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Thesis (M.A.)--Miami University, Dept. of History, 2008. / Title from first page of PDF document. Includes bibliographical references (p.58-60).

Šio mokslinio darbo tikslas: įvertinti įvairių veiksnių įtaką Lietuvoje veisiamų ristūnų veislių žirgų pajėgumui. Darbo uždaviniai: 1. ištirti genetinių veiksnių įtaką Lietuvoje veisiamų ristūnų pajėgumui; 2. ištirti negenetinių veiksnių įtaką Lietuvoje veisiamų ristūnų pajėgumui. Išvados: 1. Lietuvoje ristūnų veislė sudaro 11,8 proc. bendro arklių skaičiaus. Didžiąją dalį tikslinės grupės žirgų sudarė gimę Lietuvoje (65 proc.), 28 proc. gimę Prancūzijoje ir 7 proc. gimę kitose šalyse. 2. Per 2006 – 2012 metų laikotarpį tiriamieji žirgai startavo 2525. Daugiausia startų padarė Amerikos ristūnai (1006). Rusų ristūnai startavo 810 kartus, prancūzai – 704 kartus. Važiavimai buvo rengiami dešimtyje skirtingų Lietuvos hipodromų. Populiariausi hipodromai Širvintų (1065 startai, 1000 m. distancijos greičio vidurkis 1,2269 min.) ir Utenos (878 startai, 1000 m. distancijos greičio vidurkis 1,2258 min.). Tiek varžybų vieta (p<0,0001), tiek data (p<0,0001) turėjo įtakos varžybose užimtai vietai. 3. Iš 90 ristūnų didžioji dalis buvo gimusi Lietuvoje, jų 1000 m. distancijos greičio vidurkis 1,2292±0,0039 min., varžybose užimdavo vidutiniškai 3,3±0,0501 vietą. Geriausius rezultatus parodė Švedijoje gimę ristūnai (1000 m. distancijos rezultatų vidurkis 1,1892±0,0163 min., varžybose užimtų vietų vidurkis - 2,3±0,161 vieta). 4. Tyrimo metu buvo nustatyta, kad per tiriamąjį laikotarpį (2006 – 2012 m.) geresnius rezultatus parodė prancūzų veislės ristūnai, jų 1000 m. distancijos rezultatų... [toliau žr. visą tekstą] / The aim of the research: to evaluate the influence of different factors over the capacities of the horses, specifically the American Standardbreds, French trotters and Russian trotters, bred in Lithuania. The objects of the research: 1. to examine and analyze the influence of genetic factors over the capacities of the trotters, bred in Lithuania); 2. to examine the influence of non – genetic factors over the capacities of the trotters, bred in Lithuania). The trotters’ race sports in Lithuania bears a deep – rooted tradition, which was established nearly two centuries ago. In order to become strongly competitive with trotters, bred in other countries, the Lithuanian horse breeders seek to grade up their herds. As a consequence, the professional level of the trainers and the race drivers increases, the infrastructure of the hipodromes is improved. The research by itself was carried out in the period of two years starting from 2011 and ending in 2013, in the Republican League of Racing Horses („Respublikinė lenktyninių žirgų lyga“) and in the Lithuanian Trotter Sports Association („Lietuvos ristūnų sporto asociacija“). The Republican League of Racing Horses and the Lithuanian Trotter Sports Association kindly provided the researcher with result protocols of the trotter’s races, held in between the year 2006 and the year 2012. As a target group of the research was selected: 30 American Standardbreds, 30 French trotters, 30 Russian trotters (90 horses in total). Data, gathered... [to full text]

La convergence de la formule de Trotter en norme d'opérateur a été établie depuis 1990 avec différentes conditions pour des générateurs auto-adjoints dans un espace de Hilbert. Cette thèse étudie au contraire des semi-groupes holomorphes dont les générateurs ne sont pas auto-adjoints. Dans le premier ensemble de résultats, il s'agit d'estimations d'erreur en norme d'opérateur pour la formule de Trotter : je considère des perturbations accrétives dans un espace de Banach général, puis dans un espace de Hilbert. Dans la deuxième partie, j'étends certains résultats de convergence de la formule de Trotter au cas de générateurs m-sectoriels et pour la norme d'opérateur ou la norme de la trace. Enfin la dernière partie consiste en une généralisation de la théorie de Chernoff au cas de l'approximation des semi-groupes holomorphes en norme d'opérateur. Cette partie est fondée en particulier sur la notion nouvelle de contraction quasi-sectorielle, le résultat principal montre le lien entre la convergence généralisée (ou convergence au sens de la norme de la résolvante) des générateurs m-sectoriels et l'approximation en norme d'opérateur des semi-groupes holomorphes contractants par des puissances de contractions quasi-sectorielles.

In 1986, Gupta and Murty proved the Lang-Trotter conjecture in the case of elliptic curves having complex multiplication, conditional on the generalized Riemann hypothesis. That is, given a non-torsion point P∈E(ℚ), they showed that P (mod p) generates E(𝔽p) for infinitely many primes p, conditional on the generalized Riemann hypothesis. We demonstrate that Gupta's and Murty's result can be translated into an unconditional result in the language of Drinfeld modules. We follow the example of Hsu and Yu, who proved Artin's conjecture unconditionally in the case of sign normalized rank one Drinfeld modules. Further, we will cover all necessary background information.

In 1986, Gupta and Murty proved the Lang-Trotter conjecture in the case of elliptic curves having complex multiplication, conditional on the generalized Riemann hypothesis. That is, given a non-torsion point P∈E(ℚ), they showed that P (mod p) generates E(𝔽p) for infinitely many primes p, conditional on the generalized Riemann hypothesis. We demonstrate that Gupta's and Murty's result can be translated into an unconditional result in the language of Drinfeld modules. We follow the example of Hsu and Yu, who proved Artin's conjecture unconditionally in the case of sign normalized rank one Drinfeld modules. Further, we will cover all necessary background information.

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Mémoire numérisé par la Division de la gestion de documents et des archives de l'Université de Montréal.

Mémoire numérisé par la Division de la gestion de documents et des archives de l'Université de Montréal

In this thesis, I have explored the different approaches towards proving Artin's `primitive root' conjecture unconditionally and the elliptic curve analogue of the same. This conjecture was posed by E. Artin in the year 1927, and it still remains an open problem. In 1967, C. Hooley proved the conjecture based on the assumption of the generalized Riemann hypothesis. Thereafter, the mathematicians tried to get rid of the assumption and it seemed quite a daunting task. In 1983, the pioneering attempt was made by R. Gupta and M. Ram Murty, who proved unconditionally that there exists a specific set of 13 distinct numbers such that for at least one of them, the conjecture is true. Along the same line, using sieve theory, D. R. Heath-Brown reduced this set down to 3 distinct primes in the year 1986. This is the best unconditional result we have so far. In the first part of this thesis, we will review the sieve theoretic approach taken by Gupta-Murty and Heath-Brown. The second half of the thesis will deal with the elliptic curve analogue of the Artin's conjecture, which is also known as the Lang-Trotter conjecture. Lang and Trotter proposed the elliptic curve analogue in 1977, including the higher rank version, and also proceeded to set up the mathematical formulation to prove the same. The analogue conjecture was proved by Gupta and Murty in the year 1986, assuming the generalized Riemann hypothesis, for curves with complex multiplication. They also proved the higher rank version of the same. We will discuss their proof in details, involving the sieve theoretic approach in the elliptic curve setup. Finally, I will conclude the thesis with a refinement proposed by Gupta and Murty to find out a finite set of points on the curve such that at least one satisfies the conjecture.