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Rozprawy doktorskie na temat „Elliptio”

Autor: Grafiati

Data publikacji: 29 lipca 2024

Data aktualizacji: 30 lipca 2024

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1

Gustafson, Laura L. "Nonlethal health assessment of the freshwater mussel Elliptio complanata". NCSU, 2003. http://www.lib.ncsu.edu/theses/available/etd-01032003-130125/.

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Freshwater mussels are in decline, with over 70% of North American species categorized as endangered, threatened or of special concern. In an effort to create a nonlethal protocol for health evaluation of freshwater mussels we conducted a series of investigations on wild and captive populations of Elliptio complanata. We tested a method for nonlethal hemolymph collection and found no growth or survival effects in 30 sampled animals relative to 30 controls. We surveyed unionid populations from 19 different stream reaches from a rural region of North Carolina to provide a set of baseline ranges for hemolymph composition in healthy populations. These parameters included hemolymph calcium, magnesium, phosphorus, cell count, glucose, aspartate aminotransferase (AST), ammonia and protein. We tested these parameters in a captive population held under relatively uniform conditions and found most stable over time. Delta 15N declined substantially over time in captivity, likely in response to a large change in environmental _15N signatures. We tested health parameters in three groups of Elliptio complanata after three months under low, moderate or high feed conditions. The treatment groups varied in hemolymph glycogen, magnesium, calcium and phosphorus concentrations and in foot tissue _15N and _13C, providing possible indicators of subtle change in nutritional condition. We also transplanted Elliptio complanata from a stream enriched in _15N-N03 to a relatively depleted stream and evaluated the lag time required for mussel nitrogen isotope signatures to reflect new environmental signatures. We found a slow turnover time but relatively little variability compared to water signatures, suggesting that bivalves may be useful indicators of chronic nutrient loading in rivers and streams. We conclude that, with further research, hemolymph can be a valuable and safe tool for assessment of freshwater mussel population and habitat health.

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2

Amyot, Jean-Pierre. "Locomotion et répartition spatiale chez le bivalve d'eau douce Elliptio complanata". Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1998. http://www.collectionscanada.ca/obj/s4/f2/dsk2/ftp02/NQ35561.pdf.

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3

Jefferson, Catherine Ann. "Evaluation of histological and biochemical biomarkers for freshwater mussels, Elliptio complanata, in contaminated environments". Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1997. http://www.collectionscanada.ca/obj/s4/f2/dsk2/ftp04/mq21690.pdf.

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4

Mosher, Shad. "Biomarkers of Lead Exposure in the Freshwater Mussel Elliptio complanata For Assessing Transportation Related Impacts". NCSU, 2008. http://www.lib.ncsu.edu/theses/available/etd-08062008-130313/.

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The first phase of this study involved examination of lead (Pb) concentrations in adult Eastern elliptio (Elliptio complanata) mussel tissue and sediment at 40 sites throughout North Carolina, ranging in average daily traffic count, land-use patterns and watershed characteristics. Data from these sites revealed an increased Pb concentration of about 2 Î¼g/g in sediment downstream of bridge crossings compared to upstream for high traffic areas of >20,000 vehicle crossings/day (vc/d), as well as a significantly greater average Pb concentration in mussels from sites with traffic count >500 vc/d compared to sites with <500 vc/d. Two 28-d toxicity tests with Pb and adult Eastern elliptio mussels were conducted in the second phase of the study to compare the field-derived Pb bioaccumulation data and to examine sublethal biomarkers of Pb exposure and toxicity. Endpoints for the tests included mussel survival, metal accumulation, shell length and weight. For the first test, Î´-aminolevulinic acid dehydratase (ALAD) inhibition was assessed as a biomarker of exposure and effect in mussel hemolymph. In the second test, Na+,K+-ATPase activity in mussel gill tissue was examined as a biomarker of exposure and effect, along with measurements of hemolymph ion concentrations. Pb was measured in mussel hemolymph in both tests at near-exposure levels, and at the greatest exposure concentration in the first test (396 Î¼g/L), the hemolymph Pb concentration was 4.5 times the amount present in test water. In contrast, the greatest exposure concentration in the second test (458 Î¼g/L), had hemolymph concentrations only 0.12 times the amount present in test water. This finding suggested a threshold effect concentration for Pb exposure and hemolymph concentrations. The average Pb concentration in mussel tissue was strongly correlated with Pb exposure concentration (RÂ²= 0.99) at day 28 for both tests. The enzyme ALAD was not present in measurable concentrations in freshwater mussel hemolymph, gill or mantle tissue. The Na+,K+-ATPase activity was found to be a strong biomarker of Pb exposure in freshwater mussel gill tissue (~50% of total ATPase) using a K-free salt solution for detection, and was found to be negatively correlated with average tissue Pb concentration (R2 = 0.85) on day 28. Pb accumulated rapidly in mussel tissue during the first two weeks of the second exposure, with lesser accumulation during the final two weeks, with only the 121 Âµg/L treatment group changing significantly. Because Pb was being removed from the test water throughout the duration of exposure, I conclude that the mussels were approaching equilibrium with the aqueous environment and were eliminating the Pb in lysosomes and granulocytes through pseudo-feces. Although the major contribution of Pb to the environment from now-banned leaded gasoline is still evident in North Carolina, the concentrations measured in mussel tissue and sediment were not at levels which would cause immediate or short-term reductions in Eastern elliptio populations. Moreover, the sub-lethal effects of Pb on Na+,K+-ATPase activity, although a strong biomarker of exposure, appear not to be significantly effected at environmentally relevant concentrations of Pb. However, other species of freshwater mussels may be more sensitive to Pb contamination and further assessment is needed to verify the role Pb may be having in the overall declines in mussel species diversity being observed worldwide.

