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Two points z and z^S in C^* are symmetric with respect to a circle or straight line L if all circles and straight lines passing through z and z^S are orthogonal to L. Möbius ...

Given any two distinct points x,y, there exist neighborhoods u and v of x and y, respectively, with u intersection v=emptyset. It then follows that finite subsets are closed.

The third Brocard triangle is Gibert's term for the isogonal conjugate of the first Brocard triangle. It has trilinear vertex matrix [b^2c^2 ab^3 ac^3; a^3b a^2c^2 bc^3; a^3c ...

An extension field of a field F that is not algebraic over F, i.e., an extension field that has at least one element that is transcendental over F. For example, the field of ...

The vertex triangle of two distinct circumcevian triangles or circumanticevian triangles is perspective to the reference triangle. In addition, the vertex triangles of the ...

The system of partial differential equations (partial_t+partial_z^3+partial_(z^_)^3)v+partial_z(uv)+partial_(z^_)(vw) (1) partial_(z^_)u=3partial_zv (2) ...

A horizontal line placed above multiple quantities to indicate that they form a unit. It is most commonly used to denote 1. A radical (sqrt(12345)), 2. Repeating decimals ...

The Banach space L^1([0,1]) with the product (fg)(x)=int_0^xf(x-y)g(y)dy is a non-unital commutative Banach algebra. This algebra is called the Volterra algebra.

Recall the definition of the autocorrelation function C(t) of a function E(t), C(t)=int_(-infty)^inftyE^_(tau)E(t+tau)dtau. (1) Also recall that the Fourier transform of E(t) ...

The Woodbury formula (A+UV^(T))^(-1)=A^(-1)-[A^(-1)U(I+V^(T)A^(-1)U)^(-1)V^(T)A^(-1)] is a formula that allows a perturbed matrix to be computed for a change to a given ...