Maximal diameter of integral circulant graphs

Integral circulant graphs are proposed as models for quantum spin networks that permit a quantum phenomenon called perfect state transfer. Specifically, it is important to know how far information can potentially be transferred between nodes of the quantum networks modelled by integral circulant graphs and this task is related to calculating the maximal diameter of a graph. The integral circulant graph $ICG_n (D)$ has the vertex set $Z_n = \{0, 1, 2, \ldots, n - 1\}$ and vertices $a$ and $b$ are adjacent if $\gcd(a-b,n)\in D$, where $D \subseteq \{d : d \mid n,\ 1\leq d<n\}$. Motivated by the result on the upper bound of the diameter of $ICG_n(D)$ given in [N. Saxena, S. Severini, I. Shparlinski, \textit{Parameters of integral circulant graphs and periodic quantum dynamics}, International Journal of Quantum Information 5 (2007), 417--430], according to which $2|D|+1$ represents one such bound, in this paper we prove that the maximal value of the diameter of the integral circulant graph $ICG_n(D)$ of a given order $n$ with its prime factorization $p_1^{\alpha_1}\cdots p_k^{\alpha_k}$, is equal to $r(n)$ or $r(n)+1$, where $r(n)=k + |\{ i \ | \alpha_i> 1,\ 1\leq i\leq k \}|$, depending on whether $n\not\in 4N+2$ or not, respectively. Furthermore, we show that, for a given order $n$, a divisor set $D$ with $|D|\leq k$ can always be found such that this bound is attained. Finally, we calculate the maximal diameter in the class of integral circulant graphs of a given order $n$ and cardinality of the divisor set $t\leq k$ and characterize all extremal graphs. We actually show that the maximal diameter can have the values $2t$, $2t+1$, $r(n)$ and $r(n)+1$ depending on the values of $t$ and $n$. This way we further improve the upper bound of Saxena, Severini and Shparlinski and we also characterize all graphs whose diameters are equal to $2|D|+1$, thus generalizing a result in that paper.Comment: 29 pages, 1 figur

Sustav prigradskog autobusnog prometa u Središnjoj Hrvatskoj

This article deals with the suburban bus transport in Central Croatia. The density and structural characteristics of the bus transport network have been analysed. The centres of the bus transport were analysed according to several aspects: the number of the outgoing lines, number of destinations, the length and structure of the bus lines, the frequences and number of the bus departures. The transport flows were measured by the number of the buses passing through particular parts of the network. According to the conducted analyses, the centres of the bus transport were classified into four hierarchial categories.U radu se proučava prigradski autobusni promet u Središnjoj Hrvatskoj. Razmatrani su gustoća i strukturalana obilježja mreže autobusnog prometa. Centri autobusnog prometa analizirani su kroz nekoliko aspekata: broj polaznih linija, broj odredišta, duljinu i strukturu linija, frekvencije i broj polazaka autobusa. Prometni tokovi mjereni su brojem autobusnih veza u pojedinim dijelovima mreže. Utvrđeno je da prevladavaju linije na kratke udaljenosti. S obzirom na promatrane parametre, centri autobusnog prometa klasificirani su u četiri hijerarhijske kategorije

FAULT DETECTION USING FRA IN ORDER TO IMPROVE THE AGING MODEL OF POWER TRANSFORMER

Power transformers are constantly exposed to mechanical, thermal and electrical stresses during operation. In this paper, the authors propose an improved aging model of power transformers by adding the impact of mechanical deteriorations. In the current practice, the mechanical deformation and dislocation of the windings and core are not sufficiently distinguished as components that influence the aging of the transformer. Hence, the current aging model was expanded with a functional block that contains several typical failures in order to emphasize their impact on the lifetime of transformers and their aging as well.  The authors used the Frequency Response Analysis (FRA) method for the fault detection and location of the mechanical deformations of its active parts. The correlation function is used to determine the level of the detected failure. All presented test results are obtained in real exploitation conditions

The school of the turbulent swirling flow at the faculty of mechanical engineering university of Belgrade

