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Linear fractional transformations leave cross ratio invariant, so any linear fractional transformation that leaves the unit disk or upper half-planes stable is an isometry of the hyperbolic plane metric space. Since Henri Poincaré explicated these models they have been named after him: the Poincaré disk model and the Poincaré half-plane model.
In mathematical optimization, linear-fractional programming (LFP) is a generalization of linear programming (LP). Whereas the objective function in a linear program is a linear function, the objective function in a linear-fractional program is a ratio of two linear functions. A linear program can be regarded as a special case of a linear ...
In number theory the standard unqualified use of the term continued fraction refers to the special case where all numerators are 1, and is treated in the article continued fraction. The present article treats the case where numerators and denominators are sequences { a i } , { b i } {\displaystyle \{a_{i}\},\{b_{i}\}} of constants or functions.
Pages in category "Fractional graph theory" The following 4 pages are in this category, out of 4 total. This list may not reflect recent changes. F. Fractional coloring;
The fractional matching polytope of a graph G, denoted FMP(G), is the polytope defined by the relaxation of the above linear program, in which each x may be a fraction and not just an integer: Maximize 1 E · x. Subject to: x ≥ 0 E _____ A G · x ≤ 1 V. This is a linear program. It has m "at-least-0" constraints and n "less-than-one ...
In mathematical optimization, fractional programming is a generalization of linear-fractional programming. The objective function in a fractional program is a ratio of two functions that are in general nonlinear. The ratio to be optimized often describes some kind of efficiency of a system.
In mathematics, a Fuchsian group is a discrete subgroup of PSL(2,R).The group PSL(2,R) can be regarded equivalently as a group of orientation-preserving isometries of the hyperbolic plane, or conformal transformations of the unit disc, or conformal transformations of the upper half plane, so a Fuchsian group can be regarded as a group acting on any of these spaces.
Given a graph G = (V, E), a fractional matching in G is a function that assigns, to each edge e in E, a fraction f(e) in [0, 1], such that for every vertex v in V, the sum of fractions of edges adjacent to v is at most 1: [1]: A matching in the traditional sense is a special case of a fractional matching, in which the fraction of every edge is either 0 or 1: f(e) = 1 if e is in the matching ...