Search Results for ""

A 4-sphere has positive curvature, with R^2=x^2+y^2+z^2+w^2 (1) 2x(dx)/(dw)+2y(dy)/(dw)+2z(dz)/(dw)+2w=0. (2) Since r=xx^^+yy^^+zz^^ (3) dw = -(xdx+ydy+zdz)/w (4) = ...

(Deltau)_i^2=(u_i-u^_)^2, where u^_ is the average of {u_i}.

A module over a ring that is contained in and has the same addition as another module over the same ring.

Any sum of a selection of Pi_ks, where Pi_k denotes a k-D polytope.

A regular continued fraction is a simple continued fraction x = b_0+1/(b_1+1/(b_2+1/(b_3+...))) (1) = K_(k=1)^(infty)1/(b_k) (2) = [b_0;b_1,b_2,...], (3) where b_0 is an ...

The finite difference is the discrete analog of the derivative. The finite forward difference of a function f_p is defined as Deltaf_p=f_(p+1)-f_p, (1) and the finite ...

The term "continued fraction" is used to refer to a class of expressions of which generalized continued fraction of the form b_0+(a_1)/(b_1+(a_2)/(b_2+(a_3)/(b_3+...))) ...

Let (a)_i and (b)_i be sequences of complex numbers such that b_j!=b_k for j!=k, and let the lower triangular matrices F=(f)_(nk) and G=(g)_(nk) be defined as ...

A method for verifying the correctness of an arithmetical operation on natural numbers, based on the same principle as casting out nines. The methods of sevens takes ...

An element admitting a multiplicative or additive inverse. In most cases, the choice between these two options is clear from the context, as, for example, in a monoid, where ...