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Let mu be a positive measure on a sigma-algebra M, and let lambda be an arbitrary (real or complex) measure on M. If there is a set A in M such that lambda(E)=lambda(A ...

The metric g defined on a nonempty set X by g(x,x) = 0 (1) g(x,y) = 1 (2) if x!=y for all x,y in X. It follows that the open ball of radius r>0 and center at x_0 B(x_0,r)={x ...

A set of curves whose equations are of the same form but which have different values assigned to one or more parameters in the equations. Families of curves arise, for ...

A distribution of values of a discrete variate represented graphically by plotting points (x_1,f_1), (x_2,f_2), ..., (x_k,f_k), and drawing a set of straight line segments ...

The condition for isoenergetic nondegeneracy for a Hamiltonian H=H_0(I)+epsilonH_1(I,theta) is |(partial^2H_0)/(partialI_ipartialI_j) (partialH_0)/(partialI_i); ...

Let X be a topological vector space and for an arbitrary point x in X, denote by N_(x) the collection of all neighborhoods of x in X. A local base at x is any set B subset ...

Possessing more than one mode. A set of values having a single unique mode is said to be unimodal, one with two modes is called bimodal, and one with three modes is called ...

A line along a normal vector (i.e., perpendicular to some tangent line). If K subset R^d is a centrosymmetric set which has a twice differentiable boundary, then there are ...

If mu=(mu_1,mu_2,...,mu_n) is an arbitrary set of positive numbers, then all eigenvalues lambda of the n×n matrix a=a_(ij) lie on the disk |z|<=m_mu, where ...

The set of prime numbers, sometimes denoted P (Derbyshire 2004, p. 163), and implemented in the Wolfram Language as Primes. In the Wolfram Language, a quantity can be tested ...