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Our purpose is to solve the system of differential equations of spherical curves in 3-dimensional euclidean space using a numerical method such as the Adomian Decomposition Method. In the different values of x, we compare the Adomian decomposition method solution with the exact solution. We demonstrate the obtained numerical results on tables and figures. Thus we prove the reliability of the proposed method with an example.

Our purpose is to solve the system of differential equations of spherical curves in 3-dimensional euclidean space using a numerical method such as the Adomian Decomposition Method. In the different values of x, we compare the Adomian decomposition method solution with the exact solution. We demonstrate the obtained numerical results on tables and figures. Thus we prove the reliability of the proposed method with an example.

This study deals with the singularly perturbed multi-point boundary value problem and an effective numerical method. The method analysis singularly perturbed problem with multi-point boundary value as theoretically and experimentally. It is shown that the presented method has first-order approximation in the discrete maximum norm. The numerical results are presented in table and graphs, and these results come out the validity of the theoretical analysis of our method.

Our purpose is to solve the system of differential equations of spherical curves in 3-dimensional euclidean space using a numerical method such as the Adomian Decomposition Method. In the different values of x, we compare the Adomian decomposition method solution with the exact solution. We demonstrate the obtained numerical results on tables and figures. Thus we prove the reliability of the proposed method with an example.

Our purpose is to solve the system of differential equations of spherical curves in 3-dimensional euclidean space using a numerical method such as the Adomian Decomposition Method. In the different values of x, we compare the Adomian decomposition method solution with the exact solution. We demonstrate the obtained numerical results on tables and figures. Thus we prove the reliability of the proposed method with an example.

Our purpose is to solve the system of differential equations of spherical curves in 3-dimensional euclidean space using a numerical method such as the Adomian Decomposition Method. In the different values of x, we compare the Adomian decomposition method solution with the exact solution. We demonstrate the obtained numerical results on tables and figures. Thus we prove the reliability of the proposed method with an example.

This study deals with the singularly perturbed multi-point boundary value problem and an effective numerical method. The method analysis singularly perturbed problem with multi-point boundary value as theoretically and experimentally. It is shown that the presented method has first-order approximation in the discrete maximum norm. The numerical results are presented in table and graphs, and these results come out the validity of the theoretical analysis of our method.

Our purpose is to solve the system of differential equations of spherical curves in 3-dimensional euclidean space using a numerical method such as the Adomian Decomposition Method. In the different values of x, we compare the Adomian decomposition method solution with the exact solution. We demonstrate the obtained numerical results on tables and figures. Thus we prove the reliability of the proposed method with an example.

Pozadina istraživanja. Upotreba pšeničnih klica i njihovog ulja ograničena je zbog velike aktivnosti enzima u klicama i prisutnosti nezasićenih masnih kiselina u ulju, što zahtijeva primjenu stabilizacijskih tehnika. Eksperimentalni pristup. U ovom su istraživanju procijenjeni učinci metoda stabilizacije (suho zagrijavanje u konvekcijskoj pećnici na 90 i 160 °C, mikrovalno zračenje na 180 i 360 W i uparavanje u autoklavu) na pšenične klice i njihovo ulje. Rezultati i zaključci. Uparavanje je prouzročilo najdramatičnije promjene aktivnosti lipoksigenaze, udjela slobodnih masnih kiselina, aktivnosti uklanjanja radikala DPPH i masenih udjela tokoferola i tokotrienola. Niži peroksidni broj izmjeren je u uzorcima ulja obrađenim konvekcijskim zagrijavanjem (160 °C) i parom na temperaturama iznad 100 °C. Međutim, vrijednosti p-anisidina u uzorcima tretiranim na višim temperaturama bile su znatno veće od onih u uzorcima stabiliziranim pri nižim temperaturama. Zagrijavanje u pećnici na 160 °C je nakon uparavanja bilo jedno od najučinkovitijih postupaka za inaktivaciju lipoksigenaze. Primjena pare bitno je smanjila maseni udjel ukupnih tokoferola, što je izravno povezano s povećanim gubitkom β-tokoferola. Suprotno tome, pronađeno je znatno više γ- i δ-tokoferola te homologa tokotrienola u uparenim uzorcima. Izomeri najotporniji na procese stabilizacije bili su α-tokoferol i γ-tokotrienol. Novina i znanstveni doprinos. Ovo istraživanje pokazuje da metoda zagrijavanja u pećnici na visokoj temperaturi, koja se često koristi u industriji za toplinsku stabilizaciju pšeničnih klica, ne poboljšava njihovu oksidacijsku stabilnost u usporedbi s obradom parom i mikrovalovima. Uparavanje odgađa oksidacijske procese u klici te inhibira aktivnost lipoksigenaze, a osim toga smanjuje gubitak tokotrienola. Za industrijsku se primjenu preporučuje uporaba mikrovalne pećnice male snage (180 umjesto 360 W) i zagrijavanje u pećnici na nižoj temperaturi (90 umjesto 160 °C)., Research background. Utilization of wheat germ and wheat germ oil is limited due to high enzymatic activity and the presence of unsaturated fatty acids, which require stabilization techniques to overcome this problem. Experimental approach. In this study, the effects of stabilization methods (dry convective oven heating at 90 and 160 °C, microwave radiation at 180 and 360 W, and autoclave steaming) on both wheat germ and its oil were evaluated. Results and conclusions. Steaming caused the most dramatic changes in lipoxygenase activity, free fatty acid content, DPPH radical scavenging activity, and mass fractions of tocopherols and tocotrienols. Lower peroxide values were measured in the oil samples treated with convectional heating (160 °C) and steaming at temperatures above 100 °C. However, p-anisidine values of samples treated at higher temperatures were considerably greater than those of samples stabilized at lower temperatures. Oven heating at 160 °C was also one of the most effective treatments, after steaming, for the inactivation of lipoxygenase. Steaming significantly reduced mass fraction of total tocopherols, which was directly associated with the greater loss of β-tocopherol content. On the contrary, γ- and δ-tocopherol and tocotrienol homologues were abundant with higher amounts in steamed samples. α-Tocopherol and γ-tocotrienol were the most resistant isomers to stabilization processes. Novelty and scientific contribution. This study shows that the high temperature oven heating method, which is widely used in the industry for thermal stabilization of wheat germ, does not provide an advantage in oxidative stability compared to steaming and microwave applications. Steaming delayed oxidation in the germ, while further inhibiting lipoxygenase activity. Moreover, tocotrienols were more conservable. In industrial application, low-power microwave (180 instead of 360 W) and oven heating at lower temperature (90 instead of 160 °C) would be preferable.

In the present study, hybrid method (differential transform and finite difference methods) is selected to determine the numerical solution of the foam drainage equation. The strength of the proposed method is proven with an example for various values of c,t and x. Numerical solutions obtained with the application of the hybrid method are compared with exact solutions. Also, in the findings section the applied method was supported with tables and figures.

In the present study, hybrid method (differential transform and finite difference methods) is selected to determine the numerical solution of the foam drainage equation. The strength of the proposed method is proven with an example for various values of c,t and x. Numerical solutions obtained with the application of the hybrid method are compared with exact solutions. Also, in the findings section the applied method was supported with tables and figures.