Raider of the lost time
Join Date: Nov 2003 Posts: 5,934
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04-02-2006, 03:56 PM
| | Dysfunctional analysis
In mathematics, functional analysis studies theory of vector spaces and linear functionals. A vector space is defined as a group or set whose elements satisfy the commutative property of addition which they also satisfy the associative property of multiplication. Hence, a vector space is equivalently a linear space. However, only one to one or many to one relationship define a functional. That is to say that one or more elements in the functional domain set can be mapped to only one element in the functional range. If the relationship becomes many to many then it is defined as a dysfunctional relation and the study of these dysfunctional relations is called dysfunctional analysis. The simplest dysfunctional relation is a 2 to 2 relationship shown by the following diagram:  However, this effective relation optimizes the repulsive interactions since |j(a)|=|j(b)| and |y(a)|=|y(b)|. Furthermore, if a given j is defined as the infinitesimal orthogonal force and a given y is defined as the infinitesimal metric then the absolute product of each |j| and |y| defines a minimum energy configuration at the infinitesimal domain of spacetime. A double products of |j(a)||y(a)| and |j(b)||y(b)| defines a square of energy as an absolute quantum whose integral forms a true field of absolute vacuum.
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Time independence: [∂E(g)]²=[∂F(a)×∂r(a)]·[∂F(b)×∂r(b)] and Mass independence: ¶a(t)·¶r(t)=c²
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