Site selection criteria for the optical atmospheric visibility monitoring telescopes

A description of each of the criteria used to decide where to locate the Atmospheric Visibility Monitoring (AVM) telescope systems is given, along with a weighting factor for each of them. These criteria include low probability of clouds, fog, smog, haze, low scattering, low turbulence, availability of security and maintenance, and suitability of a site for a potential optical reception station. They will be used to determine which three of several sites under consideration will be used for monitoring visibility through the atmosphere as it applies to an optical ground-based receiving network as may be used in NASA space missions in decades to come

Equivalence of the Traditional and Non-Standard Definitions of Concepts from Real Analysis

ACL2(r) is a variant of ACL2 that supports the irrational real and complex numbers. Its logical foundation is based on internal set theory (IST), an axiomatic formalization of non-standard analysis (NSA). Familiar ideas from analysis, such as continuity, differentiability, and integrability, are defined quite differently in NSA-some would argue the NSA definitions are more intuitive. In previous work, we have adopted the NSA definitions in ACL2(r), and simply taken as granted that these are equivalent to the traditional analysis notions, e.g., to the familiar epsilon-delta definitions. However, we argue in this paper that there are circumstances when the more traditional definitions are advantageous in the setting of ACL2(r), precisely because the traditional notions are classical, so they are unencumbered by IST limitations on inference rules such as induction or the use of pseudo-lambda terms in functional instantiation. To address this concern, we describe a formal proof in ACL2(r) of the equivalence of the traditional and non-standards definitions of these notions.Comment: In Proceedings ACL2 2014, arXiv:1406.123

Perfect Numbers in ACL2

A perfect number is a positive integer n such that n equals the sum of all positive integer divisors of n that are less than n. That is, although n is a divisor of n, n is excluded from this sum. Thus 6 = 1 + 2 + 3 is perfect, but 12 < 1 + 2 + 3 + 4 + 6 is not perfect. An ACL2 theory of perfect numbers is developed and used to prove, in ACL2(r), this bit of mathematical folklore: Even if there are infinitely many perfect numbers the series of the reciprocals of all perfect numbers converges.Comment: In Proceedings ACL2 2015, arXiv:1509.0552

Formal Verification of Medina's Sequence of Polynomials for Approximating Arctangent

The verification of many algorithms for calculating transcendental functions is based on polynomial approximations to these functions, often Taylor series approximations. However, computing and verifying approximations to the arctangent function are very challenging problems, in large part because the Taylor series converges very slowly to arctangent-a 57th-degree polynomial is needed to get three decimal places for arctan(0.95). Medina proposed a series of polynomials that approximate arctangent with far faster convergence-a 7th-degree polynomial is all that is needed to get three decimal places for arctan(0.95). We present in this paper a proof in ACL2(r) of the correctness and convergence rate of this sequence of polynomials. The proof is particularly beautiful, in that it uses many results from real analysis. Some of these necessary results were proven in prior work, but some were proven as part of this effort.Comment: In Proceedings ACL2 2014, arXiv:1406.123

Site comparison for optical visibility statistics in southern Arizona

One of the best locations in the continental United States for astronomical telescopes is southern Arizona. The mountains surrounding Tucson have clear skies 80 percent of the year, with image quality generally better than 2 seconds on peaks. Two of the existing observatory sites in this area are being considered as locations for one of the three Atmospheric Visibility Monitoring (AVM) observatories. These sites are Mount Lemmon and Mount Hopkins. A comparison of the characteristics of each of the sites is made here to identify the more desirable of the two locations. It is recommended that Mount Lemmon be selected as the Arizona site for this project

Alignment of the atmospheric visibility monitoring telescope

Alignment of the first Atmospheric Visibility Monitoring Telescope has revealed errors in mount design, mount manufacture, software, and electronics. This article discusses error sources and solutions, and re-alignment results. Alignment requirements for operation are also presented. The telescope now operates with the desired accuracy and repeatability

Options for daytime monitoring of atmospheric visibility in optical communications

Techniques for daytime detection of atmospheric transmission and cloud cover to determine the capabilities of future deep-space optical communications links are considered. A modification of the planned nighttime photometry program will provide the best data while minimizing the need for further equipment. Greater degrees of modification will provide increased detection capabilities. Future testing of the equipment will better define the improvement offered by each level of modification. Daytime photometry is favored at certain wavelengths because of higher transmission and lower background noise, thus giving an increased signal-to-noise ratio. A literature search has provided a list of stars brighter than second magnitude at these wavelengths

Between anaphora and deixis...the resolution of the demonstrative noun-phrase ‘that N’

Three experiments examined the hypothesis that the demonstrative noun phrase (NP) that N, as an anadeictic expression, preferentially refers to the less salient referent in a discourse representation when used anaphorically, whereas the anaphoric pronoun he or she preferentially refers to the highly-focused referent. The findings, from a sentence completion task and two reading time experiments that used gender to create ambiguous and unambiguous coreference, reveal that the demonstrative NP specifically orients processing toward a less salient referent when there is no gender cue discriminating between different possible referents. These findings show the importance of taking into account the discourse function of the anaphor itself and its influence on the process of searching for the referent