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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.
Often, constructing local balance equations is equivalent to removing the outer summations in the global balance equations for certain terms. [ 1 ] During the 1980s it was thought local balance was a requirement for a product-form equilibrium distribution , [ 10 ] [ 11 ] but Gelenbe 's G-network model showed this not to be the case.
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 ...
Chemical equation balancing. Add languages. ... Print/export Download as PDF; Printable version; In other projects Appearance. move to sidebar hide. From Wikipedia ...
The basic equations in classical continuum mechanics are all balance equations, and as such each of them contains a time-derivative term which calculates how much the dependent variable change with time. For an isolated, frictionless / inviscid system the first four equations are the familiar conservation equations in classical mechanics.
Note finally that this last equation can be derived by solving the three-dimensional Navier–Stokes equations for the equilibrium situation where = = = = Then the only non-trivial equation is the -equation, which now reads + = Thus, hydrostatic balance can be regarded as a particularly simple equilibrium solution of the Navier–Stokes equations.