Genus Ranges of Chord Diagrams

A chord diagram consists of a circle, called the backbone, with line segments, called chords, whose endpoints are attached to distinct points on the circle. The genus of a chord diagram is the genus of the orientable surface obtained by thickening the backbone to an annulus and attaching bands to the inner boundary circle at the ends of each chord. Variations of this construction are considered here, where bands are possibly attached to the outer boundary circle of the annulus. The genus range of a chord diagram is the genus values over all such variations of surfaces thus obtained from a given chord diagram. Genus ranges of chord diagrams for a fixed number of chords are studied. Integer intervals that can, and cannot, be realized as genus ranges are investigated. Computer calculations are presented, and play a key role in discovering and proving the properties of genus ranges.Comment: 12 pages, 8 figure

An inviscid dyadic model of turbulence: the fixed point and Onsager's conjecture

Properties of an infinite system of nonlinearly coupled ordinary differential equations are discussed. This system models some properties present in the equations of motion for an inviscid fluid such as the skew symmetry and the 3-dimensional scaling of the quadratic nonlinearity. It is proved that the system with forcing has a unique equilibrium and that every solution blows up in finite time in $H^{5/6}$-norm. Onsager's conjecture is confirmed for the model system

Kvazi-klasična osnovna stanja i magnoni u monoperiodičnim spinskim sistemima

Tema ovog rada je simetrijski zasnovana analiza sistema čiji atomi (čvorovi) imaju nenulte magnetne momente (spinove), a čija je dinamika diktirana Hamiltonijanima kvadratne forme po spinovima, tj. spin-spin interakcija je zadata tenzorom drugog reda. U ovoj oblasti se obično koristi isključivo translaciona periodi ˇcnost kristala, dok se ostale simetrije naknadno razmatraju. Stoga je osnovni cilj ove studije uključivanje kompletne simetrije sistema, pre svega u modeliranje magnetnih Hamiltonijana, a potom i u nalaženje njihovih mogućih rešenja u smislu kvazi-klasičnih osnovnih stanja i odgovarajućih nisko-energijskih (heli)magnonskih spektara. Da bi se to efikasno postiglo, rad je metodološki zasnovan na strogom formalizmu koji tretira sisteme čije su geometrijske konfiguiracije invarijantne na podgrupe Euklidske grupe, a interakcije obuhvataju proizvoljan nivo susedstva. Polazeći od osobina Lijeve algebre ugaonih momenata, u kvantno-mehaničkom prostoru stanja definiše se dejstvo grupe, koje, usled principa invarijantnosti hamiltonijana, izdvaja aksijalno-vektorsku reprezentaciju uz odgovarajuća ograničenja na tenzorsko polje interakcije. Zajedno sa tim, hermitičnost hamiltonijana omogućava generalizaciju Morijinih pravila na sve dozvoljene komponente interakcije. Zbog velike dimenzije kvantnog prostora stanja, koja se skalira eksponencijalno sa brojem čvorova, rešenja ovakvih modela su, osim u najjednostavnijim slučajevima, aproksimativna. Tako, ograničavanjem probnog skupa varijacionog problema na separabilna stanja energija postaje funkcional po klasičnim vektorima (na čvorovima), koji, u opštem slučaju, nemaju med¯usobno jednake dužine. Kako je potonji uslov podrazumevan u aproksimaciji srednjeg polja, u radu se razmatraju mogu´cnosti da ovako nad¯eno osnovno stanje bude regularno, tj. invarijantno na neku spinsku grupu. U tu svrhu se pokazuje da se klasifikacija spinskih grupa može izvršiti korišćenjem realnih trodimenzionalnih reprezentacija (spinske reprezentacije) kojima se direktno određuju i sva regularna uređenja (međusobno jednakih dužina). Polazeći dalje od pretpostavke da je model takav da je optimizovan regularno ured¯enim klasičnim spinovima na ˇcvorovima, a ˇcuvaju´ci njihovu prirodu ugaonog momenta, izvedeno je preslikavanje u bozonsku sliku otklona od osnovnog stanja. Time se dinamika niskoenergijskih pobuda svodi na svojstveni problem odgovarajuće beskonačno dimenzione dinamičke matrice koji se, opet zahvaljujući simetriji, lako rešava metodom modifikovanih grupnih projektora. Kako, međutim, u opštem slučaju grupa simetrije može biti smanjena, predlaže se algoritam za rešavanje svojstvenog problema dinami čke matrice koji efektivno koristi celu grupu. Za monoperiodične sisteme koji su opisani jednom od 13 familija linijskih grupa detaljno se analiziraju transformaciona svojstva tenzora interakcije i Morijina pravila, dok se pojmovi izotropnosti i homogenosti prilagođavaju kvazi-jednodimenzionalnoj geometriji. Izdvaja se prototipni Hamiltonijan koji pored XXZ Hajzenbergovog člana