Faculty of Science, Kragujevac

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The Faculty of Science in Kragujevac is constantly evolving and is one of the leading members of the University of Kragujevac. Based on the results of scientific research and pedagogical work of its professors and staff, it is highly ranked among the leading universities in Serbia, with a dedicated and strong international cooperation. The state of Serbia and its Ministry of Education and Science provide great support and assistance to the development of the Faculty of Science and the entire University.

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Improved treatment of the turning point in tunnel ionization of atoms in a low-frequency electromagnetic field
(1998) Ristić, Vladimir; Radulović, Mirko; Krainov, V.P.
In constructing the ADK theory, the Coulomb interaction was not included as the first-order correction into the all phases, i.e., the turning point was calculated to the zero-order degree of approximation with regard to the Coulomb interaction. This was correct for fields (up to 1012 W/cm2 ) much smaller than the atomic field (1016 W/cm2 ). But as lately in experiments are used fields even greater than the atomic one (in this case ADK theory does not work), we decided to reconsider the influence of the Coulomb interaction on the turning point for the fields that are strong enough to make a difference and yet are smaller than the atomic fields (i.e.,for fields of order of magnitude of 1014 W/cm2). So, in this paper we have included the Coulomb interaction where it has been completely neglected earlier. We have shown that this more accurate approach gives somewhat different result for the ionization probability.
Wiener–type topological indices of phenylenes
(2002) Furtula, Boris; Gutman, Ivan; Tomović, Željko; Vesel, Aleksander; Pesek, Igor
Coulson function and Hosoya index
(2002) Gutman, Ivan; Vidović, Dušica; Furtula, Boris
Let G be a molecular graph, n the number of its vertices and φ(G,x) its characteristic polynomial. Already in 1940 Coulson expressed the total π-electron energy of conjugated unsaturated molecules in terms of the function F(x)=n−ixφ′(G,ix)/φ(G,ix). Recently, the Coulson function F(x) found applications also in modeling the structure-dependence of physico-chemical properties of alkanes. We now analyze the Coulson function and establish some of its hitherto unnoticed features, in particular its relations with the Hosoya index.
Coulson function and total 𝜋–electron energy
(Faculty of Science, University of Science, 2002) Gutman, Ivan; Furtula, Boris; Vidović, Dušica
It is shown that the value of the variable x, at which the Coulson function F(G,x) has its inflection point, is related to the respective total тг-electron energy (E) and depends mainly on E and the number of non-bonding molecular orbitals.
Chemical applications of the Laplacian spectrum. VII. Studies of the Wiener and Kirchhoff indices
(2003) Gutman, Ivan; Vidović, Dušica; Furtula, Boris
Wiener-type indices and internal molecular energy
(Serbian Chemical Society, 2003) Gutman, Ivan; Vidović D.; Furtula, Boris; Zenkevich, Igor G.
In earlier studies it was established that internal molecular energies (Eint) of alkanes can be reproduced, in an approximate yet reliable manner by means of a molecular-graph-based structure-descriptor U. It was also established that U is linearly correlated with the Wiener index W. We now show that the correlation between U and W is more complicated than earlier expected, and that it cannot be represented by a single line. We also show that a very good linear correlation exists between U and a modified version Wm(λ) of the Wiener index, which is thus more suitable for modeling Eint than the ordinary Wiener index. .
Timelike and null normal curves in Minkowski space
(2004) ILARSLAN, Kazim; Nešović, Emilija
Analyzing the Transition Rates of the Ionization of Atoms by Strong Fields of a CO2 Laser Including Nonzero Initial Momenta
(2008) Ristić, Vladimir M.; Miladinovic, Tatjana B.; Radulović, Mirko M.
