Optimal approximation of convex curves by functions which are piecewise linear

AbstractIn this paper an efficient method is presented for solving the problem of approximation of convex curves by functions that are piecewise linear, in such a manner that the maximum absolute value of the approximation error is minimized. The method requires the curves to be convex on the approximation interval only. The boundary values of the approximation function can be either free or specified. The method is based on the property of the optimal solution to be such that each linear segment approximates the curve on its interval optimally while the optimal error is uniformly distributed among the linear segments of the approximation function. Using this method the optimal solution can be determined analytically to the full extent in certain cases, as it was done for functions x2 and x12. In general, the optimal solution has to be computed numerically following the procedure suggested in the paper. Using this procedure, optimal solutions were computed for functions sin x, tg x, and arc tg x. Optimal solutions to these functions were used in practical applications

Roman Religion and Cults on the Danube Limes in Serbia

Among different spheres of daily life led by Roman soldiers in the forts along the Danube Limes, one of the important ones was the sphere of spiritual culture, beliefs and religion. Although with the process of Romanisation, the official pantheon of Roman deities was introduced to the indigenous population, with the building and development of the defence frontier system on the Danube and Roman legions and auxiliary units who were stationed there, came soldiers of different origin and provenience, who brought with them their own religious beliefs and deities. Epigraphic and archaeological monuments found in the Danube Limes localities testify to the degree of acceptance or resistance of the autochthonous inhabitants towards different Roman, Hellenised and Oriental cults and show some very interesting examples of syncretism of the mentioned cults with unknown, indigenous gods and goddesses

Ocena ugroženosti i zaštita od poplava bujičnih vodotoka na teritoriji grada Smedereva

On Smederevo territory around 30 torrential floods are registered and their general condition is alarming. Along with the growth of urbanization some of them are induced into sewer systems and rain collectors, which are mostly inappropriate in size to receive a lot of water. Their common characteristics are disorderliness of watershed and worrying ecologic condition of river beds (vegetation, dumps). That is the reason of frequent torrential floods, which make great damages to settlements and economy. When assessing endangerments of floods, influence of range of natural and anthropogenic factors must be analyzed as well as consequent damages. The town of Smederevo implements integral defense from floods on the whole municipal territory, both for the areas which are endangered by torrentials without protective systems and for the areas endangered by systematic watercourse. In order to reduce the damages made from torrential floods it is necessary to anticipate and realize the works by operational plans every year, to specify the flood zone, forbid every sort of construction and determine spaces for building future retentions by the General urban development plan.Na teritoriji grada Smedereva evidentirano je oko trideset bujičnih vodotoka i njihovo opšte stanje je alarmantno. S razvojem urbanizacije neki od njih su uvedeni u kanalizacione sisteme i kišne kolektore, koji su uglavnom nedovoljnih dimenzija za prijem velikih voda. Njihove zajedničke karakteristike su neuređenost sliva i zabrinjavajuće ekološko stanje rečnih korita (vegetacija, deponije). Zbog toga su česte bujične poplave, koje nanose velike štete naseljima i privredi. Pri oceni ugroženosti od plavljenja moraju se analizirati uticaji niza prirodnih i antropogenih činilaca, ali i nastale štete. Grad Smederevo sprovodi integralnu odbranu od poplava na celoj teritoriji opštine, kako za područja koja ugrožavaju bujični vodotoci bez zaštitnih sistema, tako i za prostor ugrožen uređenim vodotocima. Da bi se smanjile štete nastale od poplava bujičnih vodotoka potrebno je operativnim planovima svake godine predvideti i realizovati određene radove, Generalnim urbanističkim planom Smedereva precizirati plavne zone, zabraniti svaku vrstu gradnje u njima i odrediti prostore za gradnju budućih retenzija

Comparative analysis of the traffic accidents in the territory of the city of Užice for 2021 and 2022 using open data and the Streamlit application

Introduction/purpose: With the development of information technologies, the Internet and social networks, the amount of collected data grows year by year at high speed. Data processing and analysis is becoming a necessity without which quality business decisions cannot be made. With the development of data science, tools for processing unstructured data have also been developed. Open data is publicly available data, the processing of which allows gaining new knowledge. The goal of the work is to present the possibility of using open data for research purposes, and their processing through the Streamlit development environment. Methods: This paper will present the Streamlit framework of the Python programming language and its functionality through the analysis of a web application for data analytics. As a case study, a comparative analysis of the traffic accident data on the territory of the Užice Police Department for 2021 and 2022 will be presented. Results: The Streamlit application will be used for the automatic analysis of open data on the traffic accidents in the territory of the Republic of Serbia in order to process the data and test the hypothesis about whether there has been an increase in traffic safety in the territory of the Užice Police Department. Conclusion: This work shows the possibility of using the Streamlit framework for creating an application for processing open data

INPUT SPLITS DESIGN TECHNIQUES FOR NETWORK INTRUSION DETECTION ON HADOOP CLUSTER

Intrusion detection system (IDS) is one of the most important components being used to monitor network for possible cyber-attacks. However, the amount of data that should be inspected imposes a great challenge to IDSs. With recent emerge of variousbig data technologies, there are ways for overcoming the problem of the increased amount of data. Nevertheless, some of this technologies inherit data distribution techniques that can be a problem when splitting a sensitive data such as network data frames across a cluster nodes. The goal of this paper is design and implementation of Hadoop based IDS. In this paper we propose different input split techniques suitable for network data distribution across cloud nodes and test the performances of their Apache Hadoop implementation. Four different data split techniques will be proposed and analysed. The techniques will be described in detail. The system will be evaluated on Apache Hadoop cluster with 17 slave nodes. We will show that processing speed can differ for more than 30% depending on chosen input split design strategy. Additionally, we’ll show that malicious level of network traffic can slow down the processing time, in our case, for nearly 20%. The scalability of the system will al so be discussed

