Computer-Assisted Proving of Combinatorial Conjectures Over Finite Domains: A Case Study of a Chess Conjecture

There are several approaches for using computers in deriving mathematical proofs. For their illustration, we provide an in-depth study of using computer support for proving one complex combinatorial conjecture -- correctness of a strategy for the chess KRK endgame. The final, machine verifiable, result presented in this paper is that there is a winning strategy for white in the KRK endgame generalized to $n \times n$ board (for natural $n$ greater than $3$). We demonstrate that different approaches for computer-based theorem proving work best together and in synergy and that the technology currently available is powerful enough for providing significant help to humans deriving complex proofs

Computer-Assisted Proving of Combinatorial Conjectures Over Finite Domains: A Case Study of a Chess Conjecture

There are several approaches for using computers in deriving mathematical proofs. For their illustration, we provide an in-depth study of using computer support for proving one complex combinatorial conjecture -- correctness of a strategy for the chess KRK endgame. The final, machine verifiable, result presented in this paper is that there is a winning strategy for white in the KRK endgame generalized to $n \times n$ board (for natural $n$ greater than $3$). We demonstrate that different approaches for computer-based theorem proving work best together and in synergy and that the technology currently available is powerful enough for providing significant help to humans deriving complex proofs

Procena rizika od elementarnih nepogoda i drugih nesreća u Republici Srbiji - metodološki osvrt

One of the most serious challenges of modern society is the lack of awareness of the presence of various dangers and possibilities of influencing them. Each community takes various measures and activities to assess the degree of their vulnerability tending to a state free from danger. As the most complex part, risk assessment requires a systematic approach to identifying and analyzing hazards based on the application of appropriate criteria for calculating the level of risk presented in this paper. Each risk assessment methodology must be adapted to the context of risk assessment. For this reason, the methodology for risk assessment of natural and other disasters is an attempt to establish basic requirements and criteria for risk assessment in the field of emergency management. Due to the complexity and unpredictability of natural and technological hazards that threaten people, material resources and the environment, risk assessment methodology includes risk mapping and assessment of combinations of risks - multi-risk, as well as a cross-border dimension of risk.Jedan od najozbiljnijih izazova savremenog društva jeste nedostatak svesti o prisustvu različitih opasnosti i mogućnostima uticaja na njih. U težnji ka stanju oslobođenom opasnosti svaka društvena zajednica preduzima razne mere i aktivnosti da proceni stepen svoje ugroženosti. Kao najsloženiji deo procene ugroženosti, procena rizika zahteva sistematičan pristup u identifikovanju i analizi opasnosti, zasnovan na primeni odgovarajućih kriterijuma za izračunavanje nivoa rizika prikazanih u ovom radu. Svaka metodologija za procenu rizika mora se prilagoditi kontekstu procene rizika. Iz tog razloga, metodologija za procenu rizika od elementarnih nepogoda i drugih nesreća predstavlja pokušaj da se uspostave osnovni zahtevi i kriterijumi za procenu rizika u sferi upravljanja u vanrednim situacijama. Zbog kompleksnosti i nepredvidivosti prirodnih i tehničko-tehnoloških opasnosti koje ugrožavaju ljude, materijalna dobra i životnu sredinu, metodologijom procene rizika je obuhvaćena i izrada mapa rizika, procena kombinacija rizika - multirizika, kao i prekogranična dimenzija rizika

Transient Phenomena during the Three-Phase 300MVA Transformer Energization on the Transmission Network

Connecting the transformer to the network may incur inrush current, which is significantly higher than the rated current of the transformer. The main cause of this phenomenon lies in the nonlinearity of the magnetic circuit. The value of the inrush current depends of the time moment of the energization and the residual magnetism in the transformer core. While connecting, the operating point of the magnetization characteristic can be found deep in the saturation region resulting in occurrence of large transformer currents that can trigger the transformer protection. Tripping of protection immediately after the transformer energization raises doubts about the transformer health. Inrush current can cause a number of other disadvantages such as the negative impact on other transformers connected on the same busbar; the increase of the transformer noise due to the large current value, the increase of the voltage drops in the network. The paper presents a simulation of the 300 MVA transformer energization using the MATLAB/Simulink software. 

