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A G-space provides local notions of harmonic, hyperharmonic, and superharmonic functions. When there exists a nonconstant superharmonic function greater than 0, it is a ...

A method for predicting the onset of widespread chaos. It is based on the hypothesis that the dissolution of an invariant torus can be associated with the sudden change from ...

When a point P moves along a line through the circumcenter of a given triangle Delta, the pedal circle of P with respect to Delta passes through a fixed point (the Griffiths ...

Grimm conjectured that if n+1, n+2, ..., n+k are all composite numbers, then there are distinct primes p_(i_j) such that p_(i_j)|(n+j) for 1<=j<=k.

A formula satisfied by all Hamiltonian cycles with n nodes. Let f_j be the number of regions inside the circuit with j sides, and let g_j be the number of regions outside the ...

An approach for the calculation of a Gröbner basis into several smaller computations following a path in the Gröbner fan of the ideal generated by the system of inequalities.

A honeycomb-like packing that forms hexagons.

Given n circles and a perimeter p, the total area of the convex hull is A_(Convex Hull)=2sqrt(3)(n-1)+p(1-1/2sqrt(3))+pi(sqrt(3)-1). Furthermore, the actual area equals this ...

A dozen dozen, or the square number 144.

Consider a clause (disjunction of literals) obtained from those of a first-order logic formula Phi in Skolemized form forall x_1... forall x_nS. Then an atomic statement ...