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

Possibilities and optimization of landing on the southern hemisphere of Mars

Skoro 40 godina nakon prvog uspesnog sletanja na Mars, istrazivanje njegove povrsine pomocu kosmickih letelica i dalje predstavlja ogroman naucni i tehnoloski izazov. Ovo se pre svega odnosi na Marsove juzne visoravni, koje se protezu na velikom delu njegove juzne hemisfere, na koje do sada nije izvrseno nijedno uspesno sletanje. Sa druge strane, na severne nizije, koje se prostiru na velikom delu severne hemisfere, do sada je izvrseno 7 uspesnih sletanja. Ova razlika je posledica specicne topograje Marsove povrsine usled takozvane globalne ili hemisfericne dihotomije Marsa, koja predstavlja jedinstvenu karakteristiku u Suncevom sistemu. Usled razlike u elevaci- jama povrsine, letelice koje slecu na juzne visoravni imaju na raspolaganju tanji sloj atmosfere koji mogu da iskoriste za disipaciju kineticke energije. Buduci da letelice sa interplanetarnih putanja ulaze u atmosferu Marsa hiperbolickim brzinama, nji- hova kineticka energija je veoma velika i mogucnost da se ona smanji kroz interakciju sa atmosferom je od odlucujuceg znacaja za sletanje na lokacije sa velikom elevaci- jom. Osim topografske razlike izmed-u severnih nizija i juznih visoravni, postoji i velika razlika u broju udarnih kratera izmed-u ovih oblasti, sto ukazuje na veliku razliku u starosti. Procenjuje se da su juzne visoravni nekoliko milijardi godina starije nego severne nizije, koje su u relativno bliskoj proslosti bile izlozene snaznoj vulkanskoj aktivnosti. Ovako velika razlika u starosti predstavlja motivaciju za istrazivanje celokupne povrsine Marsa u cilju razumevanja njegove slozene geoloske evolucije. Osim toga, veliki broj otvorenih basena, koji su otkriveni na juznim visoravnima, ukazuju na to da su ove regije u proslosti mogle biti prekrivene tecnom vodom, sto predstavlja jedan od najznacajnijih razloga za istrazivanje ovih lokacija...Almost 40 years after the rst successful landing on Mars, exploration of its surface still presents enormous scientic and technological challenge. This particularly holds for the Mars southern highlands, which cover large part of the southern hemisphere where no successful landings have been achieved up to date. On the other hand, in the northern lowlands, which spans most of the northern hemisphere, there has been 7 successful landings. This difference is consequence of the specic topography of the Martian surface due to so-called global or hemispheric dichotomy, which is a unique characteristic in the Solar system. Due to the difference in the surface elevations, the vehicle trying to land on the southern highlands has thinner layer of the atmosphere that can use for the dissipation of its kinetic energy. Since the vehicles from the interplanetary trajectories enter the Martian atmosphere with hyperbolic velocities, their kinetic energy is extremely large and possibility for its dissipation through the interaction with the atmosphere has crucial importance for the landing on the locations with high elevations. Beside the differences in topography between northern lowlands and southern highlands, there is also a big difference in the number of impact craters between these two regions. This fact indicates that the southern highlands are several billion years older than the northern lowlands, which were exposed to strong volcanic activity in the relatively recent past. Such huge difference in age is strong motivation to explore the entire surface of Mars in order to understand its complex geological evolution. In addition, large number of open basins discovered in the southern highlands suggests that these regions could contain liquid water in..

Optimization of ATM filling-in with cash

This report presents an approach for modeling daily cash demand for all ATMs in the Credit Agricole Bank network in Serbia. The approach is based on time series and regression methods for forecasting an optimal amount of money that should be placed daily in the ATMs in order to meet customers’ demands and mimimize costs of the bank. Three different types of costs were considered: cash freezing costs, transportation costs and insurance costs. The performance of the resulting forecasts were compared with results of the application that bank uses for prediciton of the time and the amount of filling-in for each ATM based on historical data

Rheological properties of hydroxypropylmethyl cellulose/sodium dodecylsulfate mixtures

Rheological properties of mixtures of hydroxypropylmethyl cellulose (HPMC), a nonionic associative cellulose ether, and sodium dodecylsulfate (SDS), an anionic surfactant, were investigated by viscosity measurements performed at different shear rates (0.1-6000 s-1). HPMC/SDS mixtures containing different concentrations of SDS (CSDS=0.00-3.50 % w/w) and HPMC concentrations which corresponded to the overlap parameter c/c*=3, 6, and 12 were prepared. All HPMC/SDS mixtures were found to be shear-thinning when examined in a low-end-to mid-range of the applied shear rates. The degree of shear-thinning, n, and viscosity of the mixtures were influenced by composition of HPMC/SDS mixtures and HPMC-SDS complex formation. The changes in n ranged from values typical for highly shear thinning to almost perfectly Newtonian liquids, and were more pronounced as c/c* was increased from 3 to 6 and 12. A change in flow profile and a buildup of the first normal stress difference (N1) was observed in HPMC/SDS mixtures with c/c*=6 and 12 and CSDS 0.55-1.00 % and 0.55-2.50 %, respectively, when a critical shear rate, crit. was exceeded, suggesting that a shear-induced structure formation in the mixtures took place. [Projekat Ministartsva nauke Republike Srbije, br. Grant III 46010