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5

Molina, Reverie Alvarez. "Morphological and Genetic Description of the Freshwater Mussel, Elliptio complanata (Lightfoot, 1786) in the Cape Fear River System, N.C". NCSU, 2004. http://www.lib.ncsu.edu/theses/available/etd-05202004-184213/.

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The purpose of this research is to provide a preliminary description of the morphological and genetic variation of a cosmopolitan freshwater mussel E. complanata from one North Carolina river system, Cape Fear River (CFR). Individuals from CFR were collected and compared with known specimens of E. complanata (topotype). Multivariate analyses, such as factor and discriminant analyses were utilized to differentiate the individuals based on thirty morphological shell landmarks. Genetic analyses involved the use of diversity estimates and cluster analyses based on cytochrome oxidase I (COI) sequence and Amplified Fragment Length Polymorphism (AFLP) fingerprint data. Factor analysis suggest that E. complanata from CFR maybe differentiated based on the thickness of posterior and anterior shell angles, and obesity of the shells. Significant differences between the CFR samples and topotypes were demonstrated by discriminant analysis of morphological data and by COI gene diversity estimates. This difference corroborated earlier work suggesting geographic delineation of E. complanata shell form. Genomic fingerprinting suggests further variation even within the topotypes. Phenotype of the topotypic materials seems to support this genomic variability. Heirarchical cluster analyses of morphometry and genetic data further showed different groups supporting earlier research suggesting high form variation within the E. complanata species.

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6

Yates, Jennifer Maria. "Influences of a Cladophora Bloom on the Diets of Amblema Plicata and Elliptio Dilatata in the Upper Green River, Kentucky". TopSCHOLAR®, 2012. http://digitalcommons.wku.edu/theses/1221.

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Freshwater mussels are the most imperiled group of freshwater invertebrates globally. Recent research suggests a better understanding of mussel feeding ecology may facilitate and improve conservation efforts. The use of stable isotopes is becoming an increasingly common method to study aquatic food webs. Carbon (C) and nitrogen (N) are two of the most frequently employed elements in food web studies. Differences in natural abundance of 13C/12C can indicate which food sources are the basal sources of carbon incorporated into a consumer’s tissue, while the ratio of 15N /14N provides a method of assessing trophic position within a food web. Attached macroalgae, including the genus Cladophora, may be the dominant primary producers in running water systems. Cladophora, however, has not yet been indicated as a prominent assimilated food source for freshwater mussels. The overall purpose of this study was to assess if the diet of two common Green River mussel species, Amblema plicata (Say) and Elliptio dilatata (Rafinesque) were influenced by the seasonal change in availability of Cladophora during a summer-autumn rapid growth period. Two specific questions were asked: 1) Are the assimilated diets different between control and treatment areas, and 2) are the assimilated diets influenced by differing Cladophora levels across the study period? A mesocosm approach was employed in order to manipulate Cladophora levels within a treatment area. Seventy-two mussels, 36 each species, were sampled across four months,twice between control (= reach-scale, heavy Cladophora cover) and treatment (= localscale removal of Cladophora) areas. The freeware program, IsoSource, a concentration weighted linear mixing model, was used to determine the potential contribution of potential food sources to the diet of both mussel species. IsoSource revealed that Cladophora was the primary assimilated food source for both species across the study period. Although assimilated diets were not different between control and treatment areas, diets were, however, influenced by Cladophora availability across time. The results of this study indicate that, during bloom conditions, Cladophora is the primary carbon source for both A. plicata and E. dilatata and may form the base of food webs in the upper Green River.

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7

Pédelucq, Julie. "Etude de la présence, du devenir et de l’impact des psychotropes dans la Garonne estuarienne (France) et le fleuve Saint Laurent (Québec, Canada)". Thesis, Bordeaux, 2016. http://www.theses.fr/2016BORD0409/document.

