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Let A and B be C^*-algebras, then a linear map phi:A->B is said to be positive if phi(A_+) subset= B_+. Here, A_+ is denoted the positive part of A. For example, every ...

The power polynomials x^n are an associated Sheffer sequence with f(t)=t, (1) giving generating function sum_(k=0)^inftyx^kt^k=1/(1-tx) (2) and exponential generating ...

An algebraic extension K over a field F is a purely inseparable extension if the algebraic number minimal polynomial of any element has only one root, possibly with ...

If A moves along a known curve, then P describes a pursuit curve if P is always directed toward A and A and P move with uniform velocities. Pursuit curves were considered in ...

A congruence of the form ax^2+bx+c=0 (mod m), (1) where a, b, and c are integers. A general quadratic congruence can be reduced to the congruence x^2=q (mod p) (2) and can be ...

The amazing identity for all theta, where Gamma(z) is the gamma function. Equating coefficients of theta^0, theta^4, and theta^8 gives some amazing identities for the ...

The ratio of two numbers r and s is written r/s, where r is the numerator and s is the denominator. The ratio of r to s is equivalent to the quotient r/s. Betting odds ...

Any system of phi(n) integers, where phi(n) is the totient function, representing all the residue classes relatively prime to n is called a reduced residue system (Nagell ...

A removable singularity is a singular point z_0 of a function f(z) for which it is possible to assign a complex number in such a way that f(z) becomes analytic. A more ...

The root lattice of a semisimple Lie algebra is the discrete lattice generated by the Lie algebra roots in h^*, the dual vector space to the Cartan subalgebra.