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Let X={x_1>=x_2>=...>=x_n|x_i in R} (1) and Y={y_1>=y_2>=...>=y_n|y_i in R}. (2) Then there exists an n×n Hermitian matrix with eigenvalues X and diagonal elements Y iff ...

Let {f_n(x)} be a sequence of analytic functions regular in a region G, and let this sequence be uniformly convergent in every closed subset of G. If the analytic function ...

A theorem in the theory of univalent conformal mappings of families of domains on a Riemann surface, containing an inequality for the coefficients of the mapping functions, ...

The so-called Malthusian equation is an antiquated term for the equation N(t)=N_0e^(lambdat) describing exponential growth. The constant lambda is sometimes called the ...

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 ...

For triangles in the plane, AD·BE·CF=BD·CE·AF. (1) For spherical triangles, sinAD·sinBE·sinCF=sinBD·sinCE·sinAF. (2) This can be generalized to n-gons P=[V_1,...,V_n], where ...

A statement about theorems. It usually gives a criterion for getting a new theorem from an old one, either by changing its objects according to a rule (duality principle), or ...

The conjecture due to Pollock (1850) that every number is the sum of at most five tetrahedral numbers (Dickson 2005, p. 23; incorrectly described as "pyramidal numbers" and ...

The term "porism" is an archaic type of mathematical proposition whose historical purpose is not entirely known. It is used instead of "theorem" by some authors for a small ...

Quinn et al. (2007) investigated a class of N coupled oscillators whose bifurcation phase offset had a conjectured asymptotic behavior of sinphi∼1-c_1/N, with an experimental ...