New Examples of Systems of the Kowalevski Type

A new examples of integrable dynamical systems are constructed. An integration procedure leading to genus two theta-functions is presented. It is based on a recent notion of discriminantly separable polynomials. They have appeared in a recent reconsideration of the celebrated Kowalevski top, and their role here is analogue to the situation with the classical Kowalevski integration procedure.Comment: 17 page

Billiard algebra, integrable line congruences, and double reflection nets

The billiard systems within quadrics, playing the role of discrete analogues of geodesics on ellipsoids, are incorporated into the theory of integrable quad-graphs. An initial observation is that the Six-pointed star theorem, as the operational consistency for the billiard algebra, is equivalent to an integrabilty condition of a line congruence. A new notion of the double-reflection nets as a subclass of dual Darboux nets associated with pencils of quadrics is introduced, basic properies and several examples are presented. Corresponding Yang-Baxter maps, associated with pencils of quadrics are defined and discussed.Comment: 18 pages, 8 figure

Uticaj promene načina korišćenja zemljišta na strukturu livadske crnice u zapadnoj Srbiji

Changes in land use can significantly affect aggregate distribution and water stability of structural aggregates. This study was conducted in the Kolubara River Valley, Western Serbia, to determine the effects of land use changes on composition and water stability of aggregates in humus horizons (0-30 cm) of noncarbonated Gleyic Fluvisols. This study was conducted at nine sites, where each site contained two adjacent land uses of natural grassland and arable land which underwent crop rotation for >100 years. Soil samples were taken from depths of 0-10, 10-20 and 20-30 cm for each land use. When the grassland was converted into arable land, the content of the agronomically most valuable aggregates (0.25-10 mm) of cultivated soils for a depth of 0-30 cm was significantly reduced by 22-40%, while the percentage of cloddy aggregates (>10 mm) increased by 41-68%, compared to grassland. In addition, the long-term arable soil had significantly (p lt 0.05) lower aggregate stability, determined by wet sieving, than grassland. The lowest aggregate stability was found in aggregates > 3 mm. Their content is ≈ 2.3 times lower in arable soil (12.6%) than in grassland (28.6%) at a depth of 0-10 cm. In addition, meanweight diameters of dry and wetstable aggregates and structure coefficient showed significant differences between land use at a depth of 0-30 cm. The results showed that the conversion of natural grassland to arable land in the lowland ecosystems of Western Serbia degraded aggregate distribution and stability.Istraživanja su sprovedena u dolini reke Kolubare da bi se utvrdili efekti promene načina korišćenja zemljišta na agregatni sastav i vodootpornost strukturnih agregata u humusnom horizontu (0-30 cm) beskarbonatne livadske crnice. Izabrano je devet lokacija koje su na bliskom rastojanju imale površine pod prirodnom livadskom vegetacijom i oranice koje su stvorene pre više od 100 godina razoravanjem prirodnih livada. Nakon razoravanja prirodnih livada i njihovog pretvaranja u oranice, sadržaj agronomski najpovoljnijih strukturnih agregata (prečnika 0,25-10 mm) u oranicama na dubini 0-30 cm, značajno je smanjen, za 22-40%, dok je sadržaj grudvastih agregata (>10 mm) povećan za 41-68 %, u poređenju sa livadom. Pored toga, višegodišnje oranice imaju značajno (p lt 0,05) manju vodootpornost strukturnih agregata, određenih mokrim prosejavanjem, od livada. Najmanju vodootpornost pokazali su strukturni agregati prečnika >3 mm. Takođe, prosečni maseni prečnici suvih i vodootpornih agregata i koeficijent strukture pokazali su značajne razlike između različitih načina korišćenja zemljišta na dubini 0-30 cm. Razoravanje livadskih crnica pod prirodnom livadskom vegetacijom istraženog područja i njihova višegodišnja obrada doveli su do značajnih negativnih promena agregatnog sastava i smanjenja vodootpornosti strukturnih agregata

