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The approximation problem is a well known problem of functional analysis (Grothendieck 1955). It asks to determine whether every compact operator T from a Banach space X to a ...

The arithmetic-geometric matrix A_(AG) of a simple graph is a weighted adjacency matrix with weight f(d_i,d_j)=sqrt(d_i^2+d_j^2), (1) where d_i are the vertex degrees of the ...

Letting Lk be the linking number of the two components of a ribbon, Tw be the twist, and Wr be the writhe, then Lk(K)=Tw(K)+Wr(K). (Adams 1994, p. 187).

A polynomial Z_G(q,v) in two variables for abstract graphs. A graph with one graph vertex has Z=q. Adding a graph vertex not attached by any graph edges multiplies the Z by ...

Two figures are said to be similar when all corresponding angles are equal, and are directly similar when all corresponding angles are equal and described in the same ...

Suppose that V is a group representation of G, and W is a group representation of H. Then the vector space tensor product V tensor W is a group representation of the group ...

Given a sequence of independent random variates X_1, X_2, ..., if sigma_k^2=var(X_k) and rho_n^2=max_(k<=n)((sigma_k^2)/(s_n^2)), then lim_(n->infty)rho_n^2=0. This means ...

A ruled surface is called a generalized cylinder if it can be parameterized by x(u,v)=vp+y(u), where p is a fixed point. A generalized cylinder is a regular surface wherever ...

Let 1/p+1/q=1 (1) with p, q>1. Then Hölder's inequality for integrals states that int_a^b|f(x)g(x)|dx<=[int_a^b|f(x)|^pdx]^(1/p)[int_a^b|g(x)|^qdx]^(1/q), (2) with equality ...

A bounded plane convex region symmetric about a lattice point and with area >4 must contain at least three lattice points in the interior. In n dimensions, the theorem can be ...