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Examples of path functions include work, heat and arc length. In contrast to path functions, state functions are independent of the path taken. Thermodynamic state variables are point functions, differing from path functions. For a given state, considered as a point, there is a definite value for each state variable and state function.
In the thermodynamics of equilibrium, a state function, function of state, or point function for a thermodynamic system is a mathematical function relating several state variables or state quantities (that describe equilibrium states of a system) that depend only on the current equilibrium thermodynamic state of the system [1] (e.g. gas, liquid, solid, crystal, or emulsion), not the path which ...
However, different paths can trace the same set of points. In mathematics, a path in a topological space is a continuous function from a closed interval into . Paths play an important role in the fields of topology and mathematical analysis. For example, a topological space for which there exists a path connecting any two points is said to be ...
In vector calculus, a conservative vector field is a vector field that is the gradient of some function. [1] A conservative vector field has the property that its line integral is path independent; the choice of path between two points does not change the value of the line integral.
A Hamiltonian cycle around a network of six vertices Examples of Hamiltonian cycles on a square grid graph 8x8. In the mathematical field of graph theory, a Hamiltonian path (or traceable path) is a path in an undirected or directed graph that visits each vertex exactly once.
More simply, an augmenting path is an available flow path from the source to the sink. A network is at maximum flow if and only if there is no augmenting path in the residual network G f. The bottleneck is the minimum residual capacity of all the edges in a given augmenting path. [2] See example explained in the "Example" section of this article.
An -point function may have several different expressions: that they agree is equivalent to crossing symmetry of the four-point function, which has been checked numerically [3] [4] and proved analytically. [5] [6] Liouville theory exists not only on the sphere, but also on any Riemann surface of genus .
In numerical analysis, fixed-point iteration is a method of computing fixed points of a function.. More specifically, given a function defined on the real numbers with real values and given a point in the domain of , the fixed-point iteration is + = (), =,,, … which gives rise to the sequence,,, … of iterated function applications , (), (()), … which is hoped to converge to a point .