A Comparative Study of Coq and HOL

This paper illustrates the differences between the style of theory mechanisation of Coq and of HOL. This comparative study is based on the mechanisation of fragments of the theory of computation in these systems. Examples from these implementations are given to support some of the arguments discussed in this paper. The mechanisms for specifying definitions and for theorem proving are discussed separately, building in parallel two pictures of the different approaches of mechanisation given by these systems

Synchronization Limits of Chaotic Circuits

Through system modeling with electronic circuits, two circuits were constructed that exhibit chaos over a wide ranges of initial conditions. The two circuits were one that modeled an algebraically simple “jerk” function and a resistor-inductor-diode (RLD) circuit where the diode was reverse-biased on the positive voltage cycle of the alternating current source. Using simulation data from other experiments, the waveforms, bifurcation plots, and phase space plots of the concrete circuit were verified. Identical circuits were then built containing variable components and coupled to their original, matching circuits. The variable components were used to observe a wide range of conditions to establish the desynchronization parameters and the range of synchronization

Students\u27 Perspectives on Belonging and Scholar Identity Development

TRIO Educational Talent Search (ETS) is an educational opportunity program serving middle - high school students. It is meant to increase student admittance, enrollment, retention and graduation from post-secondary degree programs. TRIO staff must meet these goals through voluntary enrichment activities for youth in their programs. Each program must identify the best practices that will motivate and prepare students to meet and reach difficult educational goals. This research study identifies best practices in fostering belonging and scholar identity in a qualitative case study of TRIO pre-college students. The data from this qualitative study shows separate but related results about student relationships in their middle school environment as well as characteristics of student scholar identities. The findings suggest that students seek out a sense of belonging at school, but that seeking this belonging can have negative repercussions. Furthermore, participant responses suggested that there are ways for educators to encourage student motivation to work on academics through concrete learning and choice. These findings lead to two significant and possible implications. Educators must address student sense of belonging at school before creating a learning environment that fosters student motivation for academic learning. They can use tools such as experiential learning, choice and real world outcomes to foster student motivation for academic learning. If educators and programs work to address student sense of belonging and creating learning environments that foster student motivation for academic learning, students will be better poised to develop a scholar identity

Possible Distorting Effects of Gef26 in Drosophila Melanogaster

Segregation distortion is a meiotic drive system that results in the favorable inheritance of the SD chromosome over the SD+counterpart. SD produces a malfunctioning form of RanGAP, instead of being able to move in and out of the nucleus this truncated anGAP is unable to be exported and therefore aggregates within the nucleus. This appears to affect RspS during the condensation phase of spermatogenesis, but the exact mechanism for this is unknown. In order to further understand the working components of this system, specific deletions within the second chromosome were studied. The study was conducted systematically by beginning with larger deletions that had previously shown distortion and slowly reducing the size of the deletion. When these deletion stocks were combined with SD-5r7, with RspS on the Y chromosome it was found that a deletion of the region 26C1;26D1 displayed distortion whereas deletion of the region 26C3;26D1 did not. When a deletion of the 26C2;26C3 region was tested distortion was observed. Within this region the genes Cpr and Gef26 are of particular interest. Stocks containing a mutation in Cpr did not demonstrate distortion when combined with SD-5r7. However, when a stock containing a mutation in the gene Gef26 was combined with SD-5r7, distortion was noted. These results suggest that better understanding of the gene Gef26, and its function within the cell during spermatogenesis, would shed some light as to how segregation distortion takes place on a molecular level

Low-Mass X-ray Binaries and Globular Clusters in Early-Type Galaxies. I. Chandra Observations

We present a Chandra survey of LMXBs in 24 early-type galaxies. Correcting for detection incompleteness, the X-ray luminosity function (XLF) of each galaxy is consistent with a powerlaw with negative logarithmic differential slope, beta~2.0. However, beta strongly correlates with incompleteness, indicating the XLF flattens at low-Lx. The composite XLF is well-fitted by a powerlaw with a break at 2.21(+0.65,-0.56)E38 erg/s and beta=1.40(+0.10,-0.13) and 2.84(+0.39,-0.30) below and above it, respectively. The break is close to the Eddington limit for a 1.4Msun neutron-star, but the XLF shape rules out its representing the division between neutron-star and black-hole systems. Although the XLFs are similar, we find evidence of some variation between galaxies. The high-Lx XLF slope does not correlate with age, but may correlate with [alpha/Fe]. Considering only LMXBs with Lx>1E37 erg/s, matching the LMXBs with globular clusters (GCs) identified in HST observations of 19 of the galaxies, we find the probability a GC hosts an LMXB is proportional to LGC^alpha ZFe^gamma} where alpha=1.01+/-0.19 and gamma=0.33+/-0.11. Correcting for GC luminosity and colour effects, and detection incompleteness, we find no evidence that the fraction of LMXBs with Lx>1e37 erg/s in GCs (40%), or the fraction of GCs hosting LMXBs (~6.5%) varies between galaxies. The spatial distribution of LMXBs resembles that of GCs, and the specific frequency of LMXBs is proportional to the GC specific luminosity, consistent with the hypothesis that all LMXBs form in GCs. If the LMXB lifetime is tau and the duty cycle is Fd, our results imply ~1.5 (tau/1E8 yr)^-1 /Fd LMXBs are formed per Gyr per GC and we place an upper limit of 1 active LMXB in the field per 3.4E9Lsun of V-band luminosity.Comment: 24 pages, 17 figures and 6 tables. Accepted for publication in the Astrophysical Journal. Expanded discussion and various minor revisions to improve robustness of results. Conclusions unchange