Surface generating on the basis of experimental data

The problem of surface generating on the basis of experimental data is presented in this lecture. Special attention is given to the implementation of moving ordinary least squares and moving total least squares. Some results done in the Institute for Applied Mathematics in Osijek are mentioned which were published in the last several years

Analysis of solution of the least squares problem

For the given data $(p_i,t_i,f_i),$ $i=1,ldots,m$, we consider the existence problem of the best parameter approximation of the exponential model function in the sense of ordinary least squares and total least squares. Results related to that problem which have been obtained and published by the authors so far are given in the paper, as well as some new results on nonuniqueness of the best parameter approximation

APPLICATION OF ASYMETRIC S-FUNCTION FOR ANALYSIS AND VALUATION OF THE GROWTH OF BOARS

Kapacitet rasta svinja predmet je stalnih istraživania. Rast svinja različito se kvantitativno i kvalitativno ostvaruje. Gospodarska korist od svinjogojstva je u korištenju progresivne faze rasta. U radu se istražuju krivulje rasta nerastova velikog jorkšira na osnovu intenziteta prirasta u testu od 30-100 kg. Prema postignutim prosječnim dnevnim prirastima nerastovi su podjeljeni u tri skupine (0,81 - 0.90 kg, 0,91 - 1,0 kg i 1,01 - 1,10 kg). Za opisivanje rasta upotrebljena je asimetrična S-funkcija, model: F(t)=A/(1+be⁻ᶜᶢᵗ)¹¤ᶢ. Obzirom na potrebno vrijeme za postizanje određene mase, razgraničene su faze: pripreme (t=tв), rasta - progresivnog i degresivnog (t = tв = tс) i zasićenja (t = tc). Analiza je pokazala da nerastovi koji su ušli u test u mlađoj dobi imaju veći intenzitet prirasta od onih koji su započeli test u starijoj dobi (77,4; 83,4 i 82,6 dana). Kod tih nerastova faze progresivnog i degresivnog rasta nastupaju ranije i traju kraće vrijeme. Primjenjena asimetrična S-funkcija može se koristiti i za procjenu rasta nerastova u kasnijoi dobi, na osnovi početnih kontrolnih mjerenja životinja.Growth capacity of the pig is a subject of permanent research. The growth rate of pigs has different quantitative and qualitative course. Profitability of pig rearing is in use of progressive growth stage, i.e. phase. This study deals with the curves of growth of the Large White breed, based on the gain intensity of the animals tested with the body weights of 30 to 100 kg. According to the average daily gains the boars were deviced into three groups (0.81 - 0.90 kg,0.91 - 1.0 kg and 1.01 to 1.10 kg). For description of the growth rate the asymmetric S- function was used modelled as: F(t)=A/(1+be⁻ᶜᶢᵗ)¹¤ᶢ. Regarding the necessary time for achievement of certain mass, the stages are separated as: preparations (t=tв), growth-both progressive and degressive (t=tв=tс) and phase of saturation (t=tc). The analysis showed that boars, entering the test in younger age, showed higher growth intensity than those beginning the test in older age(77.4; 83.4 and 82.6 days). In these boars the stage of progressive and degressive growth occurred earlier and lasted shorter period of time. The asymmetric S-function could be there for used for valuation of the boars growth rate in older age based on the starting control measurements of animals

MODELS OF MAXIMUM GROWTH ESTIMATION IN FATTENING PROVENIENCES OF BROILERS

The objective of this study was to find the mathematical model which gives the best results in estimation of biological growth maximum of fattening chicken. Used models were: general exponential function, von Bertalanffy´s model, logistic function and generalized logistic function. In the investigations of growth characteristics Avian 24 K, Arbor Acres and Ross 208 proveniencies of broilers were used. The results of the research show that the best data for estimation of biological maximum of chicken growth in relation to sex ensures generalized logistic function with γ = 0.18 (asymmetric S-function). The asymptotic value of A for male chicken was, respectively: 5.72 kg, 5.90 kg and 4.47 kg, and for female chicken: 4.06 kg, 4.75 kg, 4.46 kg. In case of segregated fattening regarding gender, ability of live weight estimation of chicken at certain age is of great importance for optimal utilization of genetic potential and obtaining higher flock uniformity at delivery and slaughtering of the chickens

GROWTH MODELS WITH OBLIQUE ASYMPTOTE

A class of smooth functions which can be used as regression models for modelling phenomena requiring an oblique asymptote is analyzed. These types of models were defined as a product of a linear function and some well known growth models. In addition to their increasing character with an oblique asymptote, the resulting models provide curves with a single inflection point