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The components of the gradient of the one-form dA are denoted A_(,k), or sometimes partial_kA, and are given by A_(,k)=(partialA)/(partialx^k) (Misner et al. 1973, p. 62). ...

A complex magnification is a map of the form z|->az, where a is a positive real number, which corresponds to magnification about the origin of points in the complex plane by ...

A reciprocity theorem for the case n=3 solved by Gauss using "integers" of the form a+brho, when rho is a root of x^2+x+1=0 (i.e., rho equals -(-1)^(1/3) or (-1)^(2/3)) and ...

An equation of the form y=ax^3+bx^2+cx+d, (1) where the three roots are real and distinct, i.e., y = a(x-r_1)(x-r_2)(x-r_3) (2) = ...

A degree set is a set of integers that make up a degree sequence. Any set of positive integers is the degree set for some graph, because any odd integer from that set can be ...

Informally, a situation in which a decision must be made from several alternatives, none of which is obviously the optimal one. In formal logic, a dilemma is a specific type ...

Given any real number theta and any positive integer N, there exist integers h and k with 0<k<=N such that |ktheta-h|<1/N. A slightly weaker form of the theorem states that ...

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 ...

Let D be a planar Abelian difference set and t be any divisor of n. Then t is a numerical multiplier of D, where a multiplier is defined as an automorphism alpha of a group G ...

Let A be a sum of squares of n independent normal standardized variates X_i, and suppose A=B+C where B is a quadratic form in the x_i, distributed as chi-squared with h ...