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Let A be a C^*-algebra. An element a in A is called self-adjoint if a^*=a. For example, the real functions of the C^*-algebra of C([a,b]) of continuous complex-valued ...

A mathematical object defined for a set and a binary operator in which the multiplication operation is associative. No other restrictions are placed on a semigroup; thus a ...

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

Let A be a unital C^*-algebra. An element u in A is called unitary if u^*u=uu^*=1. For example, for each self-adjoint element a in A, the element ...

A W^*-algebra is a C-*-algebra A for which there is a Banach space A_* such that its dual is A. Then the space A_* is uniquely defined and is called the pre-dual of A. Every ...

The Weingarten equations express the derivatives of the normal vector to a surface using derivatives of the position vector. Let x:U->R^3 be a regular patch, then the shape ...

In the biconjugate gradient method, the residual vector r^((i)) can be regarded as the product of r^((0)) and an ith degree polynomial in A, i.e., r^((i))=P_i(A)r^((0)). (1) ...

The curl of a vector field, denoted curl(F) or del xF (the notation used in this work), is defined as the vector field having magnitude equal to the maximum "circulation" at ...

Gaussian curvature, sometimes also called total curvature (Kreyszig 1991, p. 131), is an intrinsic property of a space independent of the coordinate system used to describe ...

Let kappa_1 and kappa_2 be the principal curvatures, then their mean H=1/2(kappa_1+kappa_2) (1) is called the mean curvature. Let R_1 and R_2 be the radii corresponding to ...