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L’urbanisation croissante et la propagation des activités humaines entrainent l’augmentation de l’apport de nombreux micropolluants dans le milieu aquatique. Le compartiment aquatique est alors défini comme le réceptacle ultime de la pollution environnementale apportée par diverses sources : les effluents municipaux et industriels, les lixiviats des sites d’élimination des déchets solides, le ruissellement des eaux urbaines et des eaux des sites agricoles. Parmi les contaminants retrouvés dans l’eau, il y a les psychotropes (benzodiazépines, antidépresseurs,antiépileptiques, etc…) qui appartiennent à la grande famille des médicaments. Ce sont des molécules biologiquement actives, ubiquistes, qui sont principalement d’origine urbaine, qui sont apportées continuellement dans l’environnement aquatique et qui sont fortement consommées au niveau mondial. Depuis quelques années, les scientifiques commencent à s’intéresser à cette famille thérapeutique mais il existe encore un réel manque de connaissance sur l’intégralité du problème de diffusion des psychotropes,de leur passage en station d’épuration à leur présence dans l’environnement et enfin à leur impact sur les organismes aquatiques. Ces travaux de thèse cherchent donc à documenter ce point en se focalisant sur l’étude de la présence, du devenir et de l’impact des psychotropes dans la Garonne estuarienne (France) et le fleuve Saint Laurent (Québec, Canada). Dans un premier temps, une méthode analytique multi-résidus permettant l’analyse de 47 psychotropes dans les eaux usées et les eaux de surface a été développée et validée. Des échantillonneurs passifs de type POCIS (Polar Organic Chemical Integrative Sampler) ont été calibrés et validés afin de permettre le suivi intégratif et continu des psychotropes dans les eaux de surface.Dans un second temps, les effluents d’entrée et de sortie de station d’épuration des agglomérations de Bordeaux en France et de Repentigny et Montréal au Québec ont été caractérisés. Les résultats de cette étude montrent que les traitements épuratoires de chacune des stations d’épurations étudiées ont une efficacité limitée pour éliminer les psychotropes dans les eaux usées. Par la suite, le suivi effectué dans la Garonne estuarienne et dans le fleuve Saint Laurent a mis en évidence la présence de psychotropes dans l’environnement qui sont majoritairement apportés par l’amont des villes de Bordeaux et Montréal.La comparaison des résultats obtenus pour la France et le Québec montre qu’il existe bien des habitudes de prescriptions et de consommations différentes entre les deux pays. Même si les procédés d’épuration sont différents entre les deux pays (traitement secondaire en France et primaire au Québec),l’efficacité d’élimination sur la famille thérapeutique des psychotropes reste insuffisante. Enfin ila été observé que le débit du milieu récepteur jouait un rôle important dans la dilution et le devenir des composés.Dans un troisième et dernier temps, des études in vitro et in vivo ont montré que certains psychotropes pouvaient avoir un impact toxique sur les bivalves d’eau douce étudiés (Elliptio complanata et Corbiculafluminea) lors d’exposition de composés seuls ou en mélange à des concentrations de l’ordre du mg.L-1 (concentrations expérimentales) et même du ng.L-1 (concentrations environnementales)
Increasing urbanization and human activities cause an increase of micropollutant input in the aquatic environment. The water compartment is then defined as the ultimate receptacle of environmental pollution originating from various sources: municipal and industrial wastewaters, leachates from solidwaste disposal sites, waters of urban and agricultural runoff.Among the contaminants found in the water, there are psychotropic drugs (benzodiazepines, antidepressantsor antiepileptics) belonging to the family of pharmaceuticals. These are biologically active molecules, ubiquitous, which are mainly of urban origin, which are continuously introduced into the aquatic environment and are heavily consumed around the world.In recent years, scientists have begun to show interest for this therapeutic family, but there is still areal lack of knowledge about the full psychotropic diffusion problem; from their presence in wastewater treatment plant to their presence in the environment and finally to their impact on aquatic organisms.In this global perspective these thesis works seek to document the presence, fate and impact of psychotropic drugs in the Garonne estuarine (France) and the St. Lawrence River (Quebec, Canada).Firstly, a multi-residue analytical method for the analysis of 47 psychotropic drugs in wastewater and surface waters has been developed and validated. POCIS passive samplers were calibrated and validated for continuous integrative monitoring of psychotropic drugs in surface waters.Secondly, the treatment plant influents and effluents of Bordeaux in France and Repentigny and Montreal in Quebec have been characterized. The results of this study show that treatment processes ofstudied wastewater treatment plants have limited performances to remove psychotropic drugs in wastewaters. There after, the monitoring performed in the Garonne estuarine and in the St. Lawrence River has highlighted that the presence of psychotropic drug in the environment is mainly related toupstream input of Bordeaux and Montréal.Comparison of the results obtained in the two countries surveyed show that there are many different patterns of prescriptions and consumption between the two countries. Although the treatment processes are different between the two countries (secondary treatment in France and primary in Quebec), their removal efficiency is still insufficient for psychotropic drugs. Finally it was observed that theflow rate of the receiving environment plays an important role in the dilution and the fate of the compounds.In a third and final stage, in vitro and in vivo studies have shown that some psychotropic drugs could have a toxic impact on the studied freshwater bivalves (Elliptio complanata and Corbicula fluminea) upon exposure alone or in mixture with concentrations in the order of mg.L-1 (tests concentrations) and even ng.L-1 (environmental concentrations)

