetre, find the scale used in the computer program.
Is there a quick rule-of-thumb to estimate a gas side heat-transfer rate inside the tubes of a shell and tube heat exchanger?
What are the criteria’s involved in choosing mass balances for components?
what is fund flow definition
What is a good source of information for the design of pressure vessels?
what are the precautions u are taking while starting HT motors?
2 Answers HPCL, MRPL Mangalore Refinery and Petrochemicals Limited,
Explain how does a tank-blanketing valve operate?
-
Civil Engineering (5086) - Mechanical Engineering (4456)
- Electrical Engineering (16639)
- Electronics Communications (3918)
- Chemical Engineering (1095)
- Aeronautical Engineering (239)
- Bio Engineering (96)
- Metallurgy (361)
- Industrial Engineering (259)
- Instrumentation (3014)
- Automobile Engineering (332)
- Mechatronics Engineering (97)
- Marine Engineering (124)
- Power Plant Engineering (172)
- Textile Engineering (575)
- Production Engineering (25)
- Satellite Systems Engineering (106)
- Engineering AllOther (1379)
