Crossing-free paths in the square grid

We consider paths in the 2D square grid, composed of grid edges, given as a sequence of moves in the four cardinal compass directions, without U-turns, but possibly passing several times through the same vertex or the same edge (if the path is open, it cannot pass twice through its starting vertex). We propose an algorithm which reports a self-crossing if there is one, or otherwise draws the path without self-crossings. The algorithm follows the intuitive idea naturally applied by humans to draw a curve: at each vertex that has already been visited, it tries to insert two new segments in such a way that they do not cross the existing ones. If this is not possible, a self-crossing is reported. This procedure is supported by a data structure combining a doubly-linked circular list and a skip list. The time and space complexity is linear in the length of the path

Different structures on subspaces of OsckM

The geometry of OsckM spaces was introduced by R. Miron and Gh. Atanasiu in [6] and [7]. The theory of these spaces was developed by R. Miron and his cooperators from Romania, Japan and other countries in several books and many papers. Only some of them are mentioned in references. Here we recall the construction of adapted bases in T(OsckM) and T*(OsckM), which are comprehensive with the J structure. The theory of two complementary family of subspaces is presented as it was done in [2] and [4]. The operators J,J, θ,θ, p, p* are introduced in the ambient space and subspaces. Some new relations between them are established. The action of these operators on Liouville vector fields are examined

Contribution to the knowledge about the presence and role of Enterobacter gergoviae in sensory characteristics of dairy products

Enterobacter gergoviae KGPMF 20 was found in traditionally made cheese from Sokobanja (South-eastern Serbia). In this paper, the characteristics of the species were evaluated by investigation of adhesion to different solvents and co-aggregation ability with other species. Moreover, its enzymatic activity was evaluated by using spectrophotometric method, with the intention to detect the role of the isolate in the sensory characteristic of cheese. The results of enzymatic activity indicated that E. gergoviae KGPMF 20 has low, almost no enzymatic activity. It could be concluded that this isolate did not affect the sensory characteristic of cheese.Publishe

Operatori za multi-rezolucione komplekse Morza i ćelijske komplekse

The topic of the thesis is analysis of the topological structure of scalar fields and shapes represented through Morse and cell complexes, respectively. This is achieved by defining simplification and refinement operators on these complexes. It is shown that the defined operators form a basis for the set of operators that modify Morse and cell complexes. Based on the defined operators, a multi-resolution model for Morse and cell complexes is constructed, which contains a large number of representations at uniform and variable resolution.Тема дисертације је анализа тополошке структуре скаларних поља и облика представљених у облику комплекса Морза и ћелијских комплекса, редом. То се постиже дефинисањем оператора за симплификацију и рафинацију тих комплекса. Показано је да дефинисани оператори чине базу за скуп оператора на комплексима Морза и ћелијским комплексима. На основу дефинисаних оператора конструисан је мулти-резолуциони модел за комплексе Морза и ћелијске комплексе, који садржи велики број репрезентација униформне и варијабилне резолуције.Tema disertacije je analiza topološke strukture skalarnih polja i oblika predstavljenih u obliku kompleksa Morza i ćelijskih kompleksa, redom. To se postiže definisanjem operatora za simplifikaciju i rafinaciju tih kompleksa. Pokazano je da definisani operatori čine bazu za skup operatora na kompleksima Morza i ćelijskim kompleksima. Na osnovu definisanih operatora konstruisan je multi-rezolucioni model za komplekse Morza i ćelijske komplekse, koji sadrži veliki broj reprezentacija uniformne i varijabilne rezolucije

Tolerance of autochthonous lactic acid bacteria to different processing conditions in vitro

In this paper, the effect of different temperatures, pH, and NaCl concentration on the growth of autochthonous lactic acid bacteria isolated from traditionally made Serbian cheese (Sokobanja area) was investigated by using the spectrophotometric method. Growth of tested Lactobacillus (Lb. fermentum, Lb. plantarum, and Lb. brevis) and Lactococcus lactis subsp. lactis biovar. diacetylactis five isolates were better in acidic pH, while the growth of Enterococcus isolates (E. durans, E. faecium, and E. faecalis) was better in basic pH, at 37 °C. At 4 °C after 24 h, none of the tested bacteria showed growth. Since the autochthonous isolates were tolerant to a tested range of dairy processing conditions, further studies need to include the characterization of enzymatic activity of selected isolates, as well as the ability to use these isolates like starter cultures or food supplements in dairy or non-dairy products.Accepted for publishin