Here, the method of including nonzero initial momenta for ejected electrons in strong infrared laser fields is further developed [8]. It has been shown that, apart from being natural, including the nonzero initial momenta enables one to go into a deeper analysis of the process of tunnel ionization of atoms in strong laser fields (intensity up to 1016 W/cm2 ). This is due to looking closely at Fig. 2, which indicates that all electrons that could be ejected, under the circumstances, are ejected at a field intensity ~1013 W/cm2 , and that the effect of ionization after that is strongly diminished, which can be seen from the slope of the plates on Figs. 2 and 4. This also explains the saturation effect for fields up to 1016 W/cm2 [1, 4, 5, 7], and probably this saturation goes on until the fields raising relativistic effects ~1018 W/cm2 [7]. Opposite to what was believed earlier [7], the atomic field intensities could be increased to values over 1017 W/cm2 only when more than 10 electrons are ejected from the atom, it is shown that the properly calculated ionization of 9 electrons increases the atomic field intensity to ~1018 W/cm2
Variability of harvest index and yield components in wheat (Triticum aestivum L.)
(Akademiai Kiado, 2008-05-03) Knezevic, Desimir; Đukić, Nevena; Paunović, Aleksandar; Madic, Milomirka
Genetic determination of technological quality in Triticum durum.
(CODEN PDBIAD, 2008-10-31) Đukić, Nevena; Knežević, Desimir; Zečević, Veselinka
Ligand substitution reactions and cytotoxic properties of [Au(L)Cl2]⁺ and [AuCl2(DMSO)2]⁺ complexes (L=ethylenediamine and S-methyl-l-cysteine)
(2010) Milovanovic, Marija; Kesić, Ana; Volarevic, Vladislav; Petrović, Biljana; Arsenijevic, Nebojsa; Bugarčić Z.
We have studied the kinetics of the complex formation of gold(III) complexes, [AuCl2(en)]+ (dichlorido(ethylenediamine)aurate(III)-ion) and [AuCl2(SMC)] (dichlorido (S-methyl-l-cysteine)aurate(III)) with four biologically N-donor nucleophiles. It was shown that studied ligands have a high affinity for gold(III) complex, which may have important biological implications, since the interactions of Au(III) with DNA is thought to be responsible for the anti-tumour activity. The [AuCl2(SMC)] complex is more reactive than [AuCl2(en)]+. L-His reacts faster than the other N-donor nucleophiles in the reaction with [AuCl2(en)]+, but in the reaction with [AuCl2(SMC)] 5'-GMP is the best nucleophile. Gold(III) complexes are much more reactive than Pt(II) complexes with the same nucleophiles. The activation parameters for all studied reactions suggest an associative substitution mechanism. The cytotoxicity of gold(III) complexes, [AuCl2(en)]+, [AuCl2(SMC)] and [AuCl2(DMSO)2]+ was evaluated in vitro against chronic lymphocytic leukemia cells, obtained from blood of patients with chronic lymphocytic leukemia (CLL). The [AuCl2(en)]+ complex show comparable cytotoxicity profiles compared to cisplatin. © 2010 Elsevier Inc.
Electroanalytical study of the interaction between dsDNA and curcumin in the presence of copper(II)
(2010) Serpi C.; Stanic, Zorka; girousi, stella
As a result of the reaction between curcumin (CC) and copper(II) the characteristic peak of curcumin at -1.0 V significantly increased, and the peak at -1.6 V disappeared. Curcumin forms complex with copper(II). The interaction between double stranded (ds) calf-thymus DNA and curcumin in the presence of Cu(II) was studied in solution, by differential pulse adsorptive transfer voltammetry using carbon paste electrode (CPE) and hanging mercury drop electrode (HMDE). Cu(II)-CC complex generated changes in calf-thymus DNA. The characteristic peak of dsDNA, due to the oxidation of guanine residues, decreased. The increased DNA damage by Cu(II)-CC complex was observed in the presence of various concentrations of the transition metal ions, copper(II). © 2010.
The influence of detergents, sodium tripoly-phosphates and ethoxyled oleyl-cetyl alcohol on metabolism of the fungi Penicillium Verrucosum peyronel
(2010) Stojanović, Jelica; Jakovljević, Violeta; Matović, Ivana; Mijušković Z.; Nedeljkovic M.