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8

Mecklenburg, Trinity. "Elliptic Curves". CSUSB ScholarWorks, 2015. https://scholarworks.lib.csusb.edu/etd/186.

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The main focus of this paper is the study of elliptic curves, non-singular projective curves of genus 1. Under a geometric operation, the rational points E(Q) of an elliptic curve E form a group, which is a finitely-generated abelian group by Mordell’s theorem. Thus, this group can be expressed as the finite direct sum of copies of Z and finite cyclic groups. The number of finite copies of Z is called the rank of E(Q). From John Tate and Joseph Silverman we have a formula to compute the rank of curves of the form E: y2 = x3 + ax2 + bx. In this thesis, we generalize this formula, using a purely group theoretic approach, and utilize this generalization to find the rank of curves of the form E: y2 = x3 + c. To do this, we review a few well-known homomorphisms on the curve E: y2 = x3 + ax2 + bx as in Tate and Silverman's Elliptic Curves, and study analogous homomorphisms on E: y2 = x3 + c and relevant facts.

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9

Taufer, Daniele. "Elliptic Loops". Doctoral thesis, Università degli studi di Trento, 2020. http://hdl.handle.net/11572/265846.

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Given an elliptic curve E over Fp and an integer e ≥ 1, we define a new object, called “elliptic loop”, as the set of plane projective points over Z/p^e Z lying over E, endowed with an operation inherited by the curve addition. This object is proved to be a power-associative abelian algebraic loop. Its substructures are investigated by means of other algebraic cubics defined over the same ring, which we named “shadow curve” and “layers”. When E has trace 1, a distinctive behavior is detected and employed for producing an isomorphism attack to the discrete logarithm on this family of curves. Stronger properties are derived for small values of e, which lead to an explicit description of the infinity part and to characterizing the geometry of rational |E|-torsion points.
Data una curva ellittica E su Fp ed un intero e ≥ 1, definiamo un nuovo oggetto, chiamato "loop ellittico", come l'insieme dei punti nel piano proiettivo su Z/p^e Z che stanno sopra ad E, dotato di una operazione ereditata dalla somma di punti sulla curva. Questo oggetto si prova essere un loop algebrico con associatività delle potenze. Le sue sotto-strutture sono investigate utilizzando altre cubiche definite sullo stesso anello, che abbiamo chiamato "curva ombra" e "strati". Quando E ha traccia 1, un comportamento speciale viene notato e sfruttato per produrre un attacco di isomorfismo al problema del logaritmo discreto su questa famiglia di curve. Migliori proprietà vengono trovate per bassi valori di e, che portano ad una descrizione esplicita della parte all'infinito e alla caratterizzazione della geometria dei punti razionali di |E|-torsione.

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10

Taufer, Daniele. "Elliptic Loops". Doctoral thesis, Università degli studi di Trento, 2020. http://hdl.handle.net/11572/265846.

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Given an elliptic curve E over Fp and an integer e ≥ 1, we define a new object, called “elliptic loop”, as the set of plane projective points over Z/p^e Z lying over E, endowed with an operation inherited by the curve addition. This object is proved to be a power-associative abelian algebraic loop. Its substructures are investigated by means of other algebraic cubics defined over the same ring, which we named “shadow curve” and “layers”. When E has trace 1, a distinctive behavior is detected and employed for producing an isomorphism attack to the discrete logarithm on this family of curves. Stronger properties are derived for small values of e, which lead to an explicit description of the infinity part and to characterizing the geometry of rational |E|-torsion points.
Data una curva ellittica E su Fp ed un intero e ≥ 1, definiamo un nuovo oggetto, chiamato "loop ellittico", come l'insieme dei punti nel piano proiettivo su Z/p^e Z che stanno sopra ad E, dotato di una operazione ereditata dalla somma di punti sulla curva. Questo oggetto si prova essere un loop algebrico con associatività delle potenze. Le sue sotto-strutture sono investigate utilizzando altre cubiche definite sullo stesso anello, che abbiamo chiamato "curva ombra" e "strati". Quando E ha traccia 1, un comportamento speciale viene notato e sfruttato per produrre un attacco di isomorfismo al problema del logaritmo discreto su questa famiglia di curve. Migliori proprietà vengono trovate per bassi valori di e, che portano ad una descrizione esplicita della parte all'infinito e alla caratterizzazione della geometria dei punti razionali di |E|-torsione.

