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The contravariant four-vector arising in special and general relativity, x^mu=[x^0; x^1; x^2; x^3]=[ct; x; y; z], (1) where c is the speed of light and t is time. ...

A positive definite function f on a group G is a function for which the matrix {f(x_ix_j^(-1))} is always positive semidefinite Hermitian.

Let A be a C^*-algebra, then a linear functional f on A is said to be positive if it is a positive map, that is f(a)>=0 for all a in A_+. Every positive linear functional is ...

Let A and B be C^*-algebras, then a linear map phi:A->B is said to be positive if phi(A_+) subset= B_+. Here, A_+ is denoted the positive part of A. For example, every ...

Let f:R->R, then the positive part of f is the function f^+:R->R defined by f^+(x)=max(f(x),0) The positive part satisfies the identity f=f^+-f^-, where f^- is the negative ...

A quadratic form Q(x) is said to be positive semidefinite if it is never <0. However, unlike a positive definite quadratic form, there may exist a x!=0 such that the form is ...

A statement, also known as an axiom, which is taken to be true without proof. Postulates are the basic structure from which lemmas and theorems are derived. The whole of ...

You buy 100 pounds of potatoes and are told that they are 99% water. After leaving them outside, you discover that they are now 98% water. The weight of the dehydrated ...

The study of harmonic functions (also called potential functions).

The power circles of a reference triangle are the three circles centered at the midpoints M_A, M_B, M_C of the sides of a reference triangle DeltaABC that pass through the ...