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Some homotopy properties of classical linksVallejo, L. C. January 1986 (has links)
No description available.

2 
NonIsotopic Symplectic Surfaces in Products of Riemann SurfacesHays, Christopher January 2006 (has links)
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Let Σ<em><sub>g</sub></em> be a closed Riemann surface of genus <em>g</em>. Generalizing Ivan Smith's construction, for each <em>g</em> ≥ 1 and <em>h</em> ≥ 0 we construct an infinite set of infinite families of homotopic but pairwise nonisotopic symplectic surfaces inside the product symplectic manifold Σ<em><sub>g</sub></em> ×Σ<em><sub>h</sub></em>. In particular, we achieve all positive genera from these families, providing first examples of infinite families of homotopic but pairwise nonisotopic symplectic surfaces of even genera inside Σ<em><sub>g</sub></em> ×Σ<em><sub>h</sub></em>.

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NonIsotopic Symplectic Surfaces in Products of Riemann SurfacesHays, Christopher January 2006 (has links)
<html> <head> <meta httpequiv="ContentType" content="text/html;charset=iso88591"> </head>
Let Σ<em><sub>g</sub></em> be a closed Riemann surface of genus <em>g</em>. Generalizing Ivan Smith's construction, for each <em>g</em> ≥ 1 and <em>h</em> ≥ 0 we construct an infinite set of infinite families of homotopic but pairwise nonisotopic symplectic surfaces inside the product symplectic manifold Σ<em><sub>g</sub></em> ×Σ<em><sub>h</sub></em>. In particular, we achieve all positive genera from these families, providing first examples of infinite families of homotopic but pairwise nonisotopic symplectic surfaces of even genera inside Σ<em><sub>g</sub></em> ×Σ<em><sub>h</sub></em>.

4 
Deformações e isotopias de álgebras de Jordan / Deformations and isotopies of Jordan algebrasMaria Eugenia Martin 04 September 2013 (has links)
Neste trabalho apresentamos a classificação algébrica e geométrica das álgebras de Jordan de dimensões pequenas sobre um corpo $k$ algebricamente fechado de $char k eq 2$ e sobre o corpo dos números reais. A classificação algébrica foi realizada de duas maneiras: a menos de isomorfismos e a menos de isotopias. Enquanto que a classificação geométrica foi feita estudando as variedades de álgebras de Jordan $Jor_$ para $n \\leq 4$ e $JorR_$ para $n\\leq 3$. Provamos que $Jor_$ tem 73 órbitas sob a ação de $GL(V)$ e que é a união dos fechos de Zariski das órbitas de 10 álgebras rígidas, cada um dos quais corresponde a uma componente irredutível. Analogamente, mostramos que $JorR_$ tem 26 órbitas e é a união dos fechos de Zariski das órbitas de 8 álgebras rígidas. Também obtivemos que o número de componentes irredutíveis em $Jor_$ é $\\geq 26$. Construímos ainda três famílias de álgebras rígidas não associativas, não semisimples e indecomponíveis as quais correspondem a componentes irredutíveis de $Jor_$ e $JorR_$ para todo $n\\geq 5$. / In this work we present the algebraic and geometric classification of Jordan algebras of small dimensions over an algebraically closed field $k$ of $char k eq 2$ and over the field of real numbers. The algebraic classification was accomplished in two ways: up to isomorphism and up to isotopy. On the other hand, the geometric classification was obtained studying the varieties of Jordan algebras $Jor_$ for $n\\leq4$ and $JorR_$ for $n\\leq3$. We prove that $Jor_$ has 73 orbits under the action of $GL(V)$ and it is the union of Zariski closures of the orbits of 10 rigid algebras, each of which corresponds to one irreducible component. Analogously, we show that $JorR_$ has 26 orbits and is the union of Zariski closures of the orbits of 8 rigid algebras. Also we obtain that the number of irreducible components in $Jor_$ is $\\geq26$. We construct three families of indecomposable nonsemisimple, nonassociative rigid algebras which for any $n\\geq5$, correspond to irreducible components of $Jor_$ and $JorR_$.