Ocena ugroženosti i zaštita od poplava bujičnih vodotoka na teritoriji grada Smedereva

On Smederevo territory around 30 torrential floods are registered and their general condition is alarming. Along with the growth of urbanization some of them are induced into sewer systems and rain collectors, which are mostly inappropriate in size to receive a lot of water. Their common characteristics are disorderliness of watershed and worrying ecologic condition of river beds (vegetation, dumps). That is the reason of frequent torrential floods, which make great damages to settlements and economy. When assessing endangerments of floods, influence of range of natural and anthropogenic factors must be analyzed as well as consequent damages. The town of Smederevo implements integral defense from floods on the whole municipal territory, both for the areas which are endangered by torrentials without protective systems and for the areas endangered by systematic watercourse. In order to reduce the damages made from torrential floods it is necessary to anticipate and realize the works by operational plans every year, to specify the flood zone, forbid every sort of construction and determine spaces for building future retentions by the General urban development plan.Na teritoriji grada Smedereva evidentirano je oko trideset bujičnih vodotoka i njihovo opšte stanje je alarmantno. S razvojem urbanizacije neki od njih su uvedeni u kanalizacione sisteme i kišne kolektore, koji su uglavnom nedovoljnih dimenzija za prijem velikih voda. Njihove zajedničke karakteristike su neuređenost sliva i zabrinjavajuće ekološko stanje rečnih korita (vegetacija, deponije). Zbog toga su česte bujične poplave, koje nanose velike štete naseljima i privredi. Pri oceni ugroženosti od plavljenja moraju se analizirati uticaji niza prirodnih i antropogenih činilaca, ali i nastale štete. Grad Smederevo sprovodi integralnu odbranu od poplava na celoj teritoriji opštine, kako za područja koja ugrožavaju bujični vodotoci bez zaštitnih sistema, tako i za prostor ugrožen uređenim vodotocima. Da bi se smanjile štete nastale od poplava bujičnih vodotoka potrebno je operativnim planovima svake godine predvideti i realizovati određene radove, Generalnim urbanističkim planom Smedereva precizirati plavne zone, zabraniti svaku vrstu gradnje u njima i odrediti prostore za gradnju budućih retenzija

Marble Statue of Hercules from the territory of Bassianae

In the year of 2017, the National Museum of Serbia bought a marble statue of Hercules, found near Ruma, in Srem, at the tripoint of the villages of Budanovci, Dobrinci and Sibac. In the Roman period, this area belonged to the wider city territory of an important centre – Bassianae. The statue is preserved up to the knees, while the lower parts of the statue’s legs are missing. It can be presumed, on the basis of the preserved attributes, that the statue represents the eleventh Labour of the hero-god Hercules, since he is shown with apples from the Garden of the Hesperides. This particular Labour hasn’t been frequently depicted in Roman sculptural repertoire and the statue from Bassianae represents a unique complete figural composition in the territory of the Roman provinces in today’s Serbia so-far

Optimization of ultrasound-assisted extraction of total polyphenolic compounds from Juglans nigra L. leaves

The ultrasound-assisted extraction of Juglans nigra L. leaves was optimized with respect to total phenolic content (TP) of the extracts by varying the concentration of aqueous ethanol solution (E) and different solvent-to-solid ratio (S). The influence and optimum of the operating parameters (E and S) was examined using response surface methodology (RSM). The statistical criteria indicated the adequacy, reliability and precision of the developed RSM model. RSM showed that maximum extraction yield of TP 28.59 mg g(-1) of draw plant was achieved at the optimal values of 50% E and 20 kg kg(-1) S. Using the modelled optimized conditions, the detected relative difference between the predicted and the experimental yield was +/- 2.3 %. The determined TP content in the extracts varied from 12.54 to 29.26 mg GAE g(-1) of dry plant indicated that J. nigra is a valuable source of phenolic substances. The extracts of J. nigra leaves obtained under optimal conditions showed good antioxidant activity (IC50 = = 18.91 +/- 0.03 mu g cm(-3)) which was determined by the scavenging effect on 2,2-diphenyl-1-picrylhydrazyl radical. The optimization of the TP extraction process is the important step in improving techno-economics of the potential commercial preparation of J. nigra extracts, as natural source of antioxidants

Heavy Metals Content in Selected Medicinal Plants Produced and Consumed in Serbia and Their Daily Intake in Herbal Infusions

The heavy metals content (HMs) was investigated in 14 different medicinal plants collected from the three regions in Central Serbia, Zlatar, Sokobanja, and Kopaonik. The concentrations of Cd, Cr, Ni, Hg and Pb were determined: Cd (<0.03–2.72 mg/kg); Cr (<0.08–12.1 mg/kg); Ni (<0.08–12.2 mg/kg); Pb (0.6–49.0 mg/kg); the Hg concentration was below the detection limit of 0.06 mg/kg in all samples. The daily intake of HMs due to ingestion of 200 mL of herbal infusion was in all cases below the recommended limit prescribed by the World Health Organization. The estimated daily intake values were below the values for the oral reference dose regulated by the U.S. Environmental Protection Agency (USA EPA). The target hazard quotient and hazard index for Cd, Cr Ni, and Pb were below 1. Nevertheless, due to the tendency of heavy metals to accumulate in the organism, attention should be paid to the daily intake of herbal infusion during long-term usage. Specifically, it is recommended to consume not more than one cup (200 mL) of infusion per day made from thyme (Mt. Zlatar) and blueberry (Mt. Kopaonik), and not more than two cups per day for other herbs