Amicable pairs and aliquot cycles for elliptic curves

An amicable pair for an elliptic curve E/Q is a pair of primes (p,q) of good reduction for E satisfying #E(F_p) = q and #E(F_q) = p. In this paper we study elliptic amicable pairs and analogously defined longer elliptic aliquot cycles. We show that there exist elliptic curves with arbitrarily long aliqout cycles, but that CM elliptic curves (with j not 0) have no aliqout cycles of length greater than two. We give conjectural formulas for the frequency of amicable pairs. For CM curves, the derivation of precise conjectural formulas involves a detailed analysis of the values of the Grossencharacter evaluated at a prime ideal P in End(E) having the property that #E(F_P) is prime. This is especially intricate for the family of curves with j = 0.Comment: 53 page

On the Variability of the Length Weight Relationship for Atlantic Bluefin Tuna, Thunnus thynnus (L.)

Following extensive review, a model of the Atlantic bluefin tuna (ABFT), Thunnus thynnus (L.), length–weight relationship for the eastern Atlantic and Mediterranean (RW = 0.0000188 SFL3.01247; Ec 1) is presented on the basis of samples of ABFT spawners, with an average value of index K = 2.03 ± 0.15SD, collected by the Atlantic traps of Portugal and Spain in the Strait of Gibraltar (1963; 1996–1998; 2000–2012), and a set of samples of juvenile fishes from ICCAT–GBYP (n = 707). The resulting model (Ec 1), together with the model used for the eastern stock assessment (RW = 0.000019607 SFL3.0092; Ec 2) and a recently adopted by ICCAT Standing Committee on Research and Statistics (SCRS) (RW = 0.0000315551 SFL2.898454; EAST) are analyzed in using a bi-variant sample [SFL (cm), RW (kg)] of 474 pairs of data with the aim of validating them and establishing which model(s) best fit the reality represented by the sample and, therefore, will have the greatest descriptive and predictive power. The result of the analysis indicates that the model EAST clearly underestimates the weight of spawning ABFT and that model Ec 2 overestimates it slightly, being model Ec 1 that best explains the data of the sample. The result of the classical statistical analysis is confirmed by means of the quantile regression technique, selecting the quantiles 5, 25, 50, 75, and 95%. Other fisheries and biological indicators also conclude that the model EAST gradually underestimates the weight of ABFT spawners (of 2–3 m) by 9–12.5 %, and does not meet the criterion that for RW = 725 kg (Wmax), SFL = 319.93 ± 11.3 cm (Lmax).Cort, JL.; Estruch Fuster, VD.; Neves Dos Santos, M.; Di Natale, A.; Abid, N.; De La Serna, JM. (2015). On the Variability of the Length Weight Relationship for Atlantic Bluefin Tuna, Thunnus thynnus (L.). Reviews in Fisheries Science & Aquaculture. 23(1):23-38. doi:10.1080/23308249.2015.1008625S2338231Aguado-Giménez, F., & García-García, B. (2005). Changes in some morphometric relationships in Atlantic bluefin tuna (Thunnus thynnus thynnus Linnaeus, 1758) as a result of fattening process. Aquaculture, 249(1-4), 303-309. doi:10.1016/j.aquaculture.2005.04.064Block, B. A., Teo, S. L. H., Walli, A., Boustany, A., Stokesbury, M. J. W., Farwell, C. J., … Williams, T. D. (2005). Electronic tagging and population structure of Atlantic bluefin tuna. Nature, 434(7037), 1121-1127. doi:10.1038/nature03463Chapman, E. W., Jørgensen, C., & Lutcavage, M. E. (2011). Atlantic bluefin tuna (Thunnus thynnus): a state-dependent