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A drawing of a graph. In mathematics, graph theory is the study of graphs, which are mathematical structures used to model pairwise relations between objects. A graph in this context is made up of vertices (also called nodes or points) which are connected by edges (also called arcs, links or lines).
Thus a prism of 1 Δ would produce 1 cm visible displacement at 100 cm, or 1 meter. This can be represented mathematically as: where is the amount of prism correction in prism dioptres, and is the angle of deviation of the light. For a prism with apex angle and refractive index , .
Esophoria is an eye condition involving inward deviation of the eye, usually due to extra-ocular muscle imbalance. It is a type of heterophoria. Cause. Causes include: Refractive errors; Divergence insufficiency; Convergence excess; this can be due to nerve, muscle, congenital or mechanical anomalies.
Prism graphs are examples of generalized Petersen graphs, with parameters GP ( n ,1). They may also be constructed as the Cartesian product of a cycle graph with a single edge. [1] As with many vertex-transitive graphs, the prism graphs may also be constructed as Cayley graphs. The order- n dihedral group is the group of symmetries of a regular ...
In graph theory, a bridge, isthmus, cut-edge, or cut arc is an edge of a graph whose deletion increases the graph's number of connected components. [1] Equivalently, an edge is a bridge if and only if it is not contained in any cycle. For a connected graph, a bridge can uniquely determine a cut. A graph is said to be bridgeless or isthmus-free ...
The linear map h → J(x) ⋅ h is known as the derivative or the differential of f at x . When m = n, the Jacobian matrix is square, so its determinant is a well-defined function of x, known as the Jacobian determinant of f. It carries important information about the local behavior of f.
Convergence insufficiency. Convergence Insufficiency. Other names. Convergence disorder. Specialty. Ophthalmology, optometry. Convergence insufficiency is a sensory and neuromuscular anomaly of the binocular vision system, characterized by a reduced ability of the eyes to turn towards each other, or sustain convergence .
In graph theory, a dominating set for a graph G is a subset D of its vertices, such that any vertex of G is in D, or has a neighbor in D. The domination number γ (G) is the number of vertices in a smallest dominating set for G . The dominating set problem concerns testing whether γ (G) ≤ K for a given graph G and input K; it is a classical ...
Isomorphism. The group of fifth roots of unity under multiplication is isomorphic to the group of rotations of the regular pentagon under composition. In mathematics, an isomorphism is a structure-preserving mapping between two structures of the same type that can be reversed by an inverse mapping. Two mathematical structures are isomorphic if ...
The function f ( x) = x5 sin (1/ x) for x ≠ 0, and f (0) = 0, gives an example where f ′ ( x) and f″ ( x) are both continuous, f ′ (0) = 0 and f″ (0) = 0, and yet f ( x) does not have a local maximum, a local minimum, nor a point of inflection at 0. So, 0 is a stationary point that is not isolated.