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Two complex measures mu and nu on a measure space X, are mutually singular if they are supported on different subsets. More precisely, X=A union B where A and B are two ...

Two or more lines which have no intersections but are not parallel, also called agonic lines. Since two lines in the plane must intersect or be parallel, skew lines can exist ...

For d>=1, Omega an open subset of R^d, p in [1;+infty] and s in N, the Sobolev space W^(s,p)(R^d) is defined by W^(s,p)(Omega)={f in L^p(Omega): forall ...

"SOHCAHTOA" is a helpful mnemonic for remembering the definitions of the trigonometric functions sine, cosine, and tangent i.e., sine equals opposite side over hypotenuse, ...

Borwein et al. (2004, pp. 4 and 44) term the expression of the integrals I_1 = int_0^1x^xdx (1) = 0.783430510... (2) I_2 = int_0^1(dx)/(x^x) (3) = 1.291285997... (4) (OEIS ...

The extension field K of a field F is called a splitting field for the polynomial f(x) in F[x] if f(x) factors completely into linear factors in K[x] and f(x) does not factor ...

A second-tensor rank symmetric tensor is defined as a tensor A for which A^(mn)=A^(nm). (1) Any tensor can be written as a sum of symmetric and antisymmetric parts A^(mn) = ...

The tilde is the mark "~" placed on top of a symbol to indicate some special property. x^~ is voiced "x-tilde." The tilde symbol is commonly used to denote an operator. In ...

A total order (or "totally ordered set," or "linearly ordered set") is a set plus a relation on the set (called a total order) that satisfies the conditions for a partial ...

The triangle function is the function Lambda(x) = {0 |x|>=1; 1-|x| |x|<1 (1) = Pi(x)*Pi(x) (2) = Pi(x)*H(x+1/2)-Pi(x)*H(x-1/2), (3) where Pi(x) is the rectangle function, ...