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A concordance between knots K_0 and K_1 in S^3 is a locally flat cylinder C=S^1×[0,1] embedded in S^3×[0,1] in such a way that the ends S^1×{1} are embedded in S^3×{i} as ...

A partition p is said to contain another partition q if the Ferrers diagram of p contains the Ferrers diagram of q. For example, {3,3,2} (left figure) contains both {3,3,1} ...

A continuous map is a continuous function between two topological spaces. In some fields of mathematics, the term "function" is reserved for functions which are into the real ...

A functor F is called contravariant if it reverses the directions of arrows, i.e., every arrow f:A-->B is mapped to an arrow F(f):F(B)-->F(A).

A set X is a called a "convex cone" if for any x,y in X and any scalars a>=0 and b>=0, ax+by in X.

The first corona of a tile is the set of all tiles that have a common boundary point with that tile (including the original tile itself). The second corona is the set of ...

A requirement necessary for a given statement or theorem to hold. Also called a condition.

The 6-polyiamond illustrated above.

The system of partial differential equations iu_t+u_(xx)+alphau_(yy)+betau|u|^2-uv=0 v_(xx)+gammav_(yy)+delta(|u|^2)_(yy)=0.

The depth of a box is the horizontal distance from front to back (usually not necessarily defined to be smaller than the width, the horizontal distance from side to side).