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There are at least two meanings of the term "total derivative" in mathematics. The first is as an alternate term for the convective derivative. The total derivative is the ...

Let Omega be a bounded open set in R^d whose boundary partialOmega is at least C^1 smooth and let T:C_c^1(Omega^_)->L^p(partialOmega) (1) be a linear operator defined by ...

A "pointwise-bounded" family of continuous linear operators from a Banach space to a normed space is "uniformly bounded." Symbolically, if sup||T_i(x)|| is finite for each x ...

A left Hilbert Algebra A whose involution is an antilinear isometry is called a unimodular Hilbert algebra. The involution is usually denoted xi|->xi^*.

Given a topological vector space X and a neighborhood V of 0 in X, the polar K=K(V) of V is defined to be the set K(V)={Lambda in X^*:|Lambdax|<=1 for every x in V} and where ...

The versine, also known as the "versed sine," is a little-used trigonometric function defined by versin(z) = 2sin^2(1/2z) (1) = 1-cosz, (2) where sinz is the sine and cosz is ...

Let X=(X,tau) be a topological vector space whose continuous dual X^* may or may not separate points (i.e., may or may not be T2). The weak-* (pronounced "weak star") ...

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 ...

A complex function is said to be analytic on a region R if it is complex differentiable at every point in R. The terms holomorphic function, differentiable function, and ...

In geometry, the term "enlargement" is a synonym for expansion. In nonstandard analysis, let X be a set of urelements, and let V(X) be the superstructure with individuals in ...