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Defined for a vector field A by (A·del ), where del is the gradient operator. Applied in arbitrary orthogonal three-dimensional coordinates to a vector field B, the ...

Given a subset S subset R^n and a real function f which is Gâteaux differentiable at a point x in S, f is said to be pseudoconvex at x if del f(x)·(y-x)>=0,y in ...

The biconjugate gradient method often displays rather irregular convergence behavior. Moreover, the implicit LU decomposition of the reduced tridiagonal system may not exist, ...

For omega a differential (k-1)-form with compact support on an oriented k-dimensional manifold with boundary M, int_Mdomega=int_(partialM)omega, (1) where domega is the ...

A function f is Fréchet differentiable at a if lim_(x->a)(f(x)-f(a))/(x-a) exists. This is equivalent to the statement that phi has a removable discontinuity at a, where ...

A covariant tensor, denoted with a lowered index (e.g., a_mu) is a tensor having specific transformation properties. In general, these transformation properties differ from ...

The Reynolds transport theorem, also called simply the Reynolds theorem, is an important result in fluid mechanics that's often considered a three-dimensional analog of the ...

A vector derivative is a derivative taken with respect to a vector field. Vector derivatives are extremely important in physics, where they arise throughout fluid mechanics, ...

The convective derivative is a derivative taken with respect to a moving coordinate system. It is also called the advective derivative, derivative following the motion, ...

Green's identities are a set of three vector derivative/integral identities which can be derived starting with the vector derivative identities del ·(psidel phi)=psidel ...