Systems of Hess-Appel'rot Type and Zhukovskii Property

We start with a review of a class of systems with invariant relations, so called {\it systems of Hess--Appel'rot type} that generalizes the classical Hess--Appel'rot rigid body case. The systems of Hess-Appel'rot type carry an interesting combination of both integrable and non-integrable properties. Further, following integrable line, we study partial reductions and systems having what we call the {\it Zhukovskii property}: these are Hamiltonian systems with invariant relations, such that partially reduced systems are completely integrable. We prove that the Zhukovskii property is a quite general characteristic of systems of Hess-Appel'rote type. The partial reduction neglects the most interesting and challenging part of the dynamics of the systems of Hess-Appel'rot type - the non-integrable part, some analysis of which may be seen as a reconstruction problem. We show that an integrable system, the magnetic pendulum on the oriented Grassmannian $Gr^+(4,2)$ has natural interpretation within Zhukovskii property and it is equivalent to a partial reduction of certain system of Hess-Appel'rot type. We perform a classical and an algebro-geometric integration of the system, as an example of an isoholomorphic system. The paper presents a lot of examples of systems of Hess-Appel'rot type, giving an additional argument in favor of further study of this class of systems.Comment: 42 page

Assessment of soil erosion rates in Southeastern Serbia using nuclear techniques

Erozija zemljišta vodom predstavlja vaţan problem zaštite ţivotne sredine u Srbiji. Posledica erozije je degradacija zemljišnih resursa, smanjenje plodnosti zemljišta i redukcija poljoprivredne proizvodnje. Najveši intenzitet erozije uoţen je na obradivom zemljištu na strmim padinama. Pretvaranje pašnjaka u obradivo zemljište uticalo je na povešanje prostora zahvašenih procesom erozije. U ovom radu prikazani su preli-minarni rezultati projekta tehniţke saradnje sa MeŤunarodnom agencijom za atomsku energiju ̳Jaţanje kapaciteta za procenu intenziteta erozije zemljišta koriššenjem nuklearnih tehnika u cilju podrške odrţivom upravljanju zemljištem‘ (SRB5003) ţiji je cilj procena intenziteta erozije zemljišta 137Cs-metodom. Istraţivanja sprovedena u basenima Pţinje i Juţne Morave ukazala su na intenzivnu eroziju na ovom prostoru. Istraţivanja še biti nastavljena na nekoliko drugih lokacija, a rezultati še biti upotrebljeni za podršku nacionalnim programima konzervacije zemljišta.Soil erosion by water presents an important environmental problem in Serbia resulting in degradation of the soil resources, reducing soil fertility and agricultural production. The highest intensity of erosion was observed at cultivated land occupying steep slopes. The conversion of pastures to arable land enhances this problem. This study presents the preliminary results of Technical Cooperation Project of International Atomic Energy Agency ̳Strengthening the Capacities for Soil Erosion Assessment Using Nuclear Techniques to Support Implementation of Sustainable Land Management Practices‘(SRB5003) aimed at estimation of soil erosion rates using the 137Cs-method. The investigation of Pčinja and South Morava River Basins in southeastern Serbia revealed intensive erosion in the area. The investigation will continue at several other sites and the results will be used to support national soil conservation policy.Proceedings: [http://vinar.vin.bg.ac.rs/handle/123456789/8681]XXX симпозијум ДЗЗСЦГ (Друштва за заштиту од зрачења Србије и Црне Горе), 2- 4. октобар 2019. године, Дивчибаре, Србиј

Influence of Acidity and Extraction Time on the Recovery of Flavonoids from Grape Skin Pomace Optimized by Response Surface Methodology

Grape pomace is recognized as an economical source for the recovery of a large number of biologically active compounds, such as polyphenols. Grape pomace extracts can be successfully used as raw material for functional foods production, since they are generally recognized as safe for the food industry. This study aimed to quantify the amounts of recovered flavonoids (total flavonoids, proanthocyanidins, anthocyanins, and flavonols) from grape skin pomace (Vitis vinifera L. cv. Merlot) under conventional extraction with different acidities (0.5 % – 1 % HCl) and lengths of extraction time (30–60 minutes). The grand average values in this study were as follows: (i) proanthocyanidins 12.08±0.25 mg CE g–1 d.m., (ii) anthocyanins 2.17±1.02 mg Mvd-3-glc g–1 d.m., (iii) flavonols 7.73±0.11 mg QE g–1 d.m., and (iv) total flavonoids 36.28±0.42 mg QE g–1 d.m. The amounts of studied polyphenols generally increased with acidity and length of extraction time. This relation was more evident for flavonols and total flavonoids, while less clear for other examined phenolics