energy allocation model for growth, maturation, and reproductive investment. Canadian Journal of Fisheries and Aquatic Sciences, 68(11), 1934-1951. doi:10.1139/f2011-109Cort, J. L., Arregui, I., Estruch, V. D., & Deguara, S. (2014). Validation of the Growth Equation Applicable to the Eastern Atlantic Bluefin Tuna,Thunnus thynnus(L.), UsingLmax, Tag-Recapture, and First Dorsal Spine Analysis. Reviews in Fisheries Science & Aquaculture, 22(3), 239-255. doi:10.1080/23308249.2014.931173Cort, J. L., Deguara, S., Galaz, T., Mèlich, B., Artetxe, I., Arregi, I., … Idrissi, M. (2013). Determination ofLmaxfor Atlantic Bluefin Tuna,Thunnus thynnus(L.), from Meta-Analysis of Published and Available Biometric Data. Reviews in Fisheries Science, 21(2), 181-212. doi:10.1080/10641262.2013.793284Fraser, K.Possessed. World Record Holder for Bluefin Tuna. Kingstown, Nova Scotia: T & S Office Essentials and printing, 243 pp. (2008).Fromentin, J.-M., & Powers, J. E. (2005). Atlantic bluefin tuna: population dynamics, ecology, fisheries and management. Fish and Fisheries, 6(4), 281-306. doi:10.1111/j.1467-2979.2005.00197.xHattour, A.Contribution a l’étude des Scombridés de Tunisie. Université de Tunis. Faculté des Sciences, 168 pp. (1979).Karakulak, S., Oray, I., Corriero, A., Deflorio, M., Santamaria, N., Desantis, S., & De Metrio, G. (2004). Evidence of a spawning area for the bluefin tuna (Thunnus thynnus L.) in the eastern Mediterranean. Journal of Applied Ichthyology, 20(4), 318-320. doi:10.1111/j.1439-0426.2004.00561.xKoenker, R., & Bassett, G. (1978). Regression Quantiles. Econometrica, 46(1), 33. doi:10.2307/1913643Koenker, R. (2005). Quantile Regression. doi:10.1017/cbo9780511754098Milatou, N., & Megalofonou, P. (2014). Age structure and growth of bluefin tuna (Thunnus thynnus, L.) in the capture-based aquaculture in the Mediterranean Sea. Aquaculture, 424-425, 35-44. doi:10.1016/j.aquaculture.2013.12.037Perçin, F., & Akyol, O. (2009). Lengthâ weight and lengthâ length relationships of the bluefin tuna,Thunnus thynnusL., in the Turkish part of the eastern Mediterranean Sea. Journal of Applied Ichthyology, 25(6), 782-784. doi:10.1111/j.1439-0426.2009.01288.xPercin, F., & Akyol, O. (2010). Some Morphometric Relationships in Fattened Bluefin Tuna, Thunnus thynnus L., from the Turkish Aegean Sea. Journal of Animal and Veterinary Advances, 9(11), 1684-1688. doi:10.3923/javaa.2010.1684.1688Rooker, J. R., Alvarado Bremer, J. R., Block, B. A., Dewar, H., de Metrio, G., Corriero, A., … Secor, D. H. (2007). Life History and Stock Structure of Atlantic Bluefin Tuna (Thunnus thynnus). Reviews in Fisheries Science, 15(4), 265-310. doi:10.1080/10641260701484135Sinovcic, G., Franicevic, M., Zorica, B., & Cikes-Kec, V. (2004). Length-weight and length-length relationships for 10 pelagic fish species from the Adriatic Sea (Croatia). Journal of Applied Ichthyology, 20(2), 156-158. doi:10.1046/j.1439-0426.2003.00519.xTičina, V., Grubišić, L., Šegvić Bubić, T., & Katavić, I. (2011). Biometric characteristics of small Atlantic bluefin tuna (Thunnus thynnus, Linnaeus, 1758) of Mediterranean Sea origin. Journal of Applied Ichthyology, 27(4), 971-976. doi:10.1111/j.1439-0426.2011.01752.

An analysis of catch per unit effort as used to determine abundance, with particular reference to th

Master of ScienceNatural Resources and EnvironmentUniversity of Michiganhttp://deepblue.lib.umich.edu/bitstream/2027.42/113819/1/39015003271031.pd