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Deformações e isotopias de álgebras de Jordan / Deformations and isotopies of Jordan algebrasMartin, Maria Eugenia 04 September 2013 (has links)
Neste trabalho apresentamos a classificação algébrica e geométrica das álgebras de Jordan de dimensões pequenas sobre um corpo $k$ algebricamente fechado de $char k eq 2$ e sobre o corpo dos números reais. A classificação algébrica foi realizada de duas maneiras: a menos de isomorfismos e a menos de isotopias. Enquanto que a classificação geométrica foi feita estudando as variedades de álgebras de Jordan $Jor_$ para $n \\leq 4$ e $JorR_$ para $n\\leq 3$. Provamos que $Jor_$ tem 73 órbitas sob a ação de $GL(V)$ e que é a união dos fechos de Zariski das órbitas de 10 álgebras rígidas, cada um dos quais corresponde a uma componente irredutível. Analogamente, mostramos que $JorR_$ tem 26 órbitas e é a união dos fechos de Zariski das órbitas de 8 álgebras rígidas. Também obtivemos que o número de componentes irredutíveis em $Jor_$ é $\\geq 26$. Construímos ainda três famílias de álgebras rígidas não associativas, não semisimples e indecomponíveis as quais correspondem a componentes irredutíveis de $Jor_$ e $JorR_$ para todo $n\\geq 5$. / In this work we present the algebraic and geometric classification of Jordan algebras of small dimensions over an algebraically closed field $k$ of $char k eq 2$ and over the field of real numbers. The algebraic classification was accomplished in two ways: up to isomorphism and up to isotopy. On the other hand, the geometric classification was obtained studying the varieties of Jordan algebras $Jor_$ for $n\\leq4$ and $JorR_$ for $n\\leq3$. We prove that $Jor_$ has 73 orbits under the action of $GL(V)$ and it is the union of Zariski closures of the orbits of 10 rigid algebras, each of which corresponds to one irreducible component. Analogously, we show that $JorR_$ has 26 orbits and is the union of Zariski closures of the orbits of 8 rigid algebras. Also we obtain that the number of irreducible components in $Jor_$ is $\\geq26$. We construct three families of indecomposable nonsemisimple, nonassociative rigid algebras which for any $n\\geq5$, correspond to irreducible components of $Jor_$ and $JorR_$.

6 
O grupo de homotopia de tranças puras no disco é biordenável / The homotopy group of braids over a disc is biorderableSantos, Mirianne Andressa Silva 26 November 2018 (has links)
Em Artin (1925), Artin introduziu o estudo do grupo de tranças, o qual está intimamente relacionado ao estudo de nós e enlaçamentos. Em seu outro artigo Theory of Braids Artin (1947), ele questionou se as noções de isotopia e homotopia de tranças são as mesmas ou diferentes. Tal questão foi respondida muito mais tarde em Goldsmith (1974), onde a autora apresenta um exemplo de trança que é homotópica à trança trivial mas não é equivalente à trança trivial, caracterizando, além disso, o grupo de classes de homotopia de tranças puras no disco como um certo quociente do grupo de tranças puras original. Uma área de pesquisa mais recente nesta teoria é o estudo da ordenação destes grupos de tranças. Em Habegger e Lin (1990) os autores mostram que o grupo de classes de homotopia de tranças puras no disco é nilpotente e livre de torção. Resulta que ele é biordenado. Em Yurasovskaya (2008) a autora fornece uma ordem explícita e calculável para este grupo. Neste trabalho discutiremos e apresentaremos os principais resultados neste contexto. / In Artin (1925), Artin introduced the study of braid groups, which is closely related to the study of knots and links. In his other paper Theory of Braids Artin (1947), he asked if the notions of isotopy and homotopy of braids are different or the same. Such question was answered much later in Goldsmith (1974), where the author presents an example of braid that is homotopic to the trivial braid, but it is not equivalent to the trivial braid, characterizing, beyond that, the group of homotopy classes of braids as an certain quotient of the original braid group. One more recent research area on this theory is the study of ordenation of braid groups. In Habegger e Lin (1990) the authors show that the homotopy group classes of pure braids is nilpotent and torsion free. It follows that it is biorderable. In Yurasovskaya (2008) the author provides one explicit and evaluable order for this group. In this work, we will discuss and present the main results involved on this context.

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A Study of Topological Invariants in the Braid Group B2Sweeney, Andrew 01 May 2018 (has links)
The Jones polynomial is a special topological invariant in the field of Knot Theory. Created by Vaughn Jones, in the year 1984, it is used to study when links in space are topologically different and when they are topologically equivalent. This thesis discusses the Jones polynomial in depth as well as determines a general form for the closure of any braid in the braid group B2 where the closure is a knot. This derivation is facilitated by the help of the TemperleyLieb algebra as well as with tools from the field of Abstract Algebra. In general, the Artin braid group Bn is the set of braids on n strands along with the binary operation of concatenation. This thesis also shows results of the relationship between the closure of a product of braids in B2 and the connected sum of the closure of braids in B2. Results on the topological invariant of tricolorability of closed braids in B2 and (2,n) torus links along with their obverses are presented as well.

