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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 chemical equation is the symbolic representation of a chemical reaction in the form of symbols and chemical formulas.The reactant entities are given on the left-hand side and the product entities are on the right-hand side with a plus sign between the entities in both the reactants and the products, and an arrow that points towards the products to show the direction of the reaction. [1]
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 ...
Stoichiometry is not only used to balance chemical equations but also used in conversions, i.e., converting from grams to moles using molar mass as the conversion factor, or from grams to milliliters using density. For example, to find the amount of NaCl (sodium chloride) in 2.00 g, one would do the following:
Consider the average number of particles with particle properties denoted by a particle state vector (x,r) (where x corresponds to particle properties like size, density, etc. also known as internal coordinates and, r corresponds to spatial position or external coordinates) dispersed in a continuous phase defined by a phase vector Y(r,t) (which again is a function of all such vectors which ...
The differential mass balance is usually solved in two steps: first, a set of governing differential equations must be obtained, and then these equations must be solved, either analytically or, for less tractable problems, numerically. The following systems are good examples of the applications of the differential mass balance:
Since the balance sheet is founded on the principles of the accounting equation, this equation can also be said to be responsible for estimating the net worth of an entire company. The fundamental components of the accounting equation include the calculation of both company holdings and company debts; thus, it allows owners to gauge the total ...
A balance puzzle or weighing puzzle is a logic puzzle about balancing items—often coins—to determine which one has different weight than the rest, by using balance scales a limited number of times. The solution to the most common puzzle variants is summarized in the following table: [1]
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