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A minimal embedded surface discovered in 1992 consisting of a helicoid with a hole and handle (Science News 1992). It has the same topology as a punctured sphere with a ...

Given two modules M and N over a unit ring R, Hom_R(M,N) denotes the set of all module homomorphisms from M to N. It is an R-module with respect to the addition of maps, ...

There are two possible definitions: 1. Possessing similarity of form, 2. Continuous, one-to-one, in surjection, and having a continuous inverse. The most common meaning is ...

A linear ordinary differential equation of order n is said to be homogeneous if it is of the form a_n(x)y^((n))+a_(n-1)(x)y^((n-1))+...+a_1(x)y^'+a_0(x)y=0, (1) where ...

A univariate distribution proportional to the F-distribution. If the vector d is Gaussian multivariate-distributed with zero mean and unit covariance matrix N_p(0,I) and M is ...

A conic section that is tangent to all sides of a triangle is called an inconic. Any trilinear equation of the form ...

Assume X, Y, and Z are lotteries. Denote "X is preferred to Y" as X≻Y, and indifference between them by X∼Y. One version of the probability axioms are then given by the ...

An initial value problem is a problem that has its conditions specified at some time t=t_0. Usually, the problem is an ordinary differential equation or a partial ...

The intangents circle is the circumcircle of the intangents triangle. It has circle function l=((-a+b+c)f(a,b,c))/(8a^2b^2c^2cosAcosBcosC), (1) where (2) which is not a ...

A differential ideal is an ideal I in the ring of smooth forms on a manifold M. That is, it is closed under addition, scalar multiplication, and wedge product with an ...