Advanced hardware control for seven DOFs robotic arm-neuro arm

In this paper we will implement new hardware control for 7 DOFs (Degrees of freedom) advanced robotic arm research platform (NeuroArm) equipped with various sensors. New hardware platform consists of Nano Pi platform which is used as a PC platform for standard PLC (programmable logic controller's) unit and will replace old system that consists of 7 16-bit ATmega processors. The goal of new PLC which is based on Linux operating system (Debian distribution) that is patched by Xenomai real time system for reducing control response time and better entire system control. Robotic arm is powered by 7 DC motors which are controlled by two PWM4 (Pulse Width Modulation) modules. Position data is acquired from 1kΩ resistive sensors using RI8 (Resistive module) module and from optical quadrature encoders using one DI16 (Digital Input) module. Also other modules PWM4, RI8 and DI16 communicate with PikoAtlas CPU module by I2C bus

Systems of Hess-Appel'rot type

We construct higher-dimensional generalizations of the classical Hess-Appel'rot rigid body system. We give a Lax pair with a spectral parameter leading to an algebro-geometric integration of this new class of systems, which is closely related to the integration of the Lagrange bitop performed by us recently and uses Mumford relation for theta divisors of double unramified coverings. Based on the basic properties satisfied by such a class of systems related to bi-Poisson structure, quasi-homogeneity, and conditions on the Kowalevski exponents, we suggest an axiomatic approach leading to what we call the "class of systems of Hess-Appel'rot type".Comment: 40 pages. Comm. Math. Phys. (to appear

Population doses from terrestrial gamma exposure in Belgrade (Serbia) and their relation to geological setting

Terrestrial radiation exposure emitted from naturally occurring radionuclides, such as 40K and radionuclides from the 238U and 232Th series and their decay products represent the main external source of irradation to human body. The purpose of this study was to provide the assessment of the doses from terrestrial exposure of population in Belgrade. The gamma dose rate, annual effective doses and external hazard indexes due to terrestrial natural occurring radionuclides (226Ra, 232Th, 40K) were calculated based on their activities in soil samples in Belgrade determined by gamma-ray spectrometry. The mean value of the total absorbed gamma dose rate outdoors due to terrestrial radionuclides for Belgrade was 59 nGy/h which is close to the worldwide average value (58 nGy/h). The values of the gamma dose rate varied among sampling locations as a consequence of different geological formations in the investigated area. The mean value of annual effective dose of 73 Sv was significantly lower than the maximum allowed dose of 1 mSv for the population and was consistent with the worldwide average value. The mean value of external hazard index was found to be 0.28. The results of this assessment study pointed out that there is no significant radiation risk to the population of Belgrade due to terrestrial exposure to radiation from natural sources outdoors.I International Conference on Radiation in Various Fields of Research : RAD 2017 : book of abstracts; April 25-27, 2012; Niš, Serbi

Advanced hardware control for seven DOFs robotic arm-neuro arm

In this paper we will implement new hardware control for 7 DOFs (Degrees of freedom) advanced robotic arm research platform (NeuroArm) equipped with various sensors. New hardware platform consists of Nano Pi platform which is used as a PC platform for standard PLC (programmable logic controller's) unit and will replace old system that consists of 7 16-bit ATmega processors. The goal of new PLC which is based on Linux operating system (Debian distribution) that is patched by Xenomai real time system for reducing control response time and better entire system control. Robotic arm is powered by 7 DC motors which are controlled by two PWM4 (Pulse Width Modulation) modules. Position data is acquired from 1kΩ resistive sensors using RI8 (Resistive module) module and from optical quadrature encoders using one DI16 (Digital Input) module. Also other modules PWM4, RI8 and DI16 communicate with PikoAtlas CPU module by I2C bus