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11

Chen, Huyuan. "Fully linear elliptic equations and semilinear fractionnal elliptic equations". Thesis, Tours, 2014. http://www.theses.fr/2014TOUR4001/document.

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Cette thèse est divisée en six parties. La première partie est consacrée à l'étude de propriétés de Hadamard et à l'obtention de théorèmes de Liouville pour des solutions de viscosité d'équations aux dérivées partielles elliptiques complètement non-linéaires avec des termes de gradient,
This thesis is divided into six parts. The first part is devoted to prove Hadamard properties and Liouville type theorems for viscosity solutions of fully nonlinear elliptic partial differential equations with gradient term

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12

Fluder, Anna [Verfasser]. "Elliptic curves over function fields of elliptic curves / Anna Fluder". Berlin : Freie Universität Berlin, 2015. http://d-nb.info/1066645183/34.

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13

Nazaikinskii, Vladimir, i Boris Sternin. "Relative elliptic theory". Universität Potsdam, 2002. http://opus.kobv.de/ubp/volltexte/2008/2640/.

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This paper is a survey of relative elliptic theory (i.e. elliptic theory in the category of smooth embeddings), closely related to the Sobolev problem, first studied by Sternin in the 1960s. We consider both analytic aspects to the theory (the structure of the algebra of morphismus, ellipticity, Fredholm property) and topological aspects (index formulas and Riemann-Roch theorems). We also study the algebra of Green operators arising as a subalgebra of the algebra of morphisms.

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14

Idrees, Zunera. "Elliptic Curves Cryptography". Thesis, Linnéuniversitetet, Institutionen för datavetenskap, fysik och matematik, DFM, 2012. http://urn.kb.se/resolve?urn=urn:nbn:se:lnu:diva-17544.

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In the thesis we study the elliptic curves and its use in cryptography. Elliptic curvesencompasses a vast area of mathematics. Elliptic curves have basics in group theory andnumber theory. The points on elliptic curve forms a group under the operation of addition.We study the structure of this group. We describe Hasse’s theorem to estimate the numberof points on the curve. We also discuss that the elliptic curve group may or may not becyclic over finite fields. Elliptic curves have applications in cryptography, we describe theapplication of elliptic curves for discrete logarithm problem and ElGamal cryptosystem.

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15

Ejouamai, Rachid. "Modular elliptic surfaces". Thesis, University of Ottawa (Canada), 2006. http://hdl.handle.net/10393/27210.

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16

Saeki, Mugino. "Elliptic curve cryptosystems". Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1997. http://www.collectionscanada.ca/obj/s4/f2/dsk2/ftp04/mq29775.pdf.

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17

Greenberg, Matthew. "Constructing elliptic cohomology". Thesis, McGill University, 2002. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=29438.

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In 1986, Landweber, Ravenel, and Stong introduced a new family of generalized cohomology theories. As these theories are in a sense defined by elliptic curves, they were dubbed elliptic cohomology theories. In this thesis; we survey the mathematics behind the construction of elliptic cohomology. Topics treated include the theory of universal formal group laws and the Lazard ring, the formal group law of an elliptic curve, the group law (up-to-homotopy) on CPinfinity , oriented and complex cobordism theories, the universal elliptic genus, and Landweber's exact functor theorem.

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18

Hajir, Farshid. "Unramified elliptic units". Thesis, Massachusetts Institute of Technology, 1993. http://hdl.handle.net/1721.1/12327.

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19

Hu, Xiaodong. "Transversally elliptic operators /". The Ohio State University, 2002. http://rave.ohiolink.edu/etdc/view?acc_num=osu1486462067841539.

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20

Shipsey, Rachel Elizabeth. "Elliptic divisibility sequences". Thesis, Goldsmiths College (University of London), 2000. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.392661.

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21

Ozcan, Ayca Bahar. "Performance Analysis Of Elliptic Curve Multiplication Algorithms For Elliptic Curve Cryptography". Master's thesis, METU, 2006. http://etd.lib.metu.edu.tr/upload/12607698/index.pdf.

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Elliptic curve cryptography (ECC) has been introduced as a public-key cryptosystem, which offers smaller key sizes than the other known public-key systems at equivalent security level. The key size advantage of ECC provides faster computations, less memory consumption, less processing power and efficient bandwidth usage. These properties make ECC attractive especially for the next generation public-key cryptosystems. The implementation of ECC involves so many arithmetic operations
one of them is the elliptic curve point multiplication operation, which has a great influence on the performance of ECC protocols. In this thesis work, we have studied on elliptic curve point multiplication methods which are proposed by many researchers. The software implementations of these methods are developed in C programming language on Pentium 4 at 3 GHz. We have used NIST-recommended elliptic curves over prime and binary fields, by using efficient finite field arithmetic. We have then applied our elliptic curve point multiplication implementations to Elliptic Curve Digital Signature Algorithm (ECDSA), and compared different methods. The timing results are presented and comparisons with recent studies have been done.

