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Let A be an involutive algebra over the field C of complex numbers with involution xi|->xi^♯. Then A is a left Hilbert algebra if A has an inner product <·,·> satisfying: 1. ...

A Lie group is a group with the structure of a manifold. Therefore, discrete groups do not count. However, the most useful Lie groups are defined as subgroups of some matrix ...

A tesseral harmonic is a spherical harmonic of the form cos; sin(mphi)P_l^m(costheta). These harmonics are so named because the curves on which they vanish are l-m parallels ...

A zonal harmonic is a spherical harmonic of the form P_l(costheta), i.e., one which reduces to a Legendre polynomial (Whittaker and Watson 1990, p. 302). These harmonics are ...

Let P(1/x) be a linear functional acting according to the formula <P(1/x),phi> = Pint(phi(x))/xdx (1) = ...

The numbers of eigenvalues that are positive, negative, or 0 do not change under a congruence transformation. Gradshteyn and Ryzhik (2000) state it as follows: when a ...

Let E be a linear space over a field K. Then the vector space tensor product tensor _(lambda=1)^(k)E is called a tensor space of degree k. More specifically, a tensor space ...

An alkane graph is a tree in which vertices correspond to atoms and edges to carbon-carbon or hydrogen-carbon bonds in a chemical alkane. In chemistry, an alkane is an ...

Let L be a finite-dimensional split semisimple Lie algebra over a field of field characteristic 0, H a splitting Cartan subalgebra, and Lambda a weight of H in a ...

The integer sequence defined by the recurrence P(n)=P(n-2)+P(n-3) (1) with the initial conditions P(0)=3, P(1)=0, P(2)=2. This recurrence relation is the same as that for the ...