USING APPROXIMATION FUNCTIONS IN ANALYSIS OF TREHALOZE INTRACELLULAR CONCENTRATION L. Dan Milici, Member, IEEE, Sorin Pohoata and Mariana R. Milici Abstract: The study object is to evaluate in which measure the supplementation of yeast inoculums with linoleic acid succeed to minimize the negative effect of the thermal shock stress factor on the one side, and the subduing to repetitive running of fermentation cycles, on the other side. The study proposes to find the most efficient way to grow the intracellular trehaloze content through beer yeast suspending into trehaloze solutions by different concentrations, at different thermo-stating temperatures and in different contact times, taking into account that this technique allows the passive transfer of exogenetic trehaloze inside the cells both at a new propagated cell population, and at cells resulted from an industrial inoculums. Index Terms: approximation methods. factors of influent, ferment activity, numerical analysis. I. INTRODUCTION Choosing of a certain beer yeast stem for beer obtaining, in specific conditions to lay in one’s stock of raw materials, of endowment and of used technology, is achieved taking into account the main specific features of the beer yeast: final fermentation degree and the fermentation speed, capability to assimilate the substances which participate in metabolism, multiplication efficiency, sedimentation and flocculation capability, spectrum and quantity of secondary products of fermentation with implications in the beer taste and aroma, deterioration and contamination resistance. The rejoinder life cycle, determined by number of complete divisions of each individual cell is genetic controlled, but influenced by medium conditions. After the cell divided by a certain number, enters into the cell senescence, loosing definitively the multiplication capability and finally dies. The chronological life cycle, defined as maximum outliving time of the cells maintained in the stationary growing stage and characterized by a temporary loosing of multiplication capability due to the nutrients absence, constitutes an important controlling instrument of degeneration at the macromolecular level and of cell death rate. The study object is to evaluate in which measure the supplementation of yeast inoculums with linoleic acid succeed to minimize the negative effect of the thermal shock stress factor on the one side, and the subduing to repetitive running of fermentation cycles, on the other side. The study proposes to find the most efficient way to grow the intracellular trehaloze content through beer yeast suspending into trehaloze solutions by different concentrations, at different thermo-stating temperatures and in different contact times, taking into account that this technique allows the passive transfer of exogenetic trehaloze inside the cells both at a new propagated cell population, and at cells resulted from an industrial inoculums. II. MATHEMATICAM METHODS FOR DATA PROCESSING Because in the large majority of cases the tests direct to a real function of real variable, the approximation of this characteristic, in the specified cases, consists in the approximation of a real function, approximation named interpolation too. The approximation of the certain real function is made by simple and easy utilized functions, especially through implementation of the computing of the values of this function. Because the real function set is a linear dimensional infinite space, while the function sets in which we look for the approximation are dimensional finite spaces, in actual fact, the abstract problem that stand on the base of approximation techniques consists in replacing of one element from an dimensional infinite space by representatives of one dimensional finite space. To can specify the “approximation” notion and to can appreciate the error made through the above specified replacing, the using of “norm” mathematical concept is needed. Considering a real linear space X, we define on it the norm symbolical noted by: || || : X → ℜ, having the properties (that satisfy the axioms): a f f X b f f c f f R f X d f g f g fg X ) , ) ) , , ) , , ≥ ∀ ∈ =  = = ⋅ ∀ ∈ ∀ ∈ + ≤ + ∀ ∈ 0 0 0 α α α ( 1 ) If on the linear space X it was defined the norm || ||, X is a normalized linear space. On these terms we could specify the “approximation” of one function from normalized linear space X, defining what means a best approximation. Considering the dimensional infinite functions space X, normalized by || || and X m a linear subspace of X, dimensional finite with dim (X m )= m, we define the notion of approximation of one function f ∈ X by function g m ∈ X m considering ||f-g m || as a measure of the error that is made if instead of the function f is used the function g m . It is naturally on these terms to say that g m is the best approximation of f if: f g f g m g X m m m m - = - = ∈ inf α ( 2 ) 978-1-4244-3861-7/09/$25.00 ©2009 IEEE 156