Search Results for ""

The quantum electrodynamical law which applies to spin-1/2 particles and is the relativistic generalization of the Schrödinger equation. In 3+1 dimensions (three space ...

The curve formed by the intersection of a cylinder and a sphere is known as Viviani's curve. The problem of finding the lateral surface area of a cylinder of radius r ...

Given a curve C and O=(x_0,y_0) a fixed point called the pedal point, then for a point P on C, draw a line perpendicular to OP. The envelope of these lines as P describes the ...

A natural equation is an equation which specifies a curve independent of any choice of coordinates or parameterization. The study of natural equations began with the ...

Given a nonhomogeneous ordinary differential equation, select a differential operator which will annihilate the right side, and apply it to both sides. Find the solution to ...

There are six Painlevé transcendents, corresponding to second-order ordinary differential equations whose only movable singularities are ordinary poles and which cannot be ...

A Fredholm integral equation of the second kind phi(x)=f(x)+lambdaint_a^bK(x,t)phi(t)dt (1) may be solved as follows. Take phi_0(x) = f(x) (2) phi_1(x) = ...

Given three objects, each of which may be a point, line, or circle, draw a circle that is tangent to each. There are a total of ten cases. The two easiest involve three ...

An algorithm which finds rational function extrapolations of the form R_(i(i+1)...(i+m))=(P_mu(x))/(P_nu(x))=(p_0+p_1x+...+p_mux^mu)/(q_0+q_1x+...+q_nux^nu) and can be used ...

The Burridge-Knopoff model is a system of differential equations used to model earthquakes using n points on a straight line, each of mass m, that interact with each other ...