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When two cycles have a transversal intersection X_1 intersection X_2=Y on a smooth manifold M, then Y is a cycle. Moreover, the homology class that Y represents depends only ...

For an algebraic curve, the total number of groups of a g_N^r consisting in a point of multiplicity k_1, one of multiplicity k_2, ..., one of multiplicity k_rho, where sumk_i ...

Each double point assigned to an irreducible algebraic curve whose curve genus is nonnegative imposes exactly one condition.

A system of curvilinear coordinates. There are several different conventions for the orientation and designation of these coordinates. Arfken (1970) defines coordinates ...

Parametric equations are a set of equations that express a set of quantities as explicit functions of a number of independent variables, known as "parameters." For example, ...

A phase curve is a plot of the solution to a set of equations of motion in a phase plane (or more generally, a phase space) as a function of time (Tabor 1989, p. 14). Phase ...

A K-rational point is a point (X,Y) on an algebraic curve f(X,Y)=0, where X and Y are in a field K. For example, rational point in the field Q of ordinary rational numbers is ...

There are at least two Siegel's theorems. The first states that an elliptic curve can have only a finite number of points with integer coordinates. The second states that if ...

Special affine curvature, also called as the equi-affine or affine curvature, is a type of curvature for a plane curve that remains unchanged under a special affine ...

There are (at least) two mathematical objects known as Weierstrass forms. The first is a general form into which an elliptic curve over any field K can be transformed, given ...