A Three-Term Conjugate Gradient Method with Sufficient Descent Property for Unconstrained Optimization

Conjugate gradient methods are widely used for solving large-scale unconstrained optimization problems, because they do not need the storage of matrices. In this paper, we propose a general form of three-term conjugate gradient methods which always generate a sufficient descent direction. We give a sufficient condition for the global convergence of the proposed general method. Moreover, we present a specific three-term conjugate gradient method based on the multi-step quasi-Newton method. Finally, some numerical results of the proposed method are given

My Sunflower Sue

https://digitalcommons.library.umaine.edu/mmb-vp/2236/thumbnail.jp

Elastic Differential Cross Sections for Space Radiation Applications

The eikonal, partial wave (PW) Lippmann-Schwinger, and three-dimensional Lippmann- Schwinger (LS3D) methods are compared for nuclear reactions that are relevant for space radiation applications. Numerical convergence of the eikonal method is readily achieved when exact formulas of the optical potential are used for light nuclei (A $\le$ 16), and the momentum-space representation of the optical potential is used for heavier nuclei. The PW solution method is known to be numerically unstable for systems that require a large number of partial waves, and, as a result, the LS3D method is employed. The effect of relativistic kinematics is studied with the PW and LS3D methods and is compared to eikonal results. It is recommended that the LS3D method be used for high energy nucleon-nucleus reactions and nucleus-nucleus reactions at all energies because of its rapid numerical convergence and stability

A Third Planet Orbiting HIP 14810

We present new precision radial velocities and a three-planet Keplerian orbit fit for the V = 8.5, G5 V star HIP 14810. We began observing this star at Keck Observatory as part of the N2K Planet Search Project. Wright et al. (2007) announced the inner two planets to this system, and subsequent observations have revealed the outer planet planet and the proper orbital solution for the middle planet. The planets have minimum masses of 3.9, 1.3, and 0.6 M_Jup and orbital periods of 6.67, 147.7, and 952 d, respectively. We have numerically integrated the family of orbital solutions consistent with the data and find that they are stable for at least 10^6 yr. Our photometric search shows that the inner planet does not transit.Comment: ApJL, accepte

My Queen Irene

https://digitalcommons.library.umaine.edu/mmb-vp/4483/thumbnail.jp

Only Me

https://digitalcommons.library.umaine.edu/mmb-vp/3341/thumbnail.jp

The Sunshine of Paradise Alley

https://digitalcommons.library.umaine.edu/mmb-vp/6609/thumbnail.jp

I Love You In The Same Old Way : Darling Sue

https://digitalcommons.library.umaine.edu/mmb-vp/1676/thumbnail.jp

The Sunshine of Paradise Alley

https://digitalcommons.library.umaine.edu/mmb-vp/6610/thumbnail.jp

Retired A Stars and Their Companions VI. A Pair of Interacting Exoplanet Pairs Around the Subgiants 24 Sextanis and HD200964

We report radial velocity measurements of the G-type subgiants 24 Sextanis (=HD90043) and HD200964. Both are massive, evolved stars that exhibit periodic variations due to the presence of a pair of Jovian planets. Photometric monitoring with the T12 0.80m APT at Fairborn Observatory demonstrates both stars to be constant in brightness to <= 0.002 mag, thus strengthening the planetary interpretation of the radial velocity variations. 24 Sex b,c have orbital periods of 453.8 days and 883~days, corresponding to semimajor axes 1.333 AU and 2.08 AU, and minimum masses (Msini) 1.99 Mjup and 0.86 Mjup, assuming a stellar mass 1.54 Msun. HD200964 b,c have orbital periods of 613.8 days and 825 days, corresponding to semimajor axes 1.601 AU and 1.95 AU, and minimum masses 1.85 Mjup and 0.90 Mjup, assuming M* = 1.44 Msun. We also carry out dynamical simulations to properly account for gravitational interactions between the planets. Most, if not all, of the dynamically stable solutions include crossing orbits, suggesting that each system is locked in a mean motion resonance that prevents close encounters and provides long-term stability. The planets in the 24 Sex system likely have a period ratio near 2:1, while the HD200964 system is even more tightly packed with a period ratio close to 4:3. However, we caution that further radial velocity observations and more detailed dynamical modelling will be required to provide definitive and unique orbital solutions for both cases, and to determine whether the two systems are truly resonant.Comment: AJ accepte