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The eccentric angle of a point on an ellipse with semimajor axes of length a and semiminor axes of length b is the angle t in the parametrization x = acost (1) y = bsint, (2) ...

A quantity defined for a conic section which can be given in terms of semimajor a and semiminor axes b. interval curve e e=0 circle 0 0<e<1 ellipse sqrt(1-(b^2)/(a^2)) e=1 ...

On the Clebsch diagonal cubic, all 27 of the complex lines present on a general smooth cubic surface are real. In addition, there are 10 points on the surface where three of ...

The second-order ordinary differential equation y^('')+[(alphaeta)/(1+eta)+(betaeta)/((1+eta)^2)+gamma]y=0, where eta=e^(deltax).

The equations are x = 2/(sqrt(pi(4+pi)))(lambda-lambda_0)(1+costheta) (1) y = 2sqrt(pi/(4+pi))sintheta, (2) where theta is the solution to ...

The equations are x = ((lambda-lambda_0)(1+costheta))/(sqrt(2+pi)) (1) y = (2theta)/(sqrt(2+pi)), (2) where theta is the solution to theta+sintheta=(1+1/2pi)sinphi. (3) This ...

In two dimensions, the curve known as an "egg' is an oval with one end more pointed than the other.

Given a differential operator D on the space of differential forms, an eigenform is a form alpha such that Dalpha=lambdaalpha (1) for some constant lambda. For example, on ...

If L^~ is a linear operator on a function space, then f is an eigenfunction for L^~ and lambda is the associated eigenvalue whenever L^~f=lambdaf. Renteln and Dundes (2005) ...

If A is an n×n square matrix and lambda is an eigenvalue of A, then the union of the zero vector 0 and the set of all eigenvectors corresponding to eigenvalues lambda is ...