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e^(i(ntheta))=(e^(itheta))^n. (1) From the Euler formula it follows that cos(ntheta)+isin(ntheta)=(costheta+isintheta)^n. (2) A similar identity holds for the hyperbolic ...

Calabi-Yau spaces are important in string theory, where one model posits the geometry of the universe to consist of a ten-dimensional space of the form M×V, where M is a four ...

The Wiener-Hopf method is a powerful technique which enables certain linear partial differential equations subject to boundary conditions on semi-infinite domains to be ...

Given a first-order ordinary differential equation (dy)/(dx)=F(x,y), (1) if F(x,y) can be expressed using separation of variables as F(x,y)=X(x)Y(y), (2) then the equation ...

The continuous Fourier transform is defined as f(nu) = F_t[f(t)](nu) (1) = int_(-infty)^inftyf(t)e^(-2piinut)dt. (2) Now consider generalization to the case of a discrete ...

The polar coordinates r (the radial coordinate) and theta (the angular coordinate, often called the polar angle) are defined in terms of Cartesian coordinates by x = ...

The set of points in the space of system variables such that initial conditions chosen in this set dynamically evolve to a particular attractor.

A two-dimensional map which is conjugate to the Hénon map in its nondissipative limit. It is given by x^' = x+y^' (1) y^' = y+epsilony+kx(x-1)+muxy. (2)

For a fractal process with values y(t-Deltat) and y(t+Deltat), the correlation between these two values is given by the Brown function r=2^(2H-1)-1, also known as the ...

A Mandelbrot set-like fractal obtained by iterating the map z_(n+1)=z_n^3+(z_0-1)z_n-z_0.