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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Question 110 - When an algebraic product is defined on the space, the Lie bracket is the commutator [x,y] = xy - yx according to Lie algebra in mathematics. If [p,x] f(x) = px f(x) - xp f(x), p = -ih d / dx, find the value of [p,x] in term of i and h.

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Are there any methods of preventing cracking of carbon steel welds in refining environments?

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what are the major problem comes in the production process

2 Answers   Atul, Deepak Fertilisers,

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EXAMPLE 34.14 : For a formula of y = [ 1 - 1 / (1 + r) ^ n ] / r, let y = present value, r = interest rate / year, n = number of years to future value of 1 : (a) Find a simple mathematical relationship of y as a function of r when n = 1 million years. (b) What is the present value of $10000, if the annual discount rate is 10 %, forever?

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what is mean by refinery

3 Answers   Reliance,

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We are having proplem with the persperation smell in ETT/ECHO room in our cardiac hospital.The 2 Ton of AC is not conditioning the environment. We have to use exhaust fan to through out of the room bad air. Could anyone suggest how to coup with this effectively using chemical engineering. Any permanent solution to neutralise the bad smell.The Air freshners are not doing enough instead making a bad odour.

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what is the height between the reflux pump and condenser ?

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Why should a magnesium ribbon be cleaned before burning in air?

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what are the chemicals used in PFR and MFR to Process?

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Explain can large temperature differences in vaporizers cause operational problems?

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viscosty of crude use for petroliun?

4 Answers   ONGC,

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