ima i Džalošinski- Morijin vektor usmeren duž ose sistema. Pored tenzora, podrobno se klasifikuju spinske reprezentacije i uređenja prve (najvažnije) familije linijskih grupa; uređenja ostalih familija se dobijaju iz prve, u radu predloženim algoritmom. Konačno, navedeni teorijski koncepti se primenjuju na nedavno sintetisanim 13C nanotubama čiji su nuklearni spinovi putem lutajućih elektrona spregnuti dugo-dometnom Ruderman- Kitel-Kasuja-Josida interakcijom. Dobijena raznolikost helimagnetnih faza koje se kontrolišu naponom, osim toga što ukazuje na univerzalno ponašanje svih nanotuba, kandiduje ih, takođe, za spintroničke uređaje.Subject of this work is symmetry based analysis of systems whose atoms (sites) have non-vanishing magnetic moments (spins), and whose dynamics is governed by Hamiltonians of quadratic forms in spins, i.e. spin-spin interaction is given by the second rank tensor. Commonly, in this field, the translational periodicity of a crystal is used only, while the other symmetries are considered afterwards. Therefore, the main aim of this study is inclusion of the full symmetry of systems in the modeling of the magnetic Hamiltonians first, and then in finding their possible solutions, in particular the quasi-classical ground states and the corresponding low-energy (heli)magnons spectra. To achieve this efficiently, the work is methodologically based on rigorous formalism treating the systems whose geometrical configurations are invariant under the subgroups of the Euclidean group, and whose interactions involve arbitrary levels of neighbours. Starting from the properties of the angular momentum Lie algebra, in quantum-mechanical state space group action is defined, which, due to the invariance principle for Hamiltonian, singles out the axial-vector representation and its constrains on the interaction tensor field. Together with that, the hermiticity of Hamiltonian enables us to generalize the Moria’s rules on all of the allowed components of the interaction. Because of the large dimension of the quantum state space, which is exponentially scaled by the numbers of sites, the solutions of such models are approximate, except in the simplest cases. Thus, restricting the trial set of the variational problem to the separable states, the energy becomes a functional over the site classical vectors, which, in general case, do not have mutually equal lengths. Since, in the mean-field approximation the latter condition is defaulted, in this work, the possibilities that the ground state found in this way is regular, i.e. invariant under a spin group, are considered. For this purpose, it is shown that the classification of the spin groups can be performed using orthogonal three-dimensional real representations (spin representations), by which all the regular arrangements (of mutually equal lengths) are directly determined also. Further on, starting from the assumption that a model is optimized by the regularly arranged classical site spins, and preserving their angular momentum nature, the mapping in the bosonic picture of deviations from the ground state is derived. Thereby, the dynamics of the low-energy excitations is reduced to the eigenproblem of the corresponding infinite-dimensional dynamical matrix, which, owing to symmetry again, is easy to solve by the modified group projectors technique. However, since in general case the symmetry group can be lowered, the algorithm for solving the dynamical matrix eigenproblem, which effectively uses the whole group is proposed. For monoperiodic systems, described by one of the 13 families of the line groups, the transformational properties of interaction tensors are analysed in detail, while the notions of isotropy and homogenity are accommodated to the quasi-one-dimensional geometry. The Hamiltonian prototype, which besides the XXZ Heisenberg term has also the Dzyaloshinskii-Moria vector directed along the system axis, is singled out. In addition to the tensors, spin representations and arrangements of the first (the most important) family line groups are classified thoroughly; the arrangements of the rest of the families are to be obtained from these by the algorithm proposed in the work. Finally, the specified theoretical concepts are applied to the recently synthesized 13C nanotubes, whose nuclear spins are coupled by the long-ranged Ruderman-Kittel- Kasuya-Yosida interaction via itinerant electrons. Besides the obtained diversity of the gate-voltage controlabille helimagnetic phases reveals a universal behaviour of all the nanotubes, it makes them to be the candidates for spintronic devices, too

