42 research outputs found
Rational Periodic Sequences for the Lyness Recurrence
No full textAgraïments: The authors are partially supported by MCYT through grant DPI2008-06699-C02-02 (second author) and MTM2009-10359 (third author). The authors are also supported by the Government of Catalonia through the SGR program.Consider the celebrated Lyness recurrence xn+2 = (a + xn+1)/xn with a ∈ Q. First we prove that there exist initial conditions and values of a for which it generates periodic sequences of rational numbers with prime periods 1, 2, 3, 5, 6, 7, 8, 9, 10 or 12 and that these are the only periods that rational sequences {xn}n can have. It is known that if we restrict our attention to positive rational values of a and positive rational initial conditions the only possible periods are 1, 5 and 9. Moreover 1-periodic and 5-periodic sequences are easily obtained. We prove that for infinitely many positive values of a, positive 9-period rational sequences occur. This last result is our main contribution and answers an open question left in previous works of Bastien & Rogalski and Zeeman. We also prove that the level sets of the invariant associated to the Lyness map is a two-parameter family of elliptic curves that is a universal family of the elliptic curves with a point of order n, n ≥ 5, including n infinity. This fact implies that the Lyness map is a universal normal form for most birational maps on elliptic curves
On 2- and 3-periodic Lyness difference equations
No full textEl títol de la versió pre-print de l'article és: On two and three periodic Lyness difference equationsAgraïments: GSD-UAB and CoDALab Groups are supported by the Government of Catalonia through the SGR program. They are also supported by through grants (first and second authors) and DPI2008-06699-C02-02 (third author).We describe the sequences {xn}n given by the non-autonomous second order Lyness difference equations xn+2 = (an + xn+1)/xn, where {an}n is either a 2-periodic or a 3-periodic sequence of positive values and the initial conditions x1, x2 are as well positive. We also show an interesting phenomenon of the discrete dynamical systems associated to some of these difference equations: the existence of one oscillation of their associated rotation number functions. This behavior does not appear for the autonomous Lyness difference equations
Rational Periodic Sequences for the Lyness Recurrence
No full textAgraïments: The authors are partially supported by MCYT through grant DPI2008-06699-C02-02 (second author) and MTM2009-10359 (third author). The authors are also supported by the Government of Catalonia through the SGR program.Consider the celebrated Lyness recurrence xn+2 = (a + xn+1)/xn with a ∈ Q. First we prove that there exist initial conditions and values of a for which it generates periodic sequences of rational numbers with prime periods 1, 2, 3, 5, 6, 7, 8, 9, 10 or 12 and that these are the only periods that rational sequences {xn}n can have. It is known that if we restrict our attention to positive rational values of a and positive rational initial conditions the only possible periods are 1, 5 and 9. Moreover 1-periodic and 5-periodic sequences are easily obtained. We prove that for infinitely many positive values of a, positive 9-period rational sequences occur. This last result is our main contribution and answers an open question left in previous works of Bastien & Rogalski and Zeeman. We also prove that the level sets of the invariant associated to the Lyness map is a two-parameter family of elliptic curves that is a universal family of the elliptic curves with a point of order n, n ≥ 5, including n infinity. This fact implies that the Lyness map is a universal normal form for most birational maps on elliptic curves
On 2- and 3-periodic Lyness difference equations
No full textEl títol de la versió pre-print de l'article és: On two and three periodic Lyness difference equationsAgraïments: GSD-UAB and CoDALab Groups are supported by the Government of Catalonia through the SGR program. They are also supported by through grants (first and second authors) and DPI2008-06699-C02-02 (third author).We describe the sequences {xn}n given by the non-autonomous second order Lyness difference equations xn+2 = (an + xn+1)/xn, where {an}n is either a 2-periodic or a 3-periodic sequence of positive values and the initial conditions x1, x2 are as well positive. We also show an interesting phenomenon of the discrete dynamical systems associated to some of these difference equations: the existence of one oscillation of their associated rotation number functions. This behavior does not appear for the autonomous Lyness difference equations
Revealing the Identity, History and Nature Conservation Status of Royal Navy Vessel Steam Pinnace 744, in Lyness, Scapa Flow, Orkney Isles / Revelando la identidad, historia y estado de conservaci\uf3n de la naturaleza del buque Pinaza a Vapor 744 de la Royal Navy, en Lyness, Scapa Flow, Islas Orcadas / 揭示奥克尼群岛斯卡帕湾利内斯皇家海军蒸汽舰载艇 744 的身份、历史和自然保护状况 揭示奧克尼群島斯卡帕灣利內斯皇家海軍蒸汽艦載艇 744 的身份、歷史和自然保護狀況
No full text\ua9 2023 The Author(s). Published by Informa UK Limited, trading as Taylor & Francis Group. Presence of a steam pinnace at Lyness, Orkney Islands, was first documented in United Kingdom Hydrographic Office (UKHO) records by letter from a local scallop diver. Historic Environment Scotland (HES) tasked ORCA and Sula Diving Ltd to document this wreck during the Scapa Flow 2013 Marine Archaeology Survey. Side scan sonar and oral history provided initial clues to the identity. Reference to archival data and the Pinnace 199 renovation project (Portsmouth Historic Shipyard) enabled confirmation of its identity and understanding of how the vessel came to lie on the seabed off Rinnigal Pier. Photogrammetry revealed preservation status and during biological surveys two species of national conservation importance were recorded
Viscoplastic BEM fracture analysis of creeping metallic cracked structures in plane stress using complex variable techniques
No full textSummarization: This paper extends a boundary element approach developed earlier by the present author to the solution of viscoplastic fracture problems arising in creeping cracked metallic structural components undergoing plane stress deformation conditions. By using a plane stress viscoplastic formulation this work adopts the procedure of Lyness and Moler to express the derivative of displacement rate as the ratio of the imaginary part of the displacement rate to the imaginary part of a complex variable representing the coordinates of a collocation point. In this manner the evaluation of creep stresses at internal points is greatly simplified. The results thus obtained are highly accurate in comparison with conventional BEM. The application of the present BEM approach is illustrated by obtaining creep stress and strain distribution for center cracked and standard CT fracture specimens subjected to remote tensile and shear stress loading under plane stress deformation conditions.Παρουσιάστηκε στο: Engineering Fracture Mechanic
FPGA Control System for the Automated Test of Microshutters
No full textThe James Webb Space Telescope, scheduled to replace the Hubble in 2013, must simultaneously observe hundreds of faint galaxies. This requirement has led to the development of a programmable transmission mask which can be adapted to admit light with arbitrary pattern of galaxies into its spectrograph. This programmable mask will contain a large array of micro-electromechanical (MEMs) devices called MicroShutters. These microscopic shutters physically open and close like the shutter on a camera, except each shutter is microscopic in size and an array 365 by 171 is used to select the objects under spectroscopic observation at a given time, and to block the unwanted background light from other areas. NASA developed and is currently refining the exceptionally difficult process of manufacturing these shutters. This paper describes how the authors used LabVIEW FPGA and a reconfigurable I/O board to control the shutters in a test chamber and how the flexibility of the system allows us to continue to modify the control algorithms as NASA optimizes the performance of the MicroShutter arrays
The Wisconsin drinking culture: perceptions and drinking patterns of high school students
No full textIncludes bibliographical references
