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A set S together with a relation >= which is both transitive and reflexive such that for any two elements a,b in S, there exists another element c in S with c>=a and c>=b. In ...

The direction from an object A to another object B can be specified as a vector v=AB^-> with tail at A and head at B. However, since this vector has length equal to the ...

The curve d(u) in the ruled surface parameterization x(u,v)=b(u)+vd(u).

If, in an interval of x, sum_(r=1)^(n)a_r(x) is uniformly bounded with respect to n and x, and {v_r} is a sequence of positive non-increasing quantities tending to zero, then ...

Partial differential equation boundary conditions which give the value of the function on a surface, e.g., T=f(r,t).

Let h be a real-valued harmonic function on a bounded domain Omega, then the Dirichlet energy is defined as int_Omega|del h|^2dx, where del is the gradient.

Discrete group theory is a broad subject covering certain aspects of groups. Such topics as free groups, group presentations, fundamental groups, Kleinian groups, and ...

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 discrete space is simply a topological space equipped with the discrete topology. A discrete space is always a metric space, namely the metric space with the same ...

Two sets A_1 and A_2 are disjoint if their intersection A_1 intersection A_2=emptyset, where emptyset is the empty set. n sets A_1, A_2, ..., A_n are disjoint if A_i ...