Decidability of Univariate Real Algebra with Predicates for Rational and Integer Powers

We prove decidability of univariate real algebra extended with predicates for rational and integer powers, i.e., $(x^n \in \mathbb{Q})$ and $(x^n \in \mathbb{Z})$. Our decision procedure combines computation over real algebraic cells with the rational root theorem and witness construction via algebraic number density arguments.Comment: To appear in CADE-25: 25th International Conference on Automated Deduction, 2015. Proceedings to be published by Springer-Verla

Searching for Planets in the Hyades V: Limits on Planet Detection in the Presence of Stellar Activity

We present the results of a radial velocity survey of a sample of Hyades stars, and discuss the effects of stellar activity on radial velocity measurements. The level of radial velocity scatter due to rotational modulation of stellar surface features for the Hyades is in agreement with the predictions of Saar & Donahue (1997)- the maximum radial velocity rms of up to ~50 m/s, with an average rms of ~16 m/s. In this sample of 94 stars, we find 1 new binary, 2 stars with linear trends indicative of binary companions, and no close-in giant planets. We discuss the limits on extrasolar planet detection in the Hyades and the constraints imposed on radial velocity surveys of young stars.Comment: To appear in the June 2004 issue of A

Relating two standard notions of secrecy

Two styles of definitions are usually considered to express that a security protocol preserves the confidentiality of a data s. Reachability-based secrecy means that s should never be disclosed while equivalence-based secrecy states that two executions of a protocol with distinct instances for s should be indistinguishable to an attacker. Although the second formulation ensures a higher level of security and is closer to cryptographic notions of secrecy, decidability results and automatic tools have mainly focused on the first definition so far. This paper initiates a systematic investigation of the situations where syntactic secrecy entails strong secrecy. We show that in the passive case, reachability-based secrecy actually implies equivalence-based secrecy for digital signatures, symmetric and asymmetric encryption provided that the primitives are probabilistic. For active adversaries, we provide sufficient (and rather tight) conditions on the protocol for this implication to hold.Comment: 29 pages, published in LMC

Confirmation of the Planet Hypothesis for the Long-period Radial Velocity Variations of Beta Geminorum

We present precise stellar radial velocity measurements for the K giant star Beta Gem spanning over 25 years. These data show that the long period low amplitude radial velocity variations found by Hatzes & Cochran (1993) are long-lived and coherent. An examination of the Ca II K emission, spectral line shapes from high resolution data (R = 210,000), and Hipparcos photometry show no significant variations of these quantities with the RV period. These data confirm the planetary companion hypothesis suggested by Hatzes & Cochran (1993). An orbital solution assuming a stellar mass of 1.7 M_sun yields a period, P = 589.6 days, a minimum mass of 2.3 M_Jupiter, and a semi-major axis, and a = 1.6 AU. The orbit is nearly circular (e = 0.02). Beta Gem is the seventh intermediate mass star shown to host a sub-stellar companion and suggests that planet-formation around stars much more massive than the sun may common.Comment: 10 pages, 9 figures, Astronomy and Astrophysics, in pres

Growth and characterization of crystals for IR detectors and second harmonic gereration devices

Two types of materials, L-arginine phosphate (LAP) and doped triglycine sulfate (TGS), are examined for their growth characteristics and relevant properties for second harmonic generation and IR detector applications, respectively

Effects of a Six-Month Walking Intervention on the Physical Activity Measures Among Older Adults

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Formal Verification of Nonlinear Inequalities with Taylor Interval Approximations

We present a formal tool for verification of multivariate nonlinear inequalities. Our verification method is based on interval arithmetic with Taylor approximations. Our tool is implemented in the HOL Light proof assistant and it is capable to verify multivariate nonlinear polynomial and non-polynomial inequalities on rectangular domains. One of the main features of our work is an efficient implementation of the verification procedure which can prove non-trivial high-dimensional inequalities in several seconds. We developed the verification tool as a part of the Flyspeck project (a formal proof of the Kepler conjecture). The Flyspeck project includes about 1000 nonlinear inequalities. We successfully tested our method on more than 100 Flyspeck inequalities and estimated that the formal verification procedure is about 3000 times slower than an informal verification method implemented in C++. We also describe future work and prospective optimizations for our method.Comment: 15 page

Exploring The Frequency Of Close-In Jovian Planets Around M Dwarfs

We discuss our high precision radial velocity results of a sample of 90 M dwarfs observed with the Hobby-Eberly Telescope and the Harlan J. Smith 2.7 m Telescope at McDonald Observatory, as well as the ESO VLT and the Keck I telescopes, within the context of the overall frequency of Jupiter-mass planetary companions to main sequence stars. None of the stars in our sample show variability indicative of a giant planet in a short period orbit, with a 3.8 M_Jup and a 3.5 M_Jup and a < 0.7 AU. Our results point toward a generally lower frequency of close-in Jovian planets for M dwarfs as compared to FGK-type stars. This is an important piece of information for our understanding of the process of planet formation as a function of stellar mass

A Planetary Companion to gamma Cephei A

We report on the detection of a planetary companion in orbit around the primary star of the binary system $\gamma$ Cephei. High precision radial velocity measurements using 4 independent data sets spanning the time interval 1981--2002 reveal long-lived residual radial velocity variations superimposed on the binary orbit that are coherent in phase and amplitude with a period or 2.48 years (906 days) and a semi-amplitude of 27.5 m s$^{-1}$. We performed a careful analysis of our Ca II H & K S-index measurements, spectral line bisectors, and {\it Hipparcos} photometry. We found no significant variations in these quantities with the 906-d period. We also re-analyzed the Ca II $\lambda$8662 {\AA} measurements of Walker et al. (1992) which showed possible periodic variations with the ``planet'' period when first published. This analysis shows that periodic Ca II equivalent width variations were only present during 1986.5 -- 1992 and absent during 1981--1986.5. Furthermore, a refined period for the Ca II $\lambda$8662 {\AA} variations is 2.14 yrs, significantly less than residual radial velocity period. The most likely explanation of the residual radial velocity variations is a planetary mass companion with $M$ sin $i$ = 1.7 $M_{Jupiter}$ and an orbital semi-major axis of $a_2$ $=$ 2.13 AU. This supports the planet hypothesis for the residual radial velocity variations for $\gamma$ Cep first suggested by Walker et al. (1992). With an estimated binary orbital period of 57 years $\gamma$ Cep is the shortest period binary system in which an extrasolar planet has been found. This system may provide insights into the relationship between planetary and binary star formation.Comment: 19 pages, 15 figures, accepted in Ap. J. Includes additional data and improved orbital solutio

Effect of a Walking Program on Functional Fitness Measures in Older Adults

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