Applications of the Heine and Bauer-Muir transformations to Rogers-Ramanujan type continued fractions

In this paper we show that various continued fractions for the quotient of general Ramanujan functions G(aq, b, λq)/G(a, b, λ) may be derived from each other via Bauer-Muir transformations. The separate convergence of numerators and denominators play a key part in showing that the continued fractions and their Bauer-Muir transformations converge to the same limit. We also show that these continued fