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Gas networks simulation or gas pipeline simulation is a process of defining the mathematical model of gas transmission and gas distribution systems, which are usually composed of highly integrated pipe networks operating over a wide range of pressures. Simulation allows to predict the behaviour of gas network systems under different conditions ...
In mathematics, a linear equation is an equation that may be put in the form + … + + =, where , …, are the variables (or unknowns), and ,, …, are the coefficients, which are often real numbers. The coefficients may be considered as parameters of the equation and may be arbitrary expressions , provided they do not contain any of the variables.
In three-dimensional Euclidean space, these three planes represent solutions to linear equations, and their intersection represents the set of common solutions: in this case, a unique point. The blue line is the common solution to two of these equations. Linear algebra is the branch of mathematics concerning linear equations such as:
In linear systems, indeterminacy occurs if and only if the number of independent equations (the rank of the augmented matrix of the system) is less than the number of unknowns and is the same as the rank of the coefficient matrix. For if there are at least as many independent equations as unknowns, that will eliminate any stretches of overlap ...
This is an outline of topics related to linear algebra, the branch of mathematics concerning linear equations and linear maps and their representations in vector spaces and through matrices. Linear equations
For example, an area of excess metal may be left because it is needed to complete subsequent machining. Common cases are listed below. An allowance, which is a planned deviation from an ideal, is contrasted with a tolerance , which accounts for expected but unplanned deviations.
These equations describe boundary-value problems, in which the solution-function's values are specified on boundary of a domain; the problem is to compute a solution also on its interior. Relaxation methods are used to solve the linear equations resulting from a discretization of the differential equation, for example by finite differences. [2 ...
The scenario approach or scenario optimization approach is a technique for obtaining solutions to robust optimization and chance-constrained optimization problems based on a sample of the constraints. It also relates to inductive reasoning in modeling and decision-making.