Search Results for ""

The Zariski topology is a topology that is well-suited for the study of polynomial equations in algebraic geometry, since a Zariski topology has many fewer open sets than in ...

A hyper-Kähler manifold can be defined as a Riemannian manifold of dimension 4n with three covariantly constant orthogonal automorphisms I, J, K of the tangent bundle which ...

The standard Lorentzian inner product on R^4 is given by -dx_0^2+dx_1^2+dx_2^2+dx_3^2, (1) i.e., for vectors v=(v_0,v_1,v_2,v_3) and w=(w_0,w_1,w_2,w_3), ...

The Riemann tensor (Schutz 1985) R^alpha_(betagammadelta), also known the Riemann-Christoffel curvature tensor (Weinberg 1972, p. 133; Arfken 1985, p. 123) or Riemann ...

There are several closely related results that are variously known as the binomial theorem depending on the source. Even more confusingly a number of these (and other) ...

An affine transformation is any transformation that preserves collinearity (i.e., all points lying on a line initially still lie on a line after transformation) and ratios of ...

Some authors define a general Airy differential equation as y^('')+/-k^2xy=0. (1) This equation can be solved by series solution using the expansions y = ...

The Andrews-Gordon identity (Andrews 1974) is the analytic counterpart of Gordon's combinatorial generalization of the Rogers-Ramanujan identities (Gordon 1961). It has a ...

There are several related series that are known as the binomial series. The most general is (x+a)^nu=sum_(k=0)^infty(nu; k)x^ka^(nu-k), (1) where (nu; k) is a binomial ...

A simple way to describe a knot projection. The advantage of this notation is that it enables a knot diagram to be drawn quickly. For an oriented alternating knot with n ...