Enhancement of the electrocatalytic activity of Ni electrode for hydrogen evolution by electrodeposited V and Co on its surface

Enhancement of the electrocatalytic effect of Ni electrode for hydrogen evolution reaction (HER) by co-electrodeposited V and Co at metallic Ni (Ni-V-Co) was studied by using quasi-potentiostatic polarization technique from 1 M KOH at 25 ºC. The obtained exchange current density for HER with Ni-V-Co electrode, (5.5x10-4 Acm-2), is about two orders of magnitude higher than for metallic Ni electrode. The results suggested the existence of the synergetic effect of V and Co deposit on the catalytic activity of Ni electrode for HER. By using X-ray fluorescence (XRF) analysis the presence of Co and V at metallic Ni support was proved.Physical chemistry 2006 : 8th international conference on fundamental and applied aspects of physical chemistry; Belgrade (Serbia); 26-29 September 200

Ab Initio Study of Graphene Interaction with O-2, O, and O-

A systematic ab initio (DFT-GGA) study of adsorption of various oxygen species on graphene has been performed in order to find out general trends and provide a good starting point to analyze the oxidation of more complex carbon materials. Particular attention was paid to finding an appropriate supercell model. According to our findings, atomic O is characterized by stable adsorption on graphene and very strong adsorption on defective graphene. On the other hand, O-2 does not adsorb on graphene and is allowed to diffuse freely to the defect, where it is expected to dissociate into two strongly adsorbed O atoms. The obtained results were compared with available theoretical data in the literature and good agreement was achieved

Determination of the BTEX compounds in building materials and waste samples containing mineral oils as the main component using Headspace GC/FID

BTEX jedinjenja su lako isparlјiva aromatična jedinjenja, klasifikovana kao toksična jedinjenja i kao takva su opasna po zdravlje ljudii životnu sredinu. Predmet istraživanja u ovom radu su BTEX jedinjenja u uzorcima građevinskog materijala sa mineralnim uljima kao glavnom komponentom. S obzirom da su ona sastavni deo mineralnih ulja, važno je odrediti njihovo prisustvo, koncentraciju i dalju distribuciju u životnu sredinu. Tokom eksperimentalnog istraživanja, ispitivan je sadržaj BTEX jedinjenja: benzen, toluen, ksilen (o, p, m) i etilbenzen u uzorcima mineralnih ulja iz građevinskih materijala i otpada. Metoda za određivanje ovih jedinjenja, kao i za njihovu kvantifikaciju u uzorcima mineralnih ulja, razvijena je u Laboratoriji za fizičku hemiju, Instituta za nuklearne nauke „Vinča“, Univerziteta u Beogradu, modifikacijom i unapređenjem standardnih metoda[1, 2]. Za potrebe ovog istraživanja,u eksperimentalnom delu, primenom Headspace ekstrakcije sa GC-FID tehnikom, određen je kvalitativni i kvantitativni sadržaj BTEX jedinjenja, što istovremeno predstavlja i validaciju ispitivane metode, kao i određivanje njene merne nesigurnosti (Tabela 1.).Parametri za validaciju ove metode su bili: specifičnost, linearnost, granica detekcije (LOD), granica kvantifikacije (LOQ), ponovljivost i tačnost svakog jedinjenja. Primenom opisane metode postignuta je pouzdana identifikacija ispitivanih jedinjenja. Identifikacija se ostvaruje poređenjem retencionih vremena ispitivanih jedinjenja sa retencionim vremenima analitičkih standarda. FID detektor pokazuje linearan odgovor u opsegu 0,1 do 10 µg , odnosno R ≥ 0,99. Vrednosti standarda na kalibracionoj krivi su potvrdili preciznost metode. Relativna standardna devijacija RSD je ispod 5%, što dokazuje da je metoda tačna i reproduktivna [3-8]. Predstavljena metoda je validirana kao pouzdana, precizna i tačna za potrebe kontrole kvaliteta mineralnih ulja koja su korišćena ili će se koristiti u toku izgradnje građevinskih objekata, kao i za otpadni materijal.8th Symposium Chemistry and Environmental Protection : May 30 - June 1, Kruševac, 2018

