In mathematics, in the theory of ordinary differential equations in the complex plane C {\displaystyle \mathbb {C} } , the points of C {\displaystyle \mathbb {C} } are classified into ordinary points, at which the equation's coefficients are analytic functions, and singular points, at which some coefficient has a singularity. Then amongst singular points, an important distinction is made between a regular singular point, where the growth of solutions is bounded (in any small...

A pointing stick (nub, nipple, or clitoris) is a small joystick used as a pointing device typically mounted centrally in a computer keyboard. Like other pointing devices such as mice, touchpads or trackballs, operating system software translates manipulation of the device into movements of the pointer or cursor on the monitor. Unlike other pointing devices, it reacts to sustained force or strain rather than to gross movement, so it is called an "isometric" pointing device. IBM introduced it commercially in 1992 on its laptops under the name "TrackPoint", patented in 1997.The pointing stick senses...

In general relativity, the Gibbons–Hawking–York boundary term is a term that needs to be added to the Einstein–Hilbert action when the underlying spacetime manifold has a boundary. The Einstein–Hilbert action is the basis for the most elementary variational principle from which the field equations of general relativity can be defined. However, the use of the Einstein–Hilbert action is appropriate only when the underlying spacetime manifold M {\displaystyle {\mathcal {M}}} is closed, i.e., a manifold which is...

Renormalization is a collection of techniques in quantum field theory, the statistical mechanics of fields, and the theory of self-similar geometric structures, that are used to treat infinities arising in calculated quantities by altering values of these quantities to compensate for effects of their self-interactions. But even if no infinities arose in loop diagrams in quantum field theory, it could be shown that it would be necessary to renormalize the mass and fields appearing in the original Lagrangian.For example, an electron theory may begin by postulating an electron with an initial mass...