Operatori za multi-rezolucione komplekse Morza i ćelijske komplekse

The topic of the thesis is analysis of the topological structure of scalar fields and shapes represented through Morse and cell complexes, respectively. This is achieved by defining simplification and refinement operators on these complexes. It is shown that the defined operators form a basis for the set of operators that modify Morse and cell complexes. Based on the defined operators, a multi-resolution model for Morse and cell complexes is constructed, which contains a large number of representations at uniform and variable resolution.Тема дисертације је анализа тополошке структуре скаларних поља и облика представљених у облику комплекса Морза и ћелијских комплекса, редом. То се постиже дефинисањем оператора за симплификацију и рафинацију тих комплекса. Показано је да дефинисани оператори чине базу за скуп оператора на комплексима Морза и ћелијским комплексима. На основу дефинисаних оператора конструисан је мулти-резолуциони модел за комплексе Морза и ћелијске комплексе, који садржи велики број репрезентација униформне и варијабилне резолуције.Tema disertacije je analiza topološke strukture skalarnih polja i oblika predstavljenih u obliku kompleksa Morza i ćelijskih kompleksa, redom. To se postiže definisanjem operatora za simplifikaciju i rafinaciju tih kompleksa. Pokazano je da definisani operatori čine bazu za skup operatora na kompleksima Morza i ćelijskim kompleksima. Na osnovu definisanih operatora konstruisan je multi-rezolucioni model za komplekse Morza i ćelijske komplekse, koji sadrži veliki broj reprezentacija uniformne i varijabilne rezolucije

Stochastic Method for Measurement of Voltage and Current at High Voltage Level

У раду je обрађен проблем мерења високог напона и струје у несинусидалној високонапонској мрежи, стање технике, предлог решења које подразумева неконвенционални начин мерења ових величина, практично израђен прототип и извршена потребна мерења која су потврђена теоријски. Мерење напона у високонапонској мрежи се врши напонским мерним трансформатором без језгра и интегрисаним мерилом хармоника (IMH), а затим се стохастичком методом мере хармоници напона, смерови и протоци снаге, односно енергије. За мерења струје на високом напону предлаже се калем Роговског и стохастичка метода мерења. Стохастичка метода мерења је заснована на додавању дитерског случајног сигнала на мерени сигнал. Сметње и присуство виших хармоника у мрежном сигналу су, за ову методу, додатни дитерски сигнали који методи не смањују тачност мерења.U radu je obrađen problem merenja visokog napona i struje u nesinusidalnoj visokonaponskoj mreži, stanje tehnike, predlog rešenja koje podrazumeva nekonvencionalni način merenja ovih veličina, praktično izrađen prototip i izvršena potrebna merenja koja su potvrđena teorijski. Merenje napona u visokonaponskoj mreži se vrši naponskim mernim transformatorom bez jezgra i integrisanim merilom harmonika (IMH), a zatim se stohastičkom metodom mere harmonici napona, smerovi i protoci snage, odnosno energije. Za merenja struje na visokom naponu predlaže se kalem Rogovskog i stohastička metoda merenja. Stohastička metoda merenja je zasnovana na dodavanju diterskog slučajnog signala na mereni signal. Smetnje i prisustvo viših harmonika u mrežnom signalu su, za ovu metodu, dodatni diterski signali koji metodi ne smanjuju tačnost merenja.A problem of measurement of high voltage and current in non-sinusoidal grid is given in the thesis, along with the current state in the field, the proposed non-conventional measurement method for these values, the realized prototype and the necessary measurement results that are confirmed theoretically. Measurement of voltage in high-voltage grid is performed using the coreless high voltage transformer and the Integrated harmonic measurement device (IMH). The stochastic method is used to measure harmonics of voltage, direction and flow of power and energy. For current measurement at high voltage level a Rogowski coil along with the Stochastic measurement method is proposed. Stochastic measurement method is based on adding a arbitrary dither signal to the measured signal. Disturbances and pollution of the grid signal are, for this method, additional dither signals that do not lower the measurement accuracy

Stochastic Method for Measurement of Voltage and Current at High Voltage Level

У раду je обрађен проблем мерења високог напона и струје у несинусидалној високонапонској мрежи, стање технике, предлог решења које подразумева неконвенционални начин мерења ових величина, практично израђен прототип и извршена потребна мерења која су потврђена теоријски. Мерење напона у високонапонској мрежи се врши напонским мерним трансформатором без језгра и интегрисаним мерилом хармоника (IMH), а затим се стохастичком методом мере хармоници напона, смерови и протоци снаге, односно енергије. За мерења струје на високом напону предлаже се калем Роговског и стохастичка метода мерења. Стохастичка метода мерења је заснована на додавању дитерског случајног сигнала на мерени сигнал. Сметње и присуство виших хармоника у мрежном сигналу су, за ову методу, додатни дитерски сигнали који методи не смањују тачност мерења.U radu je obrađen problem merenja visokog napona i struje u nesinusidalnoj visokonaponskoj mreži, stanje tehnike, predlog rešenja koje podrazumeva nekonvencionalni način merenja ovih veličina, praktično izrađen prototip i izvršena potrebna merenja koja su potvrđena teorijski. Merenje napona u visokonaponskoj mreži se vrši naponskim mernim transformatorom bez jezgra i integrisanim merilom harmonika (IMH), a zatim se stohastičkom metodom mere harmonici napona, smerovi i protoci snage, odnosno energije. Za merenja struje na visokom naponu predlaže se kalem Rogovskog i stohastička metoda merenja. Stohastička metoda merenja je zasnovana na dodavanju diterskog slučajnog signala na mereni signal. Smetnje i prisustvo viših harmonika u mrežnom signalu su, za ovu metodu, dodatni diterski signali koji metodi ne smanjuju tačnost merenja.A problem of measurement of high voltage and current in non-sinusoidal grid is given in the thesis, along with the current state in the field, the proposed non-conventional measurement method for these values, the realized prototype and the necessary measurement results that are confirmed theoretically. Measurement of voltage in high-voltage grid is performed using the coreless high voltage transformer and the Integrated harmonic measurement device (IMH). The stochastic method is used to measure harmonics of voltage, direction and flow of power and energy. For current measurement at high voltage level a Rogowski coil along with the Stochastic measurement method is proposed. Stochastic measurement method is based on adding a arbitrary dither signal to the measured signal. Disturbances and pollution of the grid signal are, for this method, additional dither signals that do not lower the measurement accuracy