The LSST Era of Supermassive Black Hole Accretion Disk Reverberation Mapping

peer reviewedThe Vera C. Rubin Observatory's Legacy Survey of Space and Time (LSST) will detect an unprecedentedly large sample of actively accreting supermassive black holes with typical accretion disk (AD) sizes of a few light days. This brings us to face challenges in the reverberation mapping (RM) measurement of AD sizes in active galactic nuclei using interband continuum delays. We examine the effect of LSST cadence strategies on AD RM using our metric AGN_TimeLagMetric. It accounts for redshift, cadence, the magnitude limit, and magnitude corrections for dust extinction. Running our metric on different LSST cadence strategies, we produce an atlas of the performance estimations for LSST photometric RM measurements. We provide an upper limit on the estimated number of quasars for which the AD time lag can be computed within 0 1000 sources in each deep drilling field (DDF; (10 deg2)) in any filter, with the redshift distribution of these sources peaking at z ≍ 1. We find the LSST observation strategies with a good cadence (≲5 days) and a long cumulative season (~9 yr), as proposed for LSST DDF, are favored for the AD size measurement. We create synthetic LSST light curves for the most suitable DDF cadences and determine RM time lags to demonstrate the impact of the best cadences based on the proposed metric

Possibilities and optimization of landing on the southern hemisphere of Mars

Skoro 40 godina nakon prvog uspesnog sletanja na Mars, istrazivanje njegove povrsine pomocu kosmickih letelica i dalje predstavlja ogroman naucni i tehnoloski izazov. Ovo se pre svega odnosi na Marsove juzne visoravni, koje se protezu na velikom delu njegove juzne hemisfere, na koje do sada nije izvrseno nijedno uspesno sletanje. Sa druge strane, na severne nizije, koje se prostiru na velikom delu severne hemisfere, do sada je izvrseno 7 uspesnih sletanja. Ova razlika je posledica specicne topograje Marsove povrsine usled takozvane globalne ili hemisfericne dihotomije Marsa, koja predstavlja jedinstvenu karakteristiku u Suncevom sistemu. Usled razlike u elevaci- jama povrsine, letelice koje slecu na juzne visoravni imaju na raspolaganju tanji sloj atmosfere koji mogu da iskoriste za disipaciju kineticke energije. Buduci da letelice sa interplanetarnih putanja ulaze u atmosferu Marsa hiperbolickim brzinama, nji- hova kineticka energija je veoma velika i mogucnost da se ona smanji kroz interakciju sa atmosferom je od odlucujuceg znacaja za sletanje na lokacije sa velikom elevaci- jom. Osim topografske razlike izmed-u severnih nizija i juznih visoravni, postoji i velika razlika u broju udarnih kratera izmed-u ovih oblasti, sto ukazuje na veliku razliku u starosti. Procenjuje se da su juzne visoravni nekoliko milijardi godina starije nego severne nizije, koje su u relativno bliskoj proslosti bile izlozene snaznoj vulkanskoj aktivnosti. Ovako velika razlika u starosti predstavlja motivaciju za istrazivanje celokupne povrsine Marsa u cilju razumevanja njegove slozene geoloske evolucije. Osim toga, veliki broj otvorenih basena, koji su otkriveni na juznim visoravnima, ukazuju na to da su ove regije u proslosti mogle biti prekrivene tecnom vodom, sto predstavlja jedan od najznacajnijih razloga za istrazivanje ovih lokacija...Almost 40 years after the rst successful landing on Mars, exploration of its surface still presents enormous scientic and technological challenge. This particularly holds for the Mars southern highlands, which cover large part of the southern hemisphere where no successful landings have been achieved up to date. On the other hand, in the northern lowlands, which spans most of the northern hemisphere, there has been 7 successful landings. This difference is consequence of the specic topography of the Martian surface due to so-called global or hemispheric dichotomy, which is a unique characteristic in the Solar system. Due to the difference in the surface elevations, the vehicle trying to land on the southern highlands has thinner layer of the atmosphere that can use for the dissipation of its kinetic energy. Since the vehicles from the interplanetary trajectories enter the Martian atmosphere with hyperbolic velocities, their kinetic energy is extremely large and possibility for its dissipation through the interaction with the atmosphere has crucial importance for the landing on the locations with high elevations. Beside the differences in topography between northern lowlands and southern highlands, there is also a big difference in the number of impact craters between these two regions. This fact indicates that the southern highlands are several billion years older than the northern lowlands, which were exposed to strong volcanic activity in the relatively recent past. Such huge difference in age is strong motivation to explore the entire surface of Mars in order to understand its complex geological evolution. In addition, large number of open basins discovered in the southern highlands suggests that these regions could contain liquid water in..