Search Results for ""

Let |sum_(n=1)^pa_n|<K, (1) where K is independent of p. Then if f_n>=f_(n+1)>0 and lim_(n->infty)f_n=0, (2) it follows that sum_(n=1)^inftya_nf_n (3) converges.

The metric properties discovered for a primitive figure remain applicable, without modifications other than changes of signs, to all correlative figures which can be ...

A collection of equations satisfies the Hasse principle if, whenever one of the equations has solutions in R and all the Q_p, then the equations have solutions in the ...

Symmetric points are preserved under a Möbius transformation. The Schwarz reflection principle is sometimes called the symmetry principle (Needham 2000, p. 252).

There are at least two results known as "the area principle." The geometric area principle states that (|A_1P|)/(|A_2P|)=(|A_1BC|)/(|A_2BC|). (1) This can also be written in ...

Let u_1<=u_2<=... be harmonic functions on a connected open set U subset= C. Then either u_j->infty uniformly on compact sets or there is a finite-values harmonic function u ...

Let F be a differential field with constant field K. For f in F, suppose that the equation g^'=f (i.e., g=intf) has a solution g in G, where G is an elementary extension of F ...

In nonstandard analysis, the transfer principle is the technical form of the following intuitive idea: "Anything provable about a given superstructure V by passing to a ...

Every nonempty set of positive integers contains a smallest member.

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 ...