Search

This research aimed at investigation of growth phases of male broilers and establishment of qualitative characteristics of carcasses, as well as of chemical content of breast muscles and thighs. The research was carried out on 45 male broilers of Ross 208 provenience, which were divided into 3 groups. Broilers were fed with starter and finisher diets containing 22.67%/20.43% of crude proteins and 14.19 MJ/kg/14.18 MJ/kg ME, respectively. After 35 days of fattening broilers gained weight of 2065.75 ± ; ; ; 100.36 g. Asymmetric S-function was used for estimation of the growth phases, and parameters of the used model were the following: A=3.8 kg, b=1.41969, c=2.69601 and g=0.18. Average weight of carcasses was 1815± ; ; ; 25 g. Portions in the whole carcass were as follows: breasts 33.75%, thighs with drumsticks 30.35%, wings 11.15% and backs 22.40%. Breast muscles differed statistically (P

U članku se opisuju neka važna svojstva prostih brojeva. Pored danih primjera i zadataka, navodi se i nekoliko neriješenih problema vezanih uz proste brojeve.

Razrađen je program načinjen u Mathematici za konstrukciju spline-a pri čemu se koristi LU dekompozicija trodijagonalne vrpčaste matrice.

We consider the parameter identification problem in the mathematical model described by one differential equation whose solution cannot be represented by elementary functions. In addition to the quasilinearization method, an important method for solving this problem is smoothing the data method. Thereby smoothing the data is usually carried out by applying either the least squares spline or the moving least squares method or wavelets. The ordinary least squares method assumes that errors occur only in measurement of the dependent variable and that they are normally distributed with expectancy zero. In this paper we also assume that the additive errors can also appear in the measured values of the independent variable, as well as that among the data the so-called outliers can appear. Therefore, for smoothing the data we will use the so-called total L_1 natural cubic spline, i.e. in general, the total L_p (p equals and greater than 1) natural cubic spline. Thereby we will use the method described in the work (1). By the construction of the total L_p natural cubic spline the well known Brent method for onedimensional minimization and Nelder-Meads Downhill Simplex Method or genetic algorithm for function minimization will be used. The mentioned method for solving parameter identification problems will be tested on several numerical examples.

We consider the smoothing a data method for solving the parameter identification problem in the mathematical model described by one differential equation $\frac{;dy};{;dt};=f(t, y(t), p)$, where $p=(p_1, \ldots, p_n)^T$ is the vector of unknown parameters. We assume that the solution of the differential equation cannot be represented by elementary functions. Also, we assume that the additive errors can appear in the measured values of the independent variable $t$ and in the measured values of the dependent variable $y$, as well as among the data so-called outliers can appear. Therefore, for smoothing the data will use the so-called total $L_1$ natural cubic spline, i.e. in general, the total $L_p$, ($p\geq 1$) natural cubic spline. For the construction of the best total $L_p$ natural cubic spline we use a new approach of our own. The method will be shown on several illustrative examples.

Cilj rada bio je istražiti matematički model koji daje najbolje rezultate prilikom procjene biološkog maksimuma rasta pilića u tovu. Upotrebljeni su: opća eksponencijalna funkcija, Von Bertalanffy model, logistička funkcija i generalizirana logistička funkcija. U istraživanju specifičnosti rasta korištene su Avian 24 K, Arbor Acres i Ross 208 provenijencije tovnih pilića. Rezultati istraživanja pokazuju da najbolje podatke za procjenu biološkog maksimuma rasta pilića, s obzirom na spol, omogućava generalizirana logistička funkcija uz gama = 0, 18 (asimetrična S-funkcija) . Utvrđena vrijednost za asimptotu A kod muških pilića, prema naprijed navedenom redosljedu, iznosi: 5, 72 kg, 5, 90 kg i 4, 47 kg, a kod ženskih pilića 4, 06 kg, 4, 75 kg i 4, 46 kg. Mogućnost procjene težina pilića kod odvojitog tova prema spolu u određenoj dobi od velikog je značenja za optimalno iskorištavanje genetskog potencijala pilića i postizanje veće uniformnosti jata prilikom isporuke i klanja pilića.

This research was carried out on 115 Ross 208 female broilers. Data on live weights were collected from 91 broilers during 7 weeks of fattening which was the basis for modelling the growth curve using asymmetric S-function. The same function was used for modelling growth of Ross 208 female broilers on the basis of data obtained from technological procedure. The parameters of the model was established as well as the stages of growth and inflection point. By the model, 99.924 percent and 99.954 percent of variance was explained for live weights of female broilers from experiment and from technological procedure, respectively. This means that asymmetric S-function can be used as the model for description of broilers’ growth. Using this function it was possible to predict the future weights of boilers. It is also possible to predict the time in which broilers reach certain live weight. The birds from experiment would cease useful growth at weeks. Other 24 Ross 208 female broilers were slaughtered when they reached determined weights from 2200 to 3400 g in the period from 7th to 12th week. The data obtained by dissection of those broilers on the main parts (breast, thighs with drumstick, wings and back) were used for the analysis of relative growth by allometric equation. Growth rates (b) for the most valuable parts and abdominal fat were: breast - 1.158; thighs with drumstick - 0.869; wings - 0.725; back - 1.063 and fat - 1.519. Allometric coefficients indicate that only fat production was intensive in the studied period. This confirms the conclusion that the best age for the slaughter of broilers is that established by asymmetric S-function.

