### The distance function for computing the continuous distance of biopolymer sequences

G.H. Hakobyan^{1}, T.V. Margaryan^{2}

^{1}gaghakob@ysu.am, YSU; ^{2}

As any abstraction, sequence perception preferentially by means of discrete residue algorithmics necessarily remains one-sided. It doesn't facilitate the elucidation of those biologically meaningful molecular traits which depend, generally speaking, on a biopolymer's chain continuity and integrity.
To widen the scope of bioinformatics towards a desirably more holistic compilation of both the intrinsic molecular properties and some superordinate correlations in the living world, it is legitimate to ask in how far the use of functions in the mathematical sense of the word may assist researchers with addressing sequence-depending problems better than discrete maths does to date. Interestingly, in some applications of sequence comparison theories the actual items to be compared are not successions of discrete elements, but "continuous" functions of a continuous argument. As a rule, time plays the role of such an argument. The central role here plays the distance function of two independent variables independent of the way of introducing the metrics in the space of continuous function. The present paper is aimed to construct a distance function with the help of the given "distance" matrix D. Being itself as a continuous function it keeps all the properties which has the given distance matrix. In particular, we proved that if the given matrix satisfies the condition of triangle inequality then the constructed distance function must also satisfy this condition.
Key words: Amino acid sequence, distance matrix, distance function.