An optimal sixteenth order family of methods for solving nonlinear equations and their basins of attraction

We propose a new family of iterative methods for finding the simple roots of nonlinear equation. The proposed method is four-point method with convergence order 16, which consists of four steps: the Newton step, an optional fourth order iteration scheme, an optional eighth order iteration scheme and the step constructed using the divided difference. By reason of the new iteration scheme requiring four function evaluations and one first derivative evaluation per iteration, the method satisfies the optimality criterion in the sense of Kung-Traub\u27s conjecture and achieves a high efficiency index $16^{1/5} approx 1.7411$. Computational results support theoretical analysis and confirm the efficiency. The basins of attraction of the new presented algorithms are also compared to the existing methods with encouraging results

On the optimality of some multi-point methods for finding multiple roots of nonlinear equation

This paper deals with the problem of determining the multiple roots of nonlinear equations, where the multiplicity of the roots is known. The paper contains some remarks on the optimality of the recently published methods [B. Liu, X. Zhou, A new family of fourth-order methods for multiple roots of nonlinear equations, Nonlinear Anal. Model. Control, 18(2):143–152, 2013] and [X. Zhou, X. Chen, Y. Song, Families of third- and fourth-order methods for multiple roots of nonlinear equations, Appl. Math. Comput., 219(11):6030–6038, 2013]. Separate analysis of odd and even multiplicity, has shown the cases where those methods lose their optimal convergence properties. Numerical experiments are made and they support theoretical analysis

Application of the C-Credibility Measure

The complex logistics process involves numerous dynamic uncertainties and internal risks. Those risks alone or in interaction with other groups of risks can affect the entire system. This paper proposes the application of the new measure, c-credibility measure to the complex system such as logistic process. For this purpose, fuzzy logic system for risk assessments in logistic process is proposed. C-credibility selection through ranking is implemented in the simulation process with crh membership function definition on the fuzzy variable to calculate credibility value. Numerical analysis of the proposed approach with obtained results and the related discussion is presented

A common fixed point result in strong JS-metric space

The aim of our paper is the prove that the common fixed point result due to Sehgal and Thomas is valied in a class of generalized metric spaces in sence of Jleli and Samet.Bulletin t. 151 de l'Académie serbe des sciences et des arts, Classe des sciences mathématiques et naturelles, sciences mathematiques no 4

Kapaciteti i proizvodnja mleka u Srbiji

Milk production trends tend to rise, however due to market demands and the living standard of the population a more significant production increase is substantially limited. Considering the declining trend of milking cows a major total milk production increase may be achieved by raising the milking capacity per animal. In Serbia there is an excess of dairy plants considering the achieved milk production. This results in a declining competitiveness between dairy plants on both the domestic and foreign market. Diary plants are satisfied with the premium awards because these contribute to a continuous and permanent milk supply. Some major dairy plants offer expertise help to producers with regard to production specialization.Proizvodnja mleka je u porastu, ali je značajnije povećanje limitirano zahtevima tržišta i standardom stanovništva. Imajući u vidu trend smanjenja broja muznih krava do veće ukupne proizvodnje možemo doći jedino povećanjem mlečnosti po grlu. U odnosu na ostvarenu proizvodnju mleka Srbija ima previše mlekara. Posledica ovakvog stanja je smanjena konkurentnost mlekara na domaćem i stranom tržištu. Iako postojeći sistem isplate premija za mleko odgovara mlekarama, jer im obezbeđuje stalne dobavljače, one najveće različitim merama pružaju pomoć proizvođačima u pogledu veće specijalizacije proizvodnje

A new optimal family of three-step methods for efficient finding of a simple root of a nonlinear equation

This study presents a new efficient family of eighth order methods for finding the simple root of nonlinear equation. The new family consists of three steps: the Newton\u27s step, any optimal fourth order iteration scheme and the simply structured third step which improves the convergence order up to at least eight, and ensures the efficiency index 1.6818. For several relevant numerical test functions, the numerical performances confirm the theoretical results

Specifičnosti zahteva standarda 15: Studije na daljinu

Ovaj rad je podržan od strane projekta „Novi trendovi u nastavi i naučnim istraživanjima teorijske I primenje matematike”, Departmana za opšte discipline u tehnici, Fakulteta tehničkih nauka, Univerziteta u Novom Sadu.U skladu sa Pravilnikom o standardima i postupku akreditacije studijskih programa ("Sl. glasnik RS“ 88/17), standardom 15. Studije na daljinu, definisani su osnovni zahtevi i kriterijumi ovog standarda. Sve je veća zainteresovanost potencijalnih studenata, kao i studenata koji već studiraju, za ovom vrstom studija, što visokoškolske ustanove upućuje na akreditaciju svojih studijskih programa, prilagođavanje studijama na daljinu i novog pristupa u širenju obrazovanja. Pored osnovnih zahteva standarda za akreditaciju studijskih programa, standard 15 ima svoje specifičnosti, kako u pogledu opreme i komunikaciono-informatičke tehnologije, DLS - Distance Learning System-a, tako i edukovanih studenata i nastavnika za upotrebu i korišćenje sistema. Novo okruženje za učenje i nastavu uvodi u praksu nove metode nastave koje zahtevaju prilagođavanje i novi pristup formiranju nastavnih materijala od strane nastanika. Sistemi omogućuju niz aktivnosti u ovom smislu, a posebno ističemo formiranje testova znanja. U radu će biti razmatrani važniji zahtevi ovog standarda, i predložena određena rešenja u cilju što kvalitetnijeg ispunjenja ovih zahteva.http://www.trend.uns.ac.rs/stskup/sadrzaj-2019.htmlPublishe

