uniqueness theorem in a sentence

Examples

1. Using a uniqueness theorem and showing that a potential satisfies Laplace's equation ( second derivative of " V " should be zero i . e . in free space ) and the potential has the correct values at the boundaries, the potential is then uniquely defined.
2. The validity of the method of image charges rests upon a corollary of the uniqueness theorem, which states that the electric potential in a volume " V " is uniquely determined if both the charge density throughout the region and the value of V on all boundaries are specified.
3. A converse to this theorem is given by Alexandrov's uniqueness theorem, according to which a metric space that is locally Euclidean except for a finite number of points of positive angular defect, adding to 4?, can be realized in a unique way as the surface of a convex polyhedron.
4. Another reason follows from what are called black-hole uniqueness theorems : over time, black holes retain only a minimal set of distinguishing features ( these theorems have become known as " no-hair " theorems, since different hairstyles are a crucial part of what gives different people their different appearances ).
5. With W . Dai, C . He and D . Kong, Liu introduced dissipative hyperbolic geometric flow and Hyperbolic mean curvature flow, established the short-time existence and uniqueness theorem for them, and discuss the relation between the equations for hyperbolic mean curvature flow and the equations for extremal surfaces in the Minkowski spacetime.
6. Important applications of phase retrieval include X-ray crystallography, transmission electron microscopy and coherent diffractive imaging, for which M = 2 . ( Fienup 1982 : 2759 ) Uniqueness theorems for both 1-D and 2-D cases of the phase retrieval problem, including the phaseless 1-D inverse scattering problem, were proved by Klibanov and his collaborators ( see References ).
7. At rhumb line and Great-circle distance, we see a sentence like : " A great circle arc is, together with the rhumb line and the isoazimuthal, one of the three lines that can be drawn between any two points on the earth's surface . " The language is vague but suggests some uniqueness theorem-that these three types of arcs are unique with respect to some properties.