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  2. Balance equation - Wikipedia

    en.wikipedia.org/wiki/Balance_equation

    These balance equations were first considered by Peter Whittle. [8] [9] The resulting equations are somewhere between detailed balance and global balance equations. Any solution to the local balance equations is always a solution to the global balance equations (we can recover the global balance equations by summing the relevant local balance ...

  3. Detailed balance - Wikipedia

    en.wikipedia.org/wiki/Detailed_balance

    A Markov process is called a reversible Markov process or reversible Markov chain if there exists a positive stationary distribution π that satisfies the detailed balance equations [13] =, where P ij is the Markov transition probability from state i to state j, i.e. P ij = P(X t = j | X t − 1 = i), and π i and π j are the equilibrium probabilities of being in states i and j, respectively ...

  4. Method of dominant balance - Wikipedia

    en.wikipedia.org/wiki/Method_of_dominant_balance

    In mathematics, the method of dominant balance approximates the solution to an equation by solving a simplified form of the equation containing 2 or more of the equation's terms that most influence (dominate) the solution and excluding terms contributing only small modifications to this approximate solution.

  5. Al-Khwarizmi - Wikipedia

    en.wikipedia.org/wiki/Al-Khwarizmi

    It provided an exhaustive account of solving polynomial equations up to the second degree, [51] and discussed the fundamental method of "reduction" and "balancing", referring to the transposition of terms to the other side of an equation, that is, the cancellation of like terms on opposite sides of the equation. [52]

  6. Equation solving - Wikipedia

    en.wikipedia.org/wiki/Equation_solving

    An example of using Newton–Raphson method to solve numerically the equation f(x) = 0. In mathematics, to solve an equation is to find its solutions, which are the values (numbers, functions, sets, etc.) that fulfill the condition stated by the equation, consisting generally of two expressions related by an equals sign.

  7. Al-Jabr - Wikipedia

    en.wikipedia.org/wiki/Al-Jabr

    Al-Jabr (Arabic: الجبر), also known as The Compendious Book on Calculation by Completion and Balancing (Arabic: الكتاب المختصر في حساب الجبر والمقابلة, al-Kitāb al-Mukhtaṣar fī Ḥisāb al-Jabr wal-Muqābalah; [b] or Latin: Liber Algebræ et Almucabola), is an Arabic mathematical treatise on algebra written in Baghdad around 820 by the Persian polymath ...

  8. Element–reactant–product table - Wikipedia

    en.wikipedia.org/wiki/Element–reactant...

    An element–reaction–product table is used to find coefficients while balancing an equation representing a chemical reaction. Coefficients represent moles of a substance so that the number of atoms produced is equal to the number of atoms being reacted with. [1] This is the common setup: Element: all the elements that are in the reaction ...

  9. Hardy Cross method - Wikipedia

    en.wikipedia.org/wiki/Hardy_Cross_method

    We solve the network by method of balancing heads, following the steps outlined in method process above. 1. The initial guesses are set up so that continuity of flow is maintained at each junction in the network. 2. The loops of the system are identified as loop 1-2-3 and loop 2-3-4. 3. The head losses in each pipe are determined.

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