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Let X be a set of urelements that contains the set N of natural numbers, and let V(X) be a superstructure whose individuals are in X. Let V(^*X) be an enlargement of V(X), ...
Jackson's theorem is a statement about the error E_n(f) of the best uniform approximation to a real function f(x) on [-1,1] by real polynomials of degree at most n. Let f(x) ...
The partial differential equation 3/4U_y+W_x=0, (1) where W_y+U_t-1/4U_(xxx)+3/2UU_x=0 (2) (Krichever and Novikov 1980; Novikov 1999). Zwillinger (1997, p. 131) and Calogero ...
There are several versions of the Kaplan-Yorke conjecture, with many of the higher dimensional ones remaining unsettled. The original Kaplan-Yorke conjecture (Kaplan and ...
A theorem giving a criterion for an origami construction to be flat. Kawasaki's theorem states that a given crease pattern can be folded to a flat origami iff all the ...
Let G be a planar graph whose vertices have been properly colored and suppose v in V(G) is colored C_1. Define the C_1C_2-Kempe chain containing v to be the maximal connected ...
A knot diagram is a picture of a projection of a knot onto a plane. Usually, only double points are allowed (no more than two points are allowed to be superposed), and the ...
The Kuen surface is a special case of Enneper's negative curvature surfaces which can be given parametrically by x = (2(cosu+usinu)sinv)/(1+u^2sin^2v) (1) = ...
Every nonplanar graph contains either the utility graph K_(3,3) (i.e., the complete bipartite graph on two sets of three vertices) or the pentatope graph K_5 as a ...
The most general form of Lagrange's group theorem, also known as Lagrange's lemma, states that for a group G, a subgroup H of G, and a subgroup K of H, (G:K)=(G:H)(H:K), ...
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