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A bounded operator U on a Hilbert space H is called essentially unitary if U^*U-I and UU^*-I are compact operators.

The partial differential equation u_(xy)+(alphau_x-betau_y)/(x-y)=0.

The partial differential equation u_(xy)+(N(u_x+u_y))/(x+y)=0.

The curvature of a surface satisfies kappa=kappa_1cos^2theta+kappa_2sin^2theta, where kappa is the normal curvature in a direction making an angle theta with the first ...

Euler integration was defined by Schanuel and subsequently explored by Rota, Chen, and Klain. The Euler integral of a function f:R->R (assumed to be piecewise-constant with ...

Let f(x,y) be a homogeneous function of order n so that f(tx,ty)=t^nf(x,y). (1) Then define x^'=xt and y^'=yt. Then nt^(n-1)f(x,y) = ...

A 1-form w is said to be exact in a region R if there is a function f that is defined and of class C^1 (i.e., is once continuously differentiable in R) and such that df=w.

The exsecant is a little-used trigonometric function defined by excsc(x)=cscx-1, where cscx is the cosecant.

An exponent is the power p in an expression of the form a^p. The process of performing the operation of raising a base to a given power is known as exponentiation.

Exponential decay is the decrease in a quantity N according to the law N(t)=N_0e^(-lambdat) (1) for a parameter t and constant lambda (known as the decay constant), where e^x ...