Effects of operation temperature on thermal expansion and main parameters of radial ball bearings

The research of influence of operation temperature on the thermal expansion and main parameters of radial ball bearings is presented in this paper. The main bearing parameters are identified in accordance with the increasing requests concerning stability and load capacity. A series of finite element analyses is performed for quasi-static analysis of all identified bearing parameters during contact period in referent temperature. Then, the dependence of bearing material characteristics on the operation temperature is discussed. Few series of finite element analyses are performed for a particular radial ball bearing type, with characteristics in accordance with manufacturer specifications, for several operation temperatures. These two problems analyses include consideration of relation between the initial radial clearance, thermal expansion strains, and contact deformations of the parts of the bearing assembly. The results for radial ball bearing parameters are monitored during a ball contact period for different temperatures and the appropriate discussion and conclusions are given. The conclusions about the contribution of developed procedure in defining the optimum operation temperature range are shown

Influence of MoO3 on cordierite ceramics sintering and crystallization

The influence of MoO3 on the process of cordierite ceramics preparation, 2MgO-2Al2O3-5SiO2 (MAS) was researched by sintering followed binary systems: MgO/MoO3 (sintered at 850 ºC and 1000 ºC), Al2O3/Bi2O3 and SiO2/Bi2O3 (sintered at 850 ºC and 1000 ºC). Composition of these systems was 80 % of oxide and 20 % MoO3. The effects of sintering, the composition and morphology were followed by x-ray diffraction, scanning electron microscopy and EDS analysis. It has been found that MoO3, beside liquid phase, forms intermediary unstable compounds with MgO and Al2O3. The following research is planned to investigate the effect of 5 % mass of MoO3 on the electrical properties of cordierite ceramics

Višejedarna Rhizoctonia sp. - patogen šećerne repe i osetljivost sorti u polju

Sugar beet root rot has severely occurred in our country recently, especially in localities of Pazova, Pećinci, Ruma, Sremska Mitrovica and Šid. From diseased roots as well as from soil collected from the localities where decay occurred, fungal isolates were obtained by bait plant method. Based on their characteristics, they were identified as multinucleate Rhizoctonia sp. During the year of 2004 in Mitrosrem trial field T-11, where the presence of multinucleate Rhizoctonia sp. was confirmed, an experiment under the coordination of Committee for Acknowledgement and Registration of New Cultivars in our country was conducted in order to determine cultivars' tolerance, i.e. their susceptibility and possibility for growing on infested fields. Six cultivars of sugar beet, Laetitia (as standard) and five new ones were included in the investigation. The trial was conducted in accordance with the established and accepted method (Ministry of Agriculture, Forestry and Water Resources, Republic of Serbia). Susceptibility of investigated cultivars was evaluated according to significant production characteristics root yield, sugar content, corrected sugar content, thick juice Q, molasses sugar, content of K, Na and amino-N, polarized sugar yield and white sugar yield, as it was recommended by the method. Conducted investigations have revealed that tested sugar beet cultivars showed different reactions to natural infection with multinucleate Rhizoctonia sp. Concerning root yield as the most important agricultural characteristic, statistically significantly higher yield was obtained with the cultivar under code mark 5 (61.120 kg/ha) whereas the cultivar marked under code 6 had significantly lower yield comparing to the standard (38.100 kg/ha).Poslednjih godina uočeno je masovno propadanje šećerne repe u našoj zemlji i to u lokalitetima Pazove, Pećinaca, Rume, Sremske Mitrovice i Šida. Iz obolelih korenova i iz zemljišta prikupljenog sa terena gde je propadanje uočeno, metodom mamaka izolovana je gljiva koja je po svojim osobinama identifikovana kao višejedarna Rhizoctonia sp. U toku 2004. godine na parceli Mitrosrema T-11 gde je izolacijom dokazano prisustvo višejedarne Rhizoctonia sp., postavljen je ogled u okviru sortne komisije za priznavanje i registraciju novih sorti u našoj zemlji sa ciljem utvrđivanja tolerantnosti, odnosno osetljivosti pojedinih sorti i time njihove pogodnosti za gajenje na infestiranom zemljištu. U ispitivanja je uključeno 6 sorti šećerne repe: Laetitia (kao standard) i još pet novih sorti. Ogled je posejan po utvrđenoj i prihvaćenoj metodi sortne komisije (Ministarstvo poljoprivrede, šumarstva i vodoprivrede Republike Srbije). Osetljivost ispitivanih sorti ocenjivana je na osnovu značajnih proizvodnih osobina: prinos korena, polarizacija, korigovani sadržaj šećera Q gustog soka, sadržaja sećera u melasi, sadržaja K, Na i amino N, prinos polarizacionog šećera i prinos kristalnog šećera, kako to metoda i zahteva. Na osnovu obavljenih istraživanja ustanovljeno je da se ispitivane sorte šećerne repe različito ponašaju u uslovima prirodne zaraze višejedarnom Rhizoctonia sp. U pogledu prinosa, kao najvažnije proizvodne karakteristike, statistički značajno viši prinos od standarda ispoljila je sorta koja se vodi pod šifrom 5 (61.120 kg/ha), dok je sorta koja se vodi pod šifrom 6 imala statistički značajno niži prinos u poređenju sa standardom (38.100 kg/ha)