On the species of the fungi Penicillium verrucosum grown on liquid nutritious base, according to Czapek and on a variation of the same nutritious base with detergent MERIX ('Merima, Kruševac) and individual components of the same detergent: sodium tripolyphosphate and ethoxyled oleyl-cetyl alcohol in a concentration of 0.1 %, the following analyses were performed: pH, redox potential, proteolytic activity, the quantity of free and total organic acids, amino acids, proteins and total biomass. We can notice from the obtained results that the detergent, sodium tripoly-phosphate and ethoxyled oleyl-cetyl alcohol in a concentration of 0.1% had an inhibitory effect on protein bioproduction and total biomass on the 8th day from the day of inoculation, while the production of free and total organic acids was partially or significantly stimulated by the presence of the detergent, sodium tripoly-phosphate and ethoxyled oleyl-cetyl alcohol in a concentration of 0.1 %. With aging of the fungus culture Penicillium verrucosum, the exception was free organic acids production which was, with the age of the culture, partially inhibited by the detergent. Proteolytic activity of the fungi Penicillium verrucosum had a slightly variable value during the experimental period with added nutritions media to the detergent, sodium tripoly-phosphate and ethoxyled oleyl-cetyl alcohol in a concentration of 0.1% with a slight aberration in relation to the control in some phases of the fungal growth.
Influence of zinc (zn) on germination of wheat (triticum aestivum l.)
(2010) Stanković, Milan; Topuzovic, Marina; Markovic A.; Pavlovic D.; Đelić, Gorica; Bojovic, Biljana; Branković, Snežana
The paper presents the results of research of negative effects of zinc (Zn) on seed germination of wheat (Triticum aestivum L.). Besides the impact on the percentage of germination, the toxic effect on some morphometric characteristics was followed, too. Ripe seeds of wheat were exposed in standard laboratory conditions to the influence of zinc, in form of zinc chloride (ZnCl2), at different values of concentration. For each value of concentration it was determined the percentage of germinationed seeds, as well as the length of root and shoot. It as found the value of the concentration of ZnCl2, which inhibited completely germination of wheat. The mean values of the length of root and shoot for each concentration were compared with values obtained for the control group of seeds, which were not treated with ZnCl2. In addition to causing of inhibition of seed germination, the presence of zinc in the medium affects disorder of the physiological—biochemical processes during the growth and development of vegetative organs that it indicates the difference in the length of the root and shoot of treated seeds in relation to the control group of untreated seeds. © 2010 Taylor and Francis Group, LLC.
Concentration of some heavy metals in aquatic macrophytes in reservoir near city kragujevac (serbia)
(2010) Branković, Snežana; Pavlović-Muratspahić D.; Topuzovic, Marina; Glišić, Radmila; Stanković, Milan
In this study, concentration of metals (Fe, Mn, Cu and Pb) were investigated in some aquatic macrophytes (5 plants), mud and water in artificial lake Gruža near city Kragujevac (Serbia). The results obtained indicate important role of macrophytic vegetation in aquatic ecosystems, with respect of bioremediation and bioindication, and confirm presumption that chemical analysis of test-species can give very important data, which offer complete picture of ecological status of investigated aquatic ecosystem, and identify plant species that are well hyperaccumulators and test-species for remediation of mentioned pollutants. Aquatic macrophytes can be use in the study of ecological status of water ecosystems and in monitoring of metals and other pollutants, and theirs application can be possible in finding of solutions for problems of protection, sanation and revitalization of those areas. © 2010 Taylor and Francis Group, LLC.
