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Let any finite or infinite set of points having no finite limit point be prescribed and associate with each of its points a principal part, i.e., a rational function of the ...

The orthogonal complement of a subspace V of the vector space R^n is the set of vectors which are orthogonal to all elements of V. For example, the orthogonal complement of ...

A projection is the transformation of points and lines in one plane onto another plane by connecting corresponding points on the two planes with parallel lines. This can be ...

Proof theory, also called metamathematics, is the study of mathematics and mathematical reasoning (Hofstadter 1989) in a general and abstract sense itself. Instead of ...

Suppose that V={(x_1,x_2,x_3)} and W={(x_1,0,0)}. Then the quotient space V/W (read as "V mod W") is isomorphic to {(x_2,x_3)}=R^2. In general, when W is a subspace of a ...

The quotient space K^__1A=K_1A/{0,[-1]} of the Whitehead group K_1A is known as the reduced Whitehead group. Here, the element [-1] in K_1A denotes the order-2 element ...

A system in which words (expressions) of a formal language can be transformed according to a finite set of rewrite rules is called a reduction system. While reduction systems ...

A Taylor series remainder formula that gives after n terms of the series R_n=(f^((n+1))(x^*))/(n!p)(x-x^*)^(n+1-p)(x-x_0)^p for x^* in (x_0,x) and any p>0 (Blumenthal 1926, ...

A sheaf is a presheaf with "something" added allowing us to define things locally. This task is forbidden for presheaves in general. Specifically, a presheaf F on a ...

Measurements of a centered convex body in Euclidean n-space (for n>=3) show that its brightness function (the volume of each projection) is smaller than that of another such ...