Forest Estates/Organisational Units Ranking Model - The MRG Model

Background and Purpose: The fact that new organizational concepts require comparison and ranking of some business entities, implies the analogy that, in forestry, ranking should create the basis for differentiation of Forest Estates (FE) (seen as profit centers) according to their capability to allocate funds from rent for the utilization of forests and forest land. In this sense, it was necessary to determine the basic criteria and variables, and then to create the model for FE ranking on the basis of ecological and production potentials, and business results (economic indicators). The main idea was to create a model that can be used primarily by forest owners (which are, in certain countries such as Bosnia and Herzegovina, Croatia, Serbia, and Montenegro, mainly governments) and by public forest enterprises. The proposed models may serve to all other scientific, professional, research and other institutions, as the starting point for further research and as suggestions for possible improvements of the proposed solutions. Materials and Methods: The research was carried out within the project "Differential rent in the Republic of Srpska forestry". Total sample for the survey was 44 interviewed parties, with 118 questionnaires filled in. The methods of classification, content analysis, desk research, analysis, synthesis and comparison were used. In the concrete application of the Forest Estates/Organisational Units Ranking Model (hereinafter MRG Model; Model rangiranja šumskih gazdinstava, in Bosnian), the following methods were used: brainstorming, focus groups, survey, desk research method, Pareto analysis, modelling and induction. The statistical methods used were descriptive statistics and rank correlation. By using these methods and by combining them, a new model for forest estates ranking was created. Different input data and variables that refer to economic and natural indicators were used for ranking, all in accordance with the values for areas for which the ranking was carried out. Results: The main results are used for defining and proposal of the new model for forests estates ranking, i.e. the MRG Model. This model includes the following steps: (1) Survey, (2) Selection and scoring of specific variables, (3) Determining the intervals for specific variables, (4) Ranking of forest estates, and (5) Validation and rank correlation. This paper presented the algorithm of implementation of specific steps within the MRG Model, together with all activities that need to be implemented in order to perform forest estates ranking. It is necessary to emphasize that forest estates ranking was performed in accordance with the following three ranks: (1) for all analyzed variables, (2) for economic variables, and (3) for natural variables. Additionally, three modules for the calculation of scores for individual forest estates are the result of this research. Conclusions: The MRG Model is based on FE ranking according to deviation from the average value of the selected variables. The quality of the model lies in the fact that it is relatively simple (there are no complex statistical or other methods, necessary data can be collected easily), and that it can be applied again for similar surveys. Implementation of the MRG Model involves 5 basic steps with 7 phases to be performed in the order specified in this paper. The selection of variables which will be part of the MRG Model is crucial. The survey sample must include representatives that are directly or indirectly involved in the forestry sector. Although it might seem that all selected variables are significant, it is always necessary to give each variable the importance in accordance with the survey results. It is necessary to validate the defined model, data and final ranks on a pilot sample. Since there are three ranks, it is necessary to consider their mutual correlation, by performing statistical analysis rank correlation

In vitro synergistic antibacterial activity of Salvia officinalis L. and some preservatives

The aim of this work was to investigate the antibacterial activity of aqueous extracts of the species Salvia officinalis L. and its synergistic action with the preservatives sodium nitrite, sodium benzoate and potassium sorbate in vitro against selected food spoiling bacteria. Synergism was assessed by the checkerboard assay method and quantitatively represented by the FIC index. Synergistic action was established for aqueous extract/sodium benzoate, aqueous extract/potassium sorbate, aqueous extract/sodium nitrite combinations. Synergism was detected in relation to: Agrobacterium tumefaciens, Bacillus subtilis and Proteus sp. Synergism was established at plant extract and preservative concentrations corresponding up to 1/8 MIC values