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22

Goyal, Sarika. "Elliptic equations and non-local elliptic equations with sign-changing nonlinearities". Thesis, IIT Delhi, 2015. http://localhost:8080/xmlui/handle/12345678/6659.

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23

Bommireddipalli, Nithesh Venkata Ramana Surya. "Tutorial on Elliptic Curve Arithmetic and Introduction to Elliptic Curve Cryptography (ECC)". University of Cincinnati / OhioLINK, 2017. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1511866832906148.

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24

Savin, Anton, Bert-Wolfgang Schulze i Boris Sternin. "Elliptic operators in subspaces". Universität Potsdam, 2000. http://opus.kobv.de/ubp/volltexte/2008/2570/.

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We construct elliptic theory in the subspaces, determined by pseudodifferential projections. The finiteness theorem as well as index formula are obtained for elliptic operators acting in the subspaces. Topological (K-theoretic) aspects of the theory are studied in detail.

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25

Krupchyk, K., N. Tarkhanov i J. Tuomela. "Generalised elliptic boundary problems". Universität Potsdam, 2005. http://opus.kobv.de/ubp/volltexte/2009/2999/.

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For elliptic systems of differential equations on a manifold with boundary, we prove the Fredholm property of a class of boundary problems which do not satisfy the Shapiro-Lopatinskii property. We name these boundary problems generalised elliptic, for they preserve the main properties of elliptic boundary problems. Moreover, they reduce to systems of pseudodifferential operators on the boundary which are generalised elliptic in the sense of Saks (1997).

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26

Prendergast, Arthur Edward. "Extremal rational elliptic threefolds". Thesis, University of Cambridge, 2009. https://www.repository.cam.ac.uk/handle/1810/252154.

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27

Galbraith, Steven Douglas. "Iterations of elliptic curves". Thesis, Georgia Institute of Technology, 1991. http://hdl.handle.net/1853/28620.

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28

Miyamoto, Ian D. "Primes and elliptic curves". Thesis, McGill University, 1988. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=64085.

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29

Budd, C. J. "A semilinear elliptic problem". Thesis, University of Oxford, 1986. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.375216.

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30

McKee, James. "Some elliptic curve algorithms". Thesis, University of Cambridge, 1994. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.319564.

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31

Friedlander, Leonid. "Determinants of elliptic operators". Thesis, Massachusetts Institute of Technology, 1989. http://hdl.handle.net/1721.1/65015.

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32

McTague, Carl. "Generalizations of elliptic genera". Thesis, University of Cambridge, 2010. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.608783.

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33

Lu, Huajun. "Reduction of elliptic curves". Thesis, Bordeaux 1, 2010. http://www.theses.fr/2010BOR14129.

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Soit E une courbe elliptique sur un corps de valuation discrètecomplet K à corps résiduel algbriquement clos. Alors E a réduction semi-stable surune extension minimale L/K, galoisienne de groupe de Galois G. Soient O_{K} , O_{L} les anneaux de valuations respectives de K et L, et X , X' les modèles réguliers minimaux de E sur O_{K} et O_{L} respectivement.Premièrement nous montrons que pour tout entier naturel n, la fibre fermée infinitésimale X_{n} est déterminée par l'action du groupe G sur X'_{n+l} pour unentier naturel l assez grand (ne dépendant que du discriminant de L/K sile type de réduction de E n'est pas I*_{r} ). Deuxiémement, nous classifions àisomorphisme près la fibre fermée X_{0} en tant que courbe sur le corps résiduelde K, lorsque la caractéristique résiduelle est nulle ou au moins égale à 7. Cette classification est plus fine que la classification par le type à la Kodairaet Néron
Suppose E is an elliptic curve over a complete discrete valuationfield K whose residue field k is algebraically closed. Then E has semi-stablereduction after a minimal field extension L/K, moreover L/K is Galois andlet G be the Galois group. Let O_{K} and O_{L} be the ring of integers of K andL respectively. Let X (resp. X ') be the minimal regular model of E over O_{K}(resp. O_{L} ). In the first part of thesis, we prove that for all natural integersn, the infinitesimal fiber X_{n} is determined by the G-action on O_{K}-schemeX'_{n+l} for some positive integer l (depending only on the discriminant of L/Kif the reduction type of E is not I*_{r} ). In the second part of thesis, we classifythe special fiber X_{0} up to isomorphisms as k-curves when Char(k) >= 7. This classification is finer than the classification by Kodaira and Néron

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34

Pomponio, Alessio. "Singularity perturbed elliptic problems". Doctoral thesis, SISSA, 2004. http://hdl.handle.net/20.500.11767/4172.

