Use cases are widely used for functional requirements elicitation. However, security non-functional requirements are often neglected in this requirements analysis process. As systems become increasingly complex current means of analysis will probably prove ineffective. In the safety domain a variety of effective analysis techniques have emerged over many years. Since the safety and security dom...

1. Metric and topological spaces A metric space is a set on which we can measure distances. More precisely, we proceed as follows: let X = ∅ be a set, and let d : X ×X → [0, ∞) be a map. Property 3 is called the triangle inequality. It says that a detour via z will not give a shortcut when going from x to y. The notion of a metric space is very flexible and general, and there are many different...

Table of contents: Section 1: Overview, background 1 Section 2: Definition of Banach spaces 2 Section 3: Examples of Banach spaces 2 Section 4: L spaces 6 Section 5: L spaces 9 Section 6: Some spaces that are almost Banach, but aren’t 10 Section 7: Normed vector spaces are metric spaces 11 Section 8: How to make new spaces out of existent ones (or not) 13 Section 9: Finite-dimensional vector sp...

Definition 1.2 A real vector space X is called a real normed space if there exists a map || · || : X → IR, such that, for all λ ∈ IR and x, y ∈ X, (i) ||x|| = 0⇔ x = 0; (ii) ||λx|| = |λ| ||x||; (iii) ||x + y|| ≤ ||x|| + ||y|| (triangle inequality). The map || · || is called the norm. If || · || only satisfies (ii) and (iii) then it is called a seminorm. Note that X is automatically a metric spa...

A vector space over a field K (R or C) is a set X with operations vector addition and scalar multiplication satisfy properties in section 3.1. [1] An inner product space is a vector space X with inner product 〈·, ·〉 : X ×X → K satisfying • 〈x + y, z〉 = 〈x, z〉+〈y, z〉, • 〈αx, y〉 =α〈x, y〉, • 〈x, y〉 = 〈y, x〉, • 〈x, x〉 ≥ 0 with 〈x, x〉 = 0 ⇐⇒ x = 0. [2] An inner product induces a norm on X via ‖x‖ =p...