Research on growth capacity of different genotypes of gilts was carried out at the station for performance test of gilts. Two groups of gilts, German Landrace and Swedish Landrace, 15 each were included in the experiment, while 3rd group contained 14 crossed gilts (Swedish Landrace x Large White). Using asymmetric S-function, differences were observed in growth characteristics between genotypes of gilts. Growth curves for gilts were depicted by following models: German Landrace f(t) Swedish Landrace f(t) Crosses (SL x LW) f(t) Pigs with higher average daily gain reach maximal growth rates (inflexion point) in earlier age, and stage of progressive growth lasts shorter time than in animals with lower average daily gain. Inflexion point was reach in 166.59 days in German Landrace gilts, 171.14 days in Swedish Landrace and 168.53 days in crossed gilts (SL x LW).

In this paper we consider the total Lp norm ($p geq 1$) approximation problem for the exponential function. We give sufficient conditions which guarantee the existence of such optimal parameters.

We consider a special parameter identification problem occurring in marketing research, and give conditions on the empirical data which guarantee the existence of the solution to the problem. Furthermore, we analyze several different approaches and methods for solving this parameter identification problem.

The problem of generating a smooth surface on the basis of experimental data is considered in this paper. Special attention is given to the problem of the optimal number and optimal allocation of nodes at which local approximants will be generated. Therefore, it is possible to generate local paraboloids at chosen nodes instead of local planes, thereby even reducing the computing time, and having the obtained surface sufficiently smooth.

In this paper we suggest a method for generating a surface approximating the given scattered data. The method is based on smoothing the data by using the moving total least squares method. We determine a global approximating function by first forming, at each point, a local approximant (local plane) in the sense of total least squares. In this way it is taken into consideration that errors occur in all data coordinates. The method is tested on several examples.

U članku se navode neke zanimljive pravilnosti i matematička svojstva vezana uz šahovsku ploču i samu igru, kao primjerice magični kvadrati na šahovskoj ploči, dokaz Pitagorinog teorema na šahovskoj ploči, Pascalov trokut itd.

Solving the parameter identification problems in applied research is usually an unstable numerical process. Special (cumulative) structure of the data in new product diffusion models gives the possibility of defining an efficient method for solving the parameter identification problem in this case. The method can be used regardless of whether the analytical solution of the differential equation describing the model is known or not. Another advantage of this method is the simplicity of its implementation and negligible computing time.

The estimation of optimal parameters in a mathematical model described by the generalized logistic function with saturation level $A$ and the asymmetry coefficient $Đgamma$ is a nonlinear least squares problem. In this paper we prove the existence of optimal parameters under considerably weaker conditions than those required in Š1Ć.

In this paper we consider the existence problem of the optimal parameters for the exponential function in the sense of ordinary as well as in the sense of total least squares. By a simple mathematical procedure we prove the existence theorem of the optimal parameters in the sense of ordinary least squares. Finally, we give some generalizations and possible applications.

Promatra se najjednostavniji problem eksterne balistike za vakuum, bez utjecaja specijalnih efekata (promjena sile teže o visini, rotacija Zemlje, Coriolisova sila, utjecaj Zemljinog magnetskog polja itd.). Daju se neka svojstva sustava balističkih parabola u slučaju ako je početna brzina konstantna a varira se izlazni kut ili ako je izlazni kut konstantan, a varira se početna brzina.

U radu se analiziraju rezultati primjene metode linearizacije na određivanje intervala i područja povjerenja za nepoznate parametre logističke i 3-parametarske eksponencijalne regresije.

U radu se opisuju i daju konstrukcije nekih osnovnih nemogućih figura, primjerice nemogućeg trokuta.

Rasprostiranje slojeva tla po dubini na nekom ograničenom području moguće je procijeniti na osnovi eksperimentalnih podataka. U ovom radu dana je metoda kojom se na osnovi eksperimentalnih podataka može dobiti eksplicitna funkcija, čiji graf predstavlje donju (odnosno gornju) plohu nekog sloja. Metoda se zasniva na primjeni pomične metode najmanjih kvadrata.

Matematički model često se opisuje pomoću jedne ili više diferencijalnih jednadžbi uz izvjestan broj unaprijed nepoznatih parametara. Parametri u modelu procjenjuju se na osnovi eksperimentalnih podataka. Početni uvjeti u modelu obično nisu poznati. U ovom radu dana je učinkovita metoda kojom je moguće procijeniti optimalne početne uvjete.