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35

Thongjunthug, Thotsaphon. "Heights on elliptic curves over number fields, period lattices, and complex elliptic logarithms". Thesis, University of Warwick, 2011. http://wrap.warwick.ac.uk/35646/.

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This thesis presents some major improvements in the following computations: a lower bound for the canonical height, period lattices, and elliptic logarithms. On computing a lower bound for the canonical height, we have successfully generalised the existing algorithm of Cremona and Siksek [CS06] to elliptic curves over totally real number fields, and then to elliptic curves over number fields in general. Both results, which are also published in [Tho08] and [Tho10] respectively, will be fully explained in Chapter 2 and 3. In Chapter 4, we give a complete method on computing period lattices of elliptic curves over C, whereas this was only possible for elliptic curves over R in the past. Our method is based on the concept of arithmetic-geometric mean (AGM). In addition, we extend our method further to find elliptic logarithms of complex points. This work is done in collaboration with Professor John E. Cremona; another version of this chapter has been submitted for publication [CT]. In Chapter 5, we finally illustrate the applications of our main results towards certain computations which did not work well in the past due to lack of some information on elliptic curves. This includes determining a Mordell{Weil basis, finding integral points on elliptic curves over number fields [SS97], and finding elliptic curves with everywhere good reduction [CL07]. A number of computer programs have been implemented for the purpose of illustration and verification. Their source code (written in MAGMA) can be found in Appendix A.

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36

Bartley, Wende. "Ellipsis". Thesis, McGill University, 1988. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=61973.

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37

Birkedal, Ole Andre Blom. "Counting Points on Elliptic Curves". Thesis, Norwegian University of Science and Technology, Department of Mathematical Sciences, 2010. http://urn.kb.se/resolve?urn=urn:nbn:no:ntnu:diva-10018.

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In this paper we present the first efficient point counting algorithm due to Schoof, before giving a significant improvement due to Elkies. In the final section I give Satoh's algorithm which is even faster and has paved the way for the field of $p$-adic point counting.

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38

Yayla, Oguz. "Scalar Multiplication On Elliptic Curves". Master's thesis, METU, 2006. http://etd.lib.metu.edu.tr/upload/12607753/index.pdf.

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Elliptic curve cryptography has gained much popularity in the past decade and has been challenging the dominant RSA/DSA systems today. This is mainly due to elliptic curves offer cryptographic systems with higher speed, less memory and smaller key sizes than older ones. Among the various arithmetic operations required in implementing public key cryptographic algorithms based on elliptic curves, the elliptic curve scalar multiplication has probably received the maximum attention from the research community in the past a few years. Many methods for efficient and secure implementation of scalar multiplication have been proposed by many researchers. In this thesis, many scalar multiplication methods are studied in terms of their mathematical, computational and implementational points.

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39

Kirlar, Baris Bulent. "Elliptic Curve Pairing-based Cryptography". Phd thesis, METU, 2010. http://etd.lib.metu.edu.tr/upload/12612613/index.pdf.

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In this thesis, we explore the pairing-based cryptography on elliptic curves from the theoretical and implementation point of view. In this respect, we first study so-called pairing-friendly elliptic curves used in pairing-based cryptography. We classify these curves according to their construction methods and study them in details. Inspired of the work of Koblitz and Menezes, we study the elliptic curves in the form $y^{2}=x^{3}-c$ over the prime field $F_{q}$ and compute explicitly the number of points $#E(mathbb{F}_{q})$. In particular, we show that the elliptic curve $y^{2}=x^{3}-1$ over $mathbb{F}_{q}$ for the primes $q$ of the form $27A^{2}+1$ has an embedding degree $k=1$ and belongs to Scott-Barreto families in our classification. Finally, we give examples of those primes $q$ for which the security level of the pairing-based cryptographic protocols on the curve $y^{2}=x^{3}-1$ over $mathbb{F}_{q}$ is equivalent to 128-, 192-, or 256-bit AES keys. From the implementation point of view, it is well-known that one of the most important part of the pairing computation is final exponentiation. In this respect, we show explicitly how the final exponentiation is related to the linear recurrence relations. In particular, this correspondence gives that finding an algoritm to compute final exponentiation is equivalent to finding an algorithm to compute the $m$-th term of the associated linear recurrence relation. Furthermore, we list all those work studied in the literature so far and point out how the associated linear recurrence computed efficiently.

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40

Savin, Anton, i Boris Sternin. "Elliptic operators in even subspaces". Universität Potsdam, 1999. http://opus.kobv.de/ubp/volltexte/2008/2546/.

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An elliptic theory is constructed for operators acting in subspaces defined via even pseudodifferential projections. Index formulas are obtained for operators on compact manifolds without boundary and for general boundary value problems. A connection with Gilkey's theory of η-invariants is established.

