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Let lambda be (possibly complex) eigenvalues of a set of random n×n real matrices with entries independent and taken from a standard normal distribution. Then as n->infty, ...

With a large enough sample, any outrageous thing is likely to happen (Diaconis and Mosteller 1989). Littlewood (1986) considered an event which occurs one in a million times ...

The hypersine (n-dimensional sine function) is a function of a vertex angle of an n-dimensional parallelotope or simplex. If the content of the parallelotope is P and the ...

Given a function of the form y=Ax^B, (1) least squares fitting gives the coefficients as b = ...

For every proposition involving logical addition and multiplication ("or" and "and"), there is a corresponding proposition in which the words "addition" and "multiplication" ...

The polar sine is a function of a vertex angle of an n-dimensional parallelotope or simplex. If the content of the parallelotope is P and the lengths of the n edges of the ...

The cosine function cosx is one of the basic functions encountered in trigonometry (the others being the cosecant, cotangent, secant, sine, and tangent). Let theta be an ...

Trigonometry

The sine function sinx is one of the basic functions encountered in trigonometry (the others being the cosecant, cosine, cotangent, secant, and tangent). Let theta be an ...

Specifying two adjacent angles A and B and the side between them c uniquely (up to geometric congruence) determines a triangle with area K=(c^2)/(2(cotA+cotB)). (1) The angle ...