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Let A be a C^*-algebra, then an element u in A is called a partial isometry if uu^*u=u.

1. Zero is a number. 2. If a is a number, the successor of a is a number. 3. zero is not the successor of a number. 4. Two numbers of which the successors are equal are ...

A square matrix A such that the matrix power A^(k+1)=A for k a positive integer is called a periodic matrix. If k is the least such integer, then the matrix is said to have ...

F(x,s) = sum_(m=1)^(infty)(e^(2piimx))/(m^s) (1) = psi_s(e^(2piix)), (2) where psi_s(x) is the polygamma function.

A tensor notation which considers the Riemann tensor R_(lambdamunukappa) as a matrix R_((lambdamu)(nukappa)) with indices lambdamu and nukappa.

"Poincaré transformation" is the name sometimes (e.g., Misner et al. 1973, p. 68) given to what other authors (e.g., Weinberg 1972, p. 26) term an inhomogeneous Lorentz ...

The ordinary differential equation y^('')+k/xy^'+deltae^y=0.

Every bounded operator T acting on a Hilbert space H has a decomposition T=U|T|, where |T|=(T^*T)^(1/2) and U is a partial isometry. This decomposition is called polar ...

The homeomorphic image of a so-called "complete separable" metric space. The continuous image of a Polish space is called a Souslin set.

Let A be a C^*-algebra, then a linear functional f on A is said to be positive if it is a positive map, that is f(a)>=0 for all a in A_+. Every positive linear functional is ...