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Využití stopových prvků a izotopů Pb pro bioarcheologický výzkum vybraných pohřebišť / Use of trace elements and Pb isotopes for bioarchaeological research of selected burial groundsBartoš, Jan January 2014 (has links)
SUMMARY: Aim of this thesis is to provide, by using trace elements analysis and Pb isotopes analysis of archaeological findings from Roman era and following migration period, informations about basic bioarchaeological parameters of sites Abrahám, Rusovce II and Sládkovičovo (territory of present Slovakia) and Sopianae site (area of present Pécs city in Hugary). Analyses were performed on samples of 81 bones and 21 dental enamels. For purposes of this work most important concentrations are of Ca, P, Sr, Zn, Ba, Fe, Al, Mn and Pb (and its isotopes). They were consequently used for calculating Ca/P ratio in order to assess extent of afterburial diagenetic changes. For this purpose Al and Fe concentrations were taken into account too. Sr/Ca and Sr/Zn ratios were compared to assess prevailing type of diet. The Ba/Ca and Sr/Ca ratios were compared in order to asess supposable mobility of some individuals. By using of Pb concentrations and its isotopes contamination by this metal was assessed. During interpretations of individual conclusions useability of samples outgoing from assessment of extent of diagenetic alterations were always taken into account. Little changes in chemical composition of samples arise in case of Sopianae site, samples from other sites are greatly preserved. Using of paleodietary...

9 
Určení zdrojů Pb v malém povodí pomocí Pb isotopů / Determination of Pb sources in small catchment using Pb isotopes.Krajíčková, Michaela January 2016 (has links)
The contents and isotopic composition of lead (Pb) were studied in a small forested catchment Lesní potok. The catchment is located 30 km southeast from Prague near Jevany. Monitoring inputs and outputs in GEOMON, a network of small forested catchments in the territory of the Czech Republic, has been coordinated by the Czech Geological Survey since 1994. It was analyzed litter of spruce and beech, collected between 2013 and 2014, and an archival sample litter of spruce from 1997. Lead in soil was studied at two profiles cambisols in each diagnostic horizons. Samples of profile LP 38 were collected in 2005, the LP 39 a year later. Surface water and bulk precipitation were sampled monthly for one hydrological year 2013. The ICPMS method was used to determine the concentration and isotope ratios of lead. To determine of sources Pb were used isotope ratios 206 Pb/207 Pb and 208 Pb/206 Pb. In spruce litter (3,87 mg.kg1 ) was measured average Pb concentration higher than beech (0,98 mg.kg1 ). Topsoil horizons contain elevated concentrations of Pb (up to 100,70 mg.kg1 ) decreasing towards the deeper horizons. The Pb concentration in the soil was 61,28 mg.kg1 . Bulk precipitation in with average Pb concentrations206 Pb/207 Pb = 0.87 µg.l1 contained more Pb than surface water 206 Pb/207 Pb = 0.50 µg.l1 ....

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Geochemické a izotopové datování povodňových sedimentů / Geochemical and isotopic dating of floodplain sedimentsNováková, Tereza January 2014 (has links)
River systems are the most widespread sedimentary environment in many European countries and can be hence used for study of historical development of contamination and for evaluation of the anthropogenic impact influence at the local or regional level. The study of river sediments, however, is complicated by changes of channel morphology and sedimentation dynamics and redeposition of old sediments, whether caused naturally (flood events) or by human impact (land use changes or building of water management structures), which leads to deposition of various sedimentary facies. Identification of sedimentary facies within floodplain fill is hence necessary  character (lithology) of deposited facies influences the spatial distribution of pollutants within floodplains. Suitable sampling sites strategy and chemostratigraphic correlations of depth profiles guarantee a correct interpretation of obtained data. However, in many countries, there are still no legislative tools or universal methodology for contamination assessment respecting natural variability of sedimentary records. Regional contamination during the last centuries and identification of local pollution sources of risk elements (Pb , Zn , Cu , ...) and magnetic particles have been studied in the sediments of the Morava River, in the area between...

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