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The radical circle of the mixtilinear incircles has a center with trilinear center function alpha_(999)=cosA-2, (1) which is Kimberling center X_(999). It has radius (2) ...

The second-order ordinary differential equation y^('')+alpha(x)y^'+x^2y^n=0.

The second-order ordinary differential equation y^('')+[alpha/(cosh^2(ax))+betatanh(ax)+gamma]y=0.

The radical circle of the Neuberg circles has circle function l=(a^2b^4-b^4c^2+a^2c^4-b^2c^4)/(bc(a^2b^2+a^2c^2+b^2c^2)), (1) which does not correspond to any Kimberling ...

where del is the backward difference.

Any cubic curve that passes through eight of the nine intersections of two given cubic curves automatically passes through the ninth.

An ordinary differential equation of order n is an equation of the form F(x,y,y^',...,y^((n)))=0.

The ordinary differential equation

A similar construction can be done by initially erecting a square internally on the side BC. This leads to the A^--inscribed square. The triangle DeltaX^-Y^-Z^- of centers of ...

A partial differential equation of second-order, i.e., one of the form Au_(xx)+2Bu_(xy)+Cu_(yy)+Du_x+Eu_y+F=0, (1) is called parabolic if the matrix Z=[A B; B C] (2) ...