Natural and artificial (90Sr) radionuclides in some carbonated mineral waters used in Serbia

A radiological characterization of 7 different carbonated mineral water samples collected in the local supermarkets in the area of Belgrade (produced in Serbia) was carried out. Analysis included determination of gross alpha and gross beta activities. The obtained results showed that the natural activity concentrations of alpha and beta emitting radionuclides in carbonated mineral water samples were within World Health Organization recommended levels, except for the Heba Strong and Kiseljak samples where the beta activity exceeds 1 Bq/L. For these two water samples gamma spectrometry analysis was performed as well as determination of 90Sr by oxalic method. The instrumentation used to count the gross alpha and gross beta activities, as well as for 90Sr, was a/b low level proportional counter Thermo Eberline FHT 770 T. Gamma spectrometric measurements were performed using a HPGe Canberra detector with a counting efficiency of 20%. The annual effective dose equivalent due to ingestion of investigated waters was calculated for age group >17, and obtained values are lower than 0.1 mSv recommended reference level. Finally, a comparison of the investigated waters with worldwide data was made. [Projekat Ministarstva nauke Republike Srbije, br. III43009

Effect of estradiol or calcium treatment on mammotrophs of female middle-aged rats

The effects of estradiol dipropionate (EDP) or calcium glucoheptonate (Ca) on the morphology and stereology of the PRL cells in 14-month-oldWistar female rats were studied. The animals were treated daily with EDP in the dose of 0.625 mg/kg b.w. or calcium glucoheptonate (Ca; 11.4 mg/kg b.w.) for two weeks. The controls were injected with vehicle alone by the same schedule. Mammotrophs (PRL cells) were immunocytochemically localized by the PAP method. Blood PRL concentration was determined by Delfia procedure. In animals treated with EDP the volume of both, PRL cells and their nuclei, as well as the volume densities were significantly (p0.05) decreased compared to control rats. Serum concentration of PRL was significantly increased (p0.05) changed by 2% compared to controls. Based on these results, it can be concluded that EDP expresses a strong stimulatory effect on the morphology and function of pituitary PRL cells.Ispitivani su efekti višekratnih doza estradiol dipropionata (EDP) ili kalcijum glukoheptonata (Ca) na morfološke i stereološke karakteristike mamotropnih (PRL) ćelija u acikličnih ženki pacova. Aciklične ženke su svakodnevno tokom dve nedelje dobijale 0,625 mg/kg tm EDP-a ili 11,4 mg/kg tm Ca. PRL ćelije su imunocitohemijski obeležavane PAP metodom. U životinja tretiranih sa EDP-om zapremina ćelija i njihovih jedara kao i volumenska gustina signifikantno (p0,05) promenjeni. Koncentracija PRL u serumu značajno (p<0,05) je bila povećana (za 17%) posle tretmana estradiolom dok tretman kalcijumom nije izazvao značajne promene (2% u odnosu na kontrole). Na osnovu dobijenih rezultata može se zaključ iti da EDP ima snažan stimulatorni efekat na PRL ćelije u hipofizi.nul

