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The log-likelihood function F(theta) is defined to be the natural logarithm of the likelihood function L(theta). More precisely, F(theta)=lnL(theta), and so in particular, ...

In algebraic geometry classification problems, an algebraic variety (or other appropriate space in other parts of geometry) whose points correspond to the equivalence classes ...

For elliptic curves over the rationals Q, the group of rational points is always finitely generated (i.e., there always exists a finite set of group generators). This theorem ...

Simplemindedly, a number theoretic transform is a generalization of a fast Fourier transform obtained by replacing e^(-2piik/N) with an nth primitive root of unity. This ...

A lattice L is said to be oriented if there exists a rule which assigns a specified direction to any edge connecting arbitrary lattice points x_i,x_j in L. In that way, an ...

A hypersphere S^n is parallelizable if there are n vector fields that are linearly independent at each point. There exist only three parallelizable spheres: S^1, S^3, and S^7 ...

Let f:R×R->R be a one-parameter family of C^3 maps satisfying f(-x,mu)=-f(x,mu) (1) (partialf)/(partialx)|_(mu=0, x=0)=0 (2) (partial^2f)/(partialxpartialmu)|_(mu=0, x=0)>0 ...

The highest order power in a univariate polynomial is known as its order (or, more properly, its polynomial degree). For example, the polynomial ...

The quadratic class number constant is a constant related to the average behavior of class numbers of real quadratic fields. It is given by Q = product_(p)[1-1/(p^2(p+1))] ...

A random closed set (RACS) in R^d is a measurable function from a probability space (Omega,A,P) into (F,Sigma) where F is the collection of all closed subsets of R^d and ...