This paper is based on a previous work of the first author [13] in which a mathematical model of the computer has been presented. The model deals with random access memory, such as RASP of C. C.â€¦ (More)

Let S be a many sorted signature. A gate of S is an element of the operation symbols of S. Let A be a set and let f be a function. One can check that A 7âˆ’â†’ f is function yielding. Let f , g beâ€¦ (More)

In this paper p, p1, q are points of E 2 T . The following three propositions are true: (1) Let P be a compact non empty subset of E T . Suppose P is a simple closed curve. Then W-minP âˆˆ LowerArcPâ€¦ (More)

The papers [21], [11], [1], [22], [20], [4], [5], [6], [12], [10], [3], [14], [16], [23], [9], [7], [2], [15], [18], [17], [19], and [8] provide the notation and terminology for this paper. Forâ€¦ (More)

We prove some results on SCM needed for the proof of the correctness of Euclidâ€™s algorithm. We introduce the following concepts: starting finite partial state (Start-At(l)), then assigns to theâ€¦ (More)

We present a formalization of the seminal paper by W. W. Armstrong [1] on functional dependencies in relational data bases. The paper is formalized in its entirety including examples andâ€¦ (More)

This article is the last in a series of four articles (preceded by [23,22,21]) about modelling circuits by many sorted algebras. The notion of a circuit computation is defined as a sequence ofâ€¦ (More)

This article is the third in a series of four articles (preceded by [19,20] and continued in [18]) about modelling circuits by many sorted algebras. A circuit is defined as a locally-finite algebraâ€¦ (More)

In this paper we first defined the partial-union sequence, the partial-intersection sequence, and the partial-difference-union sequence of given sequence of subsets, and then proved the additiveâ€¦ (More)

(2)1 For every real number a such that 1 â‰¤ a holds a â‰¤ a2. (3) For every real number a such that âˆ’1 â‰¥ a holds âˆ’a â‰¤ a2. (4) For every real number a such that âˆ’1 > a holds âˆ’a < a2. (5) For all realâ€¦ (More)