Contemporary mathematical problems

U ovom radu je predstavljen koncept procesa neizvesnosti, kao proširenje teorije neizvesnosti (uncertainty theory). Proces neizvesnosti, zasnovan na Liovom integralu, predstavlja niz promenljivih indeksiranih kroz vreme. U cilju proučavanja integrala (defnisanih u ovoj teoriji) u različitim procesima neizvesnosti, uvedeni su osnovni pojmovi i razmatrane neke osobine i tvrđenja.http://www.mk.rs.ba/wp-content/uploads/2018/07/call_for_papers_2018-2.pdfPublishe

Adaptive Fuzzy Model for Determining Quality Assessment Services in the Supply Chain

The problem that is being addressed in this paper is to improve the services provided by company and achieve better communication between companies in the supply chain. Therefore, a qualitative assessment of service has been required. This service is characterized by a group of parameters, which are often inaccurately estimated values, as well as their importance for the evaluation system. This is often the result of assessor´s uncertainty, variability of conditions, etc. Therefore, in the context of AM4SCM (Adaptive Model for Supply Chain Management) a mathematical model for evaluating the quality of services has been developed (FAM4QS - Fuzzy Aggregation Method for Quality Service) which is based on the fuzzy arithmetic. Selection of different values for the degrees of fuzzy power mean, which are used for evaluation of parameters or groups of parameters of the system and the service, contributes to a better assessment and it is due to the varying nature of the parameters. The observed model was simulated on 17 supply chains on the territory of the Republic of Serbia. Service quality assessment is carried out based on data from the user requirements - participants of supply chains binding the so-called fuzzy aggregation function

Produktivnost i profitabilnost u proizvodnji kupusa

The authors perform an analysis of economic indicators in the production of cabbage in the Republic of Macedonia, based on statistics (2005- 2009) and data from directly interviewed thirty family holdings. In doing so, they found that cabbage in this country is produced on average area of 3,947 hectares. Total production, with an average yield of 22,342 kg/ha, is 88,182 tones in average, which is 11.4% of the total production of horticultural products. Production of cabbage is mainly concentrated in three statistical regions, as follows: 37.43% in the Southeast region, 12.54% in Pelagonia region and 11.15% in Polog region of the total area in the country. Because of that, surveys are carried out in these three regions. Labor productivity varies between 30.0 kg/h in the Southeast and 34.9 kg/h in Polog region and inside the region 26.7 to 39.2 kg/h. Although average yields at the surveyed producers are largest in Polog region (on average 39,980 kg/ha), the efficiency of invested assets is lowest. The profit is 211.6 EUR/ha in average. This is why they sell the entire production on the wholesale market where the purchase price is lowest. In contrast, highest profit (on average 1,389.4 EUR/ha) accomplish the producers from Pelagonia region because they produce with lowest unit costs and sell the products with highest price, compared to other producers.Autori su, na bazi statističkih (2005-2009) i podataka direktno anketiranih trideset porodičnih gazdinstava, izvršili analizu ekonomskih pokazatelja u proizvodnji kupusa u Republici Makedoniji. Utvrdili su da se u Republici Makedoniji kupus proizvodi na prosečnoj površini od 3. 947 hektara. Ukupna proizvodnja, pri prosečnom prinosu od 22.342 kg/ha, iznosi 88.182 tona, što je 11,4% od ukupne proizvodnje povrtarskih proizvoda. Proizvodnja kupusa uglavnom je koncentrisana u tri statističkih regiona, i to: 37,43% u Jugoistočnom regionu, 12,54% u Pelagonijskom regionu i u Pološkom regionu 11,15% od ukupne površine u zemlji. Produktivnost rada kreće se između 30,0 kg/h u Jugoistočnom i 34,9 kg/h u Pološkom regionu, a unutar regiona od 26,7 do 39,2 kg/h. Iako su prosečni prinosi kod anketiranih proizvođači iz Pološkog regiona najveći (u proseku 39.980 kg/ha), efikasnost uloženih sredstava je najniža. Profit u proseku iznosi 211,6 EUR/ha jer poizvođači svu proizvodnju plasiraju na kvantaškim pijacama, gde je otkupna cena najniža. Nasuprot ovome, najveći profit (u proseku 1.389,4 EUR/ha) ostvaruju proizvođači iz Pelagonijskog regiona, zato što proizvode po najnižoj ceni koštanja, a prodaju po najvišoj prodajnoj ceni u poređenju sa ostalim proizvođačima