A New Protection System Design of Active MV Distribution Network

The increasing implementation of renewable energy sources (RES), along with the diversity of energy source types, has additionally imposed significant operational and management problems in distribution networks. These problems are manifested in voltage regulations, system stability and coordination of protection, both in the distribution and transmission networks. For the medium voltage (MV) network, this includes new energy sources and higher amounts of fault currents, invisibility of several faults in the existing protection scheme, reduction of the range of protection devices and reduction of the possibility of detecting small fault currents with existing protection relays. Such changes significantly reduce the possibility of proper distribution system protection, both in subordinate and superior networks. The subject of this paper is the presentation of a new concept of the use of automation in the management and arrangement of power system protection dependent on the scheme and configuration of an active MV network. The goals of this analysis and research are to find and define the necessary architecture in which the scheme and appearance of the MV network should be automatically detected, and based on network topology to establish new settings of protection devices (ground fault, overcurrent and short circuit protection). The contributions of generation units of RES in the MV network must be considered. This paper specifically analyses the problems of power system management with simultaneous harmonization of protection systems both in the transmission and in the radial distribution network, offering optimization algorithms that have the ability of achieving the optimal solution. The implementation of the proposed technique was tested on a radial connection integrated with a microgrid (MG) which has the possibility of two-way power supply. The obtained results indicate that the proposed technique can solve described problems in the coordination of protection system and network management, even with the dynamic character of operation mode of the networks

Phylogeographic study of brown trout from Serbia, based on mitochondrial DNA control region analysis

In order to illuminate the phylogeography of brown trout (Salmo trutta) populations in the Balkan state of Serbia, the 561 bp 5'-end of mtDNA control region of 101 individuals originating from upland tributaries of the Danubian, Aegean and Adriatic drainages were sequenced and compared to corresponding brown trout sequences obtained in previous studies. Among 15 haplotypes found, 14 were considered native, representing the Danubian and Adriatic lineages of the brown trout, while one haplotype (ATcs1), found only in two individuals originating from two stocked rivers, corresponded to the Atlantic lineage and was considered introduced. Native haplotypes exhibited a strong geographic pattern of distribution: the Danubian haplotypes were strictly confined to the Danubian drainage, while the Adriatic haplotypes dominated in the Aegean and Adriatic drainages; most of the total molecular variance (69%) was attributed to differences among the drainages. Phylogenetic reconstruction, supplemented with seven haplotypes newly described in this study, suggested a sister position of the Atlantic-Danubian and Adriatic-Mediterranean-marmoratus ("southern") phylogenetic group, and pointed to the existence of a distinct clade, detected within the "southern" group. The data obtained confirmed our expectation of the existence of high genetic diversity in Balkan trout populations, and we recommend more widespread surveys covering trout stocks from the region

The Role and Status of Croatian Academic and Research Network - CARNet

This report describes the role of CARNet in academic and scientific community and the society as a whole. The goals and concepts are explained. The current status and future plans are presented.Ovaj izvještaj opisuje djelovanje Hrvatske akademske i istraživačke mreže - CARNet u akademskoj i znanstvenoj zajednici, te u društvu opcenito. Objašnjeni su ciljevi i pristupi, predočeni su trenutačno stanje i planovi za budućnost.</p

Integration of Solar Power Plant in Distribution Network

This paper presents the integration of the solar power plant SE Gumiimpex, rated power of  1 MW in Croatian distribution network. Basic data of solar power plant are presented as well as the analysis of its impact on the distribution network. Power quality measurements, seven days before and seven days after the connection of PV plant to the grid are performed and obtained power quality indices are compared to those stated in the power quality standard HRN EN 50160/2012 and Croatian grid code. There are also presented results of the simulation of protection relays selection and coordinatio

Mathematical Optimization for the Train Timetabling Problem

AMS Subj. Classification: 90C57; 90C10;Rail transportation is very rich in terms of problems that can be modelled and solved using mathematical optimization techniques. The train scheduling problem as the most important part of a rail operating policy has a very significant impact on a rail company profit considering the fact that from the quality of a train timetable depends a flow of three most important resources on rail network: cars, locomotives and crews. The train timetabling problem aims at determining a periodic timetable for a set of trains that does not violate track capacities and satisfies some operational constraints. In this paper, we developed an integer programming approach for determining an optimal train schedule for a single, one-way track linking two major stations, with a number of intermediate stations between. The application has been tested on a realistic example suggested by the PE “Serbian Railways”. Obtained results show a potential for a practical application of proposed approach

Improving the Conditions in a Radial Distribution Feeder by Implementing Distributed Generation

Distribution feeder is the final stage in the delivery of electricity to consumers. The feeder can be radial or networked. Radial feeders leave the power station towards the consumers without any connection to other power supply. Networked feeders have multiple connections to other supply points. It is common for long radial feeders for voltage to drop along the way and for losses to increase with increasing consumer’s power or the number of consumers. In order to minimize feeder losses and improve voltage profile distributed generation (DG) can be implemented. It is important to define the optimal location and power of distributed generation in a specific feeder to obtain its maximum potential benefits. This paper presents a solution for optimal DG placement by selecting the right terminal and power of DG using the Genetic Algorithm (GA) and the Artificial Neural Network (ANN) hybrid method. The method is tested on a part of Croatian distribution network and verified by DIgSILENT PowerFactory software and the analytical approach. The results and comparison thereof and presented in clear and legible form