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A complex manifold for which the exterior derivative of the fundamental form Omega associated with the given Hermitian metric vanishes, so dOmega=0. In other words, it is a ...

A knot invariant is a function from the set of all knots to any other set such that the function does not change as the knot is changed (up to isotopy). In other words, a ...

A theorem which plays a fundamental role in computer science because it is one of the main tools for showing that certain orderings on trees are well-founded. These orderings ...

Mann's theorem is a theorem widely circulated as the "alpha-beta conjecture" that was subsequently proven by Mann (1942). It states that if A and B are sets of integers each ...

The "mathematical paradigm" is a term that may be applied to the fundamental idea that events in the world can be described by mathematical equations, and that solutions to ...

The fundamental theorem of game theory which states that every finite, zero-sum, two-person game has optimal mixed strategies. It was proved by John von Neumann in 1928. ...

Let a module M in an integral domain D_1 for R(sqrt(D)) be expressed using a two-element basis as M=[xi_1,xi_2], where xi_1 and xi_2 are in D_1. Then the different of the ...

A number which is simultaneously a nonagonal number N_m and hexagonal number Hex_n and therefore satisfies the Diophantine equation 1/2m(7m-5)=n(2n-1). (1) Completing the ...

The ordered pair (s,t), where s is the number of real embeddings of the number field and t is the number of complex-conjugate pairs of embeddings. The degree of the number ...

If G is a weighted tree with weights w_i>1 assigned to each vertex v_i, then G is perfectly weighted if the matrix M_G=[w_1 0 ... 0; 0 w_2 ... 0; | ... ... |; 0 0 ... ...