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41

Savin, Anton, i Boris Sternin. "Elliptic operators in odd subspaces". Universität Potsdam, 1999. http://opus.kobv.de/ubp/volltexte/2008/2547/.

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An elliptic theory is constructed for operators acting in subspaces defined via even pseudodifferential projections. Index formulas are obtained for operators on compact manifolds without boundary and for general boundary value problems. A connection with Gilkey's theory of η-invariants is established.

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42

Nazaikinskii, Vladimir, i Boris Sternin. "On surgery in elliptic theory". Universität Potsdam, 2000. http://opus.kobv.de/ubp/volltexte/2008/2587/.

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We prove a general theorem on the behavior of the relative index under surgery for a wide class of Fredholm operators, including relative index theorems for elliptic operators due to Gromov-Lawson, Anghel, Teleman, Booß-Bavnbek-Wojciechowski, et al. as special cases. In conjunction with additional conditions (like symmetry conditions), this theorem permits one to compute the analytical index of a given operator. In particular, we obtain new index formulas for elliptic pseudodifferential operators and quantized canonical transformations on manifolds with conical singularities.

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43

Gil, Juan B., Thomas Krainer i Gerardo A. Mendoza. "Resolvents of elliptic cone operators". Universität Potsdam, 2004. http://opus.kobv.de/ubp/volltexte/2008/2682/.

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We prove the existence of sectors of minimal growth for general closed extensions of elliptic cone operators under natural ellipticity conditions. This is achieved by the construction of a suitable parametrix and reduction to the boundary. Special attention is devoted to the clarification of the analytic structure of the resolvent.

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44

Dines, Nicoleta, X. Liu i Bert-Wolfgang Schulze. "Edge quantisation of elliptic operators". Universität Potsdam, 2004. http://opus.kobv.de/ubp/volltexte/2008/2683/.

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The ellipticity of operators on a manifold with edge is defined as the bijectivity of the components of a principal symbolic hierarchy σ = (σψ, σ∧), where the second component takes value in operators on the infinite model cone of the local wedges. In general understanding of edge problems there are two basic aspects: Quantisation of edge-degenerate operators in weighted Sobolev spaces, and verifying the elliptcity of the principal edge symbol σ∧ which includes the (in general not explicitly known) number of additional conditions on the edge of trace and potential type. We focus here on these queations and give explicit answers for a wide class of elliptic operators that are connected with the ellipticity of edge boundary value problems and reductions to the boundary. In particular, we study the edge quantisation and ellipticity for Dirichlet-Neumann operators with respect to interfaces of some codimension on a boundary. We show analogues of the Agranovich-Dynin formula for edge boundary value problems, and we establish relations of elliptic operators for different weights, via the spectral flow of the underlying conormal symbols.

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45

Steen, Johan. "Correction Classes and Elliptic Cohomology". Thesis, Norges teknisk-naturvitenskapelige universitet, Institutt for matematiske fag, 2010. http://urn.kb.se/resolve?urn=urn:nbn:no:ntnu:diva-8575.

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46

Nkgau, Tallman Zacharia. "Elliptic curve cryptosystems, a survey". Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1999. http://www.collectionscanada.ca/obj/s4/f2/dsk1/tape7/PQDD_0022/MQ50845.pdf.

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47

Johnstone, Jennifer Ann. "Congruent numbers and elliptic curves". Thesis, University of British Columbia, 2010. http://hdl.handle.net/2429/26993.

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Throughout this thesis we will be primarily concerned with the area of a rational right angle triangle, also known as a congruent number. The purpose of this thesis is to present a family of congruent number elliptic curves with rank at least three, as well as provide some insight into the distribution of congruent numbers. We provide an in depth background on congruent numbers and elliptic curves, as well as an overview of one of the key methods that will be used in determining the rank of an elliptic curve.

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48

Meier, Lennart [Verfasser]. "United Elliptic Homology / Lennart Meier". Bonn : Universitäts- und Landesbibliothek Bonn, 2012. http://d-nb.info/1044082070/34.

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49

Nkgau, Tallman Zacharia. "Elliptic curve cryptosystems : a survey". Thesis, McGill University, 1998. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=21614.

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Elliptic curves have been a subject of much mathematical study since early in the past century. Recently, through the work of Koblitz and Miller, they have found application in the area of publickey cryptography. The basic reason is that, elliptic curves over finite fields provide an abundance of finite abelian groups which could be used as a basis for public-key cryptosystems. The objective of this thesis is to survey the field of elliptic curve public-key cryptography as it exists now, with an attempt to identify key ideas and contributions. We are particularly interested in elliptic curve cryptosystems defined over Zp (p > 3 and prime) and the ring Zn (n is a product of two large distinct primes).

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50

Plater, Andrew John. "Height pairings on elliptic curves". Thesis, University of Cambridge, 1991. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.387103.

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