Search Results for ""

A set in R^n which can be reduced to one of its points, say P, by a continuous deformation, is said to be contractible. The transformation is such that each point of the set ...

A second-order ordinary differential equation arising in the study of stellar interiors, also called the polytropic differential equations. It is given by ...

Two planes always intersect in a line as long as they are not parallel. Let the planes be specified in Hessian normal form, then the line of intersection must be ...

The fraction of odd values of the partition function P(n) is roughly 50%, independent of n, whereas odd values of Q(n) occur with ever decreasing frequency as n becomes ...

An inner product is a generalization of the dot product. In a vector space, it is a way to multiply vectors together, with the result of this multiplication being a scalar. ...

Let X_1,X_2,...,X_N be a set of N independent random variates and each X_i have an arbitrary probability distribution P(x_1,...,x_N) with mean mu_i and a finite variance ...

The hypothesis that an integer n is prime iff it satisfies the condition that 2^n-2 is divisible by n. Dickson (2005, p. 91) stated that Leibniz believe to have proved that ...

A circle that in internally tangent to two sides of a triangle and to the circumcircle is called a mixtilinear incircle. There are three mixtilinear incircles, one ...

An Ore graph is a graph that satisfies Ore's theorem, i.e., a graph G for which the sums of the degrees of nonadjacent vertices is greater than or equal to the number of ...

The necessary condition for the polychoron to be regular (with Schläfli symbol {p,q,r}) and finite is cos(pi/q)<sin(pi/p)sin(pi/r). Sufficiency can be established by ...