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A field which is complete with respect to a discrete valuation is called a local field if its field of residue classes is finite. The Hasse principle is one of the chief ...

Call a graph vertex m(a,b,c) a median of a graph G if it lies on all shortest paths between each pair of vertices (a,b), (b,a), and (c,a) in G. A median graph is then defined ...

An optical illusion in which the orientation of arrowheads makes one line segment look longer than another. In the above figure, the line segments on the left and right are ...

A parallelogram polyomino is a polyomino such that the intersection with every line perpendicular to the main diagonal is a connected segment. The number of parallelogram ...

The theory of non-uniformly hyperbolic diffeomorphisms.

Let f:R×R->R be a one-parameter family of C^3 maps satisfying f(-x,mu)=-f(x,mu) (1) (partialf)/(partialx)|_(mu=0, x=0)=0 (2) (partial^2f)/(partialxpartialmu)|_(mu=0, x=0)>0 ...

A property that is always fulfilled by the product of topological spaces, if it is fulfilled by each single factor. Examples of productive properties are connectedness, and ...

Any ideal of a ring which is strictly smaller than the whole ring. For example, 2Z is a proper ideal of the ring of integers Z, since 1 not in 2Z. The ideal <X> of the ...

The Prosthaphaeresis formulas, also known as Simpson's formulas, are trigonometry formulas that convert a product of functions into a sum or difference. They are given by ...

The nth Ramanujan prime is the smallest number R_n such that pi(x)-pi(x/2)>=n for all x>=R_n, where pi(x) is the prime counting function. In other words, there are at least n ...