Strong chemisorption of CO2_2 on B10_{10}-B13_{13} planar-type clusters

An ab initio density functional study was performed investigating the adsorption of CO$_2$ on the neutral boron B$_{n}$ ($n = 10-13$) clusters, characterized by planar and quasiplanar ground-state atomic structures. For all four clusters, we found strong chemisorption energy of CO$_2$ reaching 1.6 eV for B$_{12}$ at the cluster edge sites with the adsorbed molecule in the plane of the cluster. A configuration with chemisorbed dissociated CO$_2$ molecule also exists for B$_{11}$ and B$_{13}$ clusters. The strong adsorption is due to the bending of the CO$_2$ molecule, which provides energetically accessible fully in-plane frontier molecular orbitals matching the edge states of the clusters. At the same time, the intrinsic dipole moment of a bent CO$_2$ molecule facilitates the transfer of excess electronic charge from the cluster edges to the molecule.Comment: 18 pages, 7 figure

Određivanje koncentracija metamizol-natrijuma u inflamiranim zglobovima svinja posle intravenske i elektroforetske aplikacije

Concentrations of the NSAID metamizol sodium (MmNa) in the synovial fluid and hyaline cartilage of inflamed knee and elbow joints of pigs after i.v. application and iontophoresis (IPh) were investigated. The research was conducted on 14 male pigs divided equally into two experimental groups and exposed to artificial inflammation of knees and elbows prior to the application of MmNa. The first group (A) was administered 2.5 g (twice the maximum therapeutic dose) MmNa intravenously, whilst the second group (B) was exposed to the same dose, but applied by IPh into contralateral knee and elbow joints. Four hours after the application of MmNa biopsies of the affected knee and elbow joints were performed. The average concentration of MmNa in the synovial fluid of inflamed joints in group A was 9.81±1.96μg/g, while in group B was 170.66±2.07 μg/g, being 17 times higher. The average concentration of MmNa in the hyaline cartilage was 2.29±1.16μg/g following i.v. administration and 98.36±21.58μg/g after IPh, i.e. approximatelly 43 times higher. This led to the conclusion that IPh of MmNa, resulting in incomparably higher concentrations in inflamed joints without any adverse systemic effects, has an advantage over i.v. application.U sinovijalnoj tečnosti i hijalinoj hrskavici inflamiranog kolenog i lakatnog zgloba svinja određivane su koncentracije metamizol-natrijuma (MmNa) aplikovanog i.v. i putem elektroforeze. Arteficijelno zapaljenje kolena i lakta prasadi izazvano je terpentinskim uljem. Metamizol-natrijum je primenjen u dozi od 2.5 g u prvoj grupi prasadi intravenski, a u drugoj putem elektroforeze u kontalateralni koleni i lakatni zglob. Četiri sata posle aplikacije MmNa urađena je biopsija tretiranih zglobova. Prosečna koncentracija MmNa u sinovijalnoj tečnosti inflamiranih zglobova prasadi posle i.v. aplikacije iznosila je 9,81±1,96μg/g, a posle elektroforeze bila je 170,66±2,07μg/g tkiva, odnosno oko 17 puta viša. Izmerena prosečna koncentracija MmNa u hijalinoj hrskavici iznosila je 2,29±1,16μg/g posle i.v. aplikacije i 98,36±21,58μg/g posle aplikacije elektroforezom, odnosno oko 43 puta više. Zaključujeno je da MmNa primenjen elektroforezom postiže statistički veoma značajno više prosečne koncentracije u inflamiranim zglobovima u odnosu na i.v. aplikaciju. Primena MmNa elektroforezom ima značajnu prednost nad i.v. aplikacijom ovog leka ne samo zbog postizanja značajno viših koncentracija u inflamiranim zglobovima, već i zbog izostajanja sistemskih neželjenih reakcija