Failure criteria of fibre reinforced composites in homogeneous temperature field
(2010) Milosavljevic, Dragan; Bogdanovic, Gordana; Veljovic Lljiljana; Radakovic, Aleksandar; Lazić, Mirjana
The present paper examines the failure criteria of layered composites with orthotropic properties in the homogeneous temperature field. The composite has modeled by two mechanically equivalent families of fibres. The paper formulates constitutive equations in terms of intrinsic preferred directions, which are defined by the orientation of fibers at any point of the composite. A uniformly heated, thermoelastic solid undergoes distortion as well as volume change because it experiences differential expansions in different directions. This effect is more complicated if, in addition of being anisotropic, the material is inhomogeneous, as in the case with laminated materials. In order to illustrate the influence of temperature on the failure of this group of materials constitutive equations are derived and adoptedforuse in failure criteria, without the influence of temperatures, and with the influence of increased temperature.
Ihara coefficients: A flexible tool for higher order learning
(2010) Ren, Peng; Aleksic, Tatjana; Wilson, Richard; Hancock, Edwin
The aim of this paper is to seek a compact characterization of irregular unweighted hypergraphs for the purposes of clustering. To this end, we propose a novel hypergraph characterization method by using the Ihara coefficients, i.e. the characteristic polynomial coefficients extracted from the Ihara zeta function. We investigate the flexibility of the Ihara coefficients for learning relational structures with different relational orders. Furthermore, we introduce an efficient method for computing the coefficients. Our representation for hypergraphs takes into account not only the vertex connections but also the hyperedge cardinalities, and thus can distinguish different relational orders, which is prone to ambiguity in the hypergraph Laplacian. In experiments we demonstrate the effectiveness of the proposed characterization for clustering irregular unweighted hypergraphs and its advantages over the spectral characterization of the hypergraph Laplacian. © 2010 Springer-Verlag Berlin Heidelberg.
Maxima and minima of the Hosoya index and the Merrifield-Simmons index, a survey of results and techniques
(2010) Wagner, Stephan; Gutman, Ivan
The Hosoya index and the Merrifield-Simmons index are typical examples of graph invariants used in mathematical chemistry for quantifying relevant details of molecular structure. In recent years, quite a lot of work has been done on the extremal problem for these two indices, i.e., the problem of determining the graphs within certain prescribed classes that maximize or minimize the index value. This survey collects and classifies these results, and also provides some useful auxiliary results, tools and techniques that are frequently used in the study of this type of problem. © 2010 Springer Science+Business Media B.V.
Synthesis, cytotoxic activity, and thermal studies of novel N-[(1,3-diphenylpyrazol-4-yl)methyl] α-amino acids
(2010) Joksović, Milan; Bogdanovic, Gordana; Kojić, Vesna; Mészáros Szécsényi, Katalin; Leovac V.; Jakimov, Dimitar; Trifunović, Snežana; Marković, Violeta; Joksović, Ljubinka
(Chemical Equation Presented) New N-[(1,3-diphenylpyrazol-4-yl)methyl]a- amino acids (1a-i) have been synthesized and tested in vitro for their antiproliferative activity against human myelogenous leukemia K562, colon adenocarcinoma HT-29, cervix carcinoma HeLa, and normal fetal lung fibroblasts, MRC-5. Compounds derived from both phenylalanine enantiomer precursors appeared to be the most active against myelogenous leukemia K562 cell lines with a high cytotoxic potential. © 2010 HeteroCorporation.
Estimating the higher-order Randić index
(2010) Gonzalez Yero, Ismael; Rodriguez Velazquez, Juan Alberto; Gutman, Ivan
Let G be a (molecular) graph with vertex set V = {v1, v2, ..., vn}. Let δ (vi) be the degree of the vertex vi ∈ V. If the vertices vi1, vi2, ..., vih + 1 form a path of length h, h ≥ 1, in the graph G, then the hth order Randić index Rh of G is defined as the sum of the terms 1 / sqrt(δ (vi1) δ (vi2), ..., δ (vih + 1)) over all paths of length h contained (as subgraphs) in G. Lower and upper bounds for Rh are obtained, in terms of the vertex degree sequence of G. Closed formulas for Rh are obtained for the case when G is regular or semiregular bipartite. © 2010 Elsevier B.V. All rights reserved.

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