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If all the eigenvalues of a real matrix A have real parts, then to an arbitrary negative definite quadratic form (x,Wx) with x=x(t) there corresponds a positive definite ...

If a sphere is covered by three closed sets, then one of them must contain a pair of antipodal points.

If f(x) is positive and decreases to 0, then an Euler constant gamma_f=lim_(n->infty)[sum_(k=1)^nf(k)-int_1^nf(x)dx] can be defined. For example, if f(x)=1/x, then ...

The inverse curve of the Maclaurin trisectrix with inversion center at the negative x-intercept is a Tschirnhausen cubic.

Let R(x) be the revenue for a production x, C(x) the cost, and P(x) the profit. Then P(x)=R(x)-C(x), and the marginal profit for the x_0th unit is defined by ...

The Diophantine equation x^2+y^2+z^2=3xyz. The Markov numbers m are the union of the solutions (x,y,z) to this equation and are related to Lagrange numbers.

A sequence X_1, X_2, ... of random variates is called Markov (or Markoff) if, for any n, F(X_n|X_(n-1),X_(n-2),...,X_1)=F(X_n|X_(n-1)), i.e., if the conditional distribution ...

Matrix decomposition refers to the transformation of a given matrix (often assumed to be a square matrix) into a given canonical form.

A matrix each of whose elements is a variate. These variates need not be independent, and if they are not, a correlation is said to exist between them.

The maximal irredundance polynomial R_G(x) for the graph G may be defined as the polynomial R_G(x)=sum_(k=ir(G))^(IR(G))r_kx^k, where ir(G) is the (lower) irredundance ...