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The negative derivative S(v)=-D_(v)N (1) of the unit normal N vector field of a surface is called the shape operator (or Weingarten map or second fundamental tensor). The ...

Given a Hilbert space H, the sigma-strong operator topology is the topology on the algebra L(H) of bounded operators from H to itself defined as follows: A sequence S_i of ...

The sigmoid function, also called the sigmoidal curve (von Seggern 2007, p. 148) or logistic function, is the function y=1/(1+e^(-x)). (1) It has derivative (dy)/(dx) = ...

Simple harmonic motion refers to the periodic sinusoidal oscillation of an object or quantity. Simple harmonic motion is executed by any quantity obeying the differential ...

Given a simple harmonic oscillator with a quadratic perturbation, write the perturbation term in the form alphaepsilonx^2, x^..+omega_0^2x-alphaepsilonx^2=0, (1) find the ...

A single-valued function is function that, for each point in the domain, has a unique value in the range. It is therefore one-to-one or many-to-one. A single-valued complex ...

Two complex measures mu and nu on a measure space X, are mutually singular if they are supported on different subsets. More precisely, X=A union B where A and B are two ...

Given an ordinary differential equation y^'=f(x,y), the slope field for that differential equation is the vector field that takes a point (x,y) to a unit vector with slope ...

A four-vector a_mu is said to be spacelike if its four-vector norm satisfies a_mua^mu>0. One should note that the four-vector norm is nothing more than a special case of the ...

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 ...