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Two closed simply connected 4-manifolds are homeomorphic iff they have the same bilinear form beta and the same Kirby-Siebenmann invariant kappa. Any beta can be realized by ...

A congruence of the form f(x)=g(x) (mod n), where f(x) and g(x) are both integer polynomials. Functional congruences are sometimes also called "identical congruences" (Nagell ...

Two unit-speed plane curves which have the same curvature differ only by a Euclidean motion.

On a Riemannian manifold, there is a unique connection which is torsion-free and compatible with the metric. This connection is called the Levi-Civita connection.

Gives a lower bound for the inner product (Lu,u), where L is a linear elliptic real differential operator of order m, and u has compact support.

If x_1<x_2<...<x_n denote the zeros of p_n(x), there exist real numbers lambda_1,lambda_2,...,lambda_n such that ...

The zeros of the derivative P^'(z) of a polynomial P(z) that are not multiple zeros of P(z) are the positions of equilibrium in the field of force due to unit particles ...

The Gelfand-Naimark theorem states that each C^*-algebra is isometrically *-isomorphic to a closed *-subalgebra of the algebra B(H) consisting of all bounded operators acting ...

A cylindrical algebraic decomposition that omits sets of measure zero. Generic cylindrical algebraic decompositions are generally much quicker to compute than are normal ...

A perspective collineation in which the center and axis are not incident. The term was first used by Poncelet (Cremona 1960, p. ix).