This review paper provides data about research activities at the School of the turbulent swirling flow at the Faculty of Mechanical Engineering, University of Belgrade, conducted in the period 1941 up to date. An overview is provided of the main directions in this research area. First papers dealt with the turbulent swirling flow in hydraulic turbines to be continued by the experimental and analytical approaches on the axial fans pressure side. The complexity of 3-D, non-homogeneous, anisotropic turbulent velocity fields required complex experimental and theoretical approach, associated with the complex numerical procedures. Analytical approaches, complex statistical analyses and experimental methods and afterwards CFD employed in the research are presented in this paper. The 150 scientific papers, numerous diploma works, several master of science (magister) theses, six Ph. D. theses and two in progress, 40 researchers, national and international projects are the facts about the School. Scientific references are chronologically presented. Numerous abstracts from scientific conferences, presentations, projects with industry and lectures are not given here

Uloga različitih preparata gvožđa u sprečavanju trkačke anemije konja

The hypothesis that a high hematocrit value and high hemoglobin concentration are the most important conditions which have to be fulfilled in order to achieve top racing results has resulted in a massive use of iron preparations in healthy horses. This specially implies in racing horses during intensive training aiming at the prevention of the so-called racing anemia. By studying the effects of the most commonly used iron preparations in Serbia and Montenegro (Fedex®, as the representative of dextrane iron preparations; Hippirion® as a well known representative of iron complexed to saccharate and Hemo® 15 which is a representative of complex iron preparations which contain other hemantics) the expected changes in erythrocyte count, hemoglobin concentration and hematocrit value were recorded. However, the recorded changes in hematological values did differ between used iron preparations. The best effects were exhibited by Hemo®15, the application of which resulted in a prompt and significant increase in erythrocyte count, MCH, MCHC and hemoglobin concentration.Hipoteza da je za postizanje vrhunskih rezultata na trkama najvažniji preduslov visoka koncentracija hemoglobina i vrednost hematokrita, dovela je do masovne primene različitih preparata za podsticanje hematopoeze kod zdravih konja. Ovo se pre svega odnosi na konje u treningu, u cilju preveniranja takozvanih trkačkih anemija. U ovom radu su spitivanjem uticaja tri najčešće korišćena preparata gvožđa kod trkačkih konja u našoj zemlji (Fedex kao predstavnik dekstranskih preparata gvožđa, Hippiron kao najpoznatiji predstavnik gvožđa u kompleksu sa saharatom i Hemo 15 koji je predstavnik kompleksnih preparata koji uz gvožđe sadrže i druge hematinike) utvrđene očekivane promene u broju eritrocita, koncentraciji hemoglobina i hematokritskoj vrednosti. Primena sva tri preparata gvožđa dovela je do povećanja vrednosti svih ispitivanih hematoloških parametara kod trkačkih konja. Najbolji efekat ispoljio je preparat Hemo 15 čija je primena dovela do najvećeg povećanja broja eritrocita, MCH, MCHC i koncentracije hemoglobina, a i sam efekat je nastajao najbrže

General procedures in diagnosis of malignant diseases in dogs and cats

Tumors occur in all domestic and wild animals. They are most often diagnosed in dogs and cats, and their numbers increase from year to year. In the recent years, cancer is believed to be the most frequent cause of pet deaths. A speedy and reliable diagnosis is of paramount importance because it enables the veterinarian to begin therapy and make a prognosis. The objective of an early diagnosis is to enable the detection of neoplastic diseases before the tumor spreads throughout the organism, consequently enabling the timely administration of therapy and providing greater chances for curing the animal. A tumor is diagnosed on the grounds of the anamnesis, clinical picture, and special diagnostic procedures. The most frequently applied diagnostic procedures are laboratory diagnostics, cytology, biopsy and pathohistology, imaging diagnostics (roentgenography and roentgenoscopy, ultrasound diagnostics, endoscopy, computer tomography, magnetic resonance, and scintigraphy) and molecular diagnostics. Each of these methods has its advantages and faults in connection with costs, availability, sensitivity, specificity and quality of anatomic vs functional pictures. Every one of these techniques has its own field of implementation and each one provides different and additional information in connection with the nature and position of the primary lesion and the presence of metastases

Centres of Bus Traffic in Hrvatsko zagorje Region

U članku se proučava autobusni promet Hrvatskog zagorja kao faktor lokalne i regionalne organizacije prostora. Osim međusobne povezanosti pojedinih naselja, analizira se i broj autobusnih linija u polasku, da bi se istakli glavni centri autobusnog prometa.The bus traffic in the region Hrvatsko zagorje as a factor of local and regional organization id discussed in the paper. Besides mutual connection of particular settlements, the number of outgoing bus lines (i.e. number of bus departures) is analyzed in order to distinguish the main centres of bus traffic in the region