U radu je pokazana primjena potpune metode najmanjih kvadrata za procjenu parametara u matematičkom modelu. Ta metoda naročito je podesna ako su pogreške sadržane u izmjerenim vrijednostima i zavisne i nezavisne varijable. Metoda je ilustrirana primjerima linearne regresije.

U radu se analiziraju neki poznati modeli difuzije novog proizvoda u odnosu na pretpostavke o kretanju stope rasta difuzije. Na toj osnovi predlaže se jedan novi model difuzije novog proizvoda. Za navedene modele analiziraju se također broj i vrsta potrošačkih kategorija.

U radu je pokazana primjena neinterpolirajuće pomične metode najmanjih kvadrata za rješavanje problema identifikacije parametara u matematičkom modelu. Metoda je ilustrirana jednim numeričkim primjerom.

U radu su prikazane neke nove strategije otplate zajma kao dopuna radu (4) uz mogućnost proširenja navedenog softwarea.

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 progessive growth stage, i.e. phase. This study with the curves of growth of the Large White breed based on the gain intensity of the animals tested with the body weights 30 to 100 kg. According to the average daily gains the boars were devided into three groups (0.81-0.90 kg, 0.91-1.1 kg and 1.01 to 1.10 kg). For description of the growth rate asymmetric S- function was used modelled as: \[f(t)=\frac{; ; ; ; A}; ; ; ; {; ; ; ; /(1+be^{; ; ; ; -c \gamma t}; ; ; ; )^{; ; ; ; 1/\gamma}; ; ; ; }; ; ; ; .\] Regarding the neceessary time for achievement of certain mass, the stages are separated as: preparations $(t=t_B)$, growth-both progressive and degressive $(t=t_B=t_C)$ and phase saturation $(t=t_C)$. 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 time. The asymmetric S-function could be therefore used for valuation of the boars growth rate in older age based on the starting control measurements of animals.

U radu razmatramo jednu generalizaciju zakona rasta sa zasićenjem. Pokazano je kako se na osnovi zadanih podatka, primjenom Eulerove metode za rješavanje diferencijalnih jednadžbi i metode najmanjih kvadrata mogu dobiti optimalni parametri u modelu.

U radu je prikazan software kojim korisnik može birati strategiju otplate zajma uz minimalne uvjete, koji su unaprijed zadani. Predlaže se strategija konstantne otplate, strategija prema očekivanoj dobiti i strategija koju uz neke uvjete kreira sam korisnik.

Over-determined linear system is presented. Four types of feasible solutions are given: mean value of all determined subsystems, mean value of determined subsystem which solutions are in the confidence interval, minimum square values for absolute differences and minimum relative square values of all equations. The feasibility of solutions is discussed.

U radu je prikazan model optimalnog proizvodnog programa mesne industrije na osnovi kojeg je izrađen i odgovarajući korisnički software. Model ne daje kompleksno rješenje za definiranje optimalnog proizvodnog programa u mesnoj industriji, ali može predstavljati važan instrument u donošenju brzih poslovnih odluka.

U radu su prikazani matematički modeli koji služe za opisivanje ponašanja prirodnih zakona u različitim primjenjenim istraživanjima. Matematički gledano, to su nelinearni problemi najmanjih kvadrata. Korisnički program koji podržava ove modele omogućava raznovrsnu primjenu u poljoprivredi, kao i u drugim područjima.

U ekonomskim istraživanjimma često je potrebno neku pojavu opisati funkcijom čija se vrijednost asimptotski približava razini zasićenja. U radu se promatra klasa tzv. S-funkcija, koje služe za kratkoročne i dugoročne prognoze. Poseban naglasak dat je na analizu klasa funkcija, koje ovisno o parametru, mogu imati pozitivnu ili negativnu asimetriju ili se mogu preobraziti u poznatu logističku funkciju. Procjenjivanje parametara ovakvih funkcija je složen nelinearni problem najmanjih kvadrata, koji ne mora uvijek imati rješenje. Ekonomska interpretacija svojstava tih funkcija je izuzetno značajna za strategijsko upravljanje ekonomskim sistemima.

U radu se razmatraju problemi najmanjih kvadrata. Dan je pregled matematičkih modela koji se najčešće javljaju u različitim znanstvenim područjima. Ukazano je na najvažnije metode za rješavanje i osnovne uvjete vezane uz egzistenciju rješenja ovih problema. Na kraju je detaljnije analizirana jedna klasa matematičkih modela koji se javljaju u širokom području znanstvenih istraživanja.

Certain economic phenomena are often considered in research through rate of change. Rates of change represent information which enable researchers to come to conclusions about tendencies and the intensities of observed phenomena. In applications the computation of rate of change is mostly carried out by using the geometric mean of ratios of data. The basic disadvantage of such an approach is the elimination of the influence of all data (except two of them), because the conclusions is carried out on the basis of the first and last datum. Besides, using the geometric mean, the rate of change can be computed only for the equidistant distributed data, and this also represents a limitation in its application. This paper points out the disadvantages of such an approach, introduces precise definition of the rate of change and proposes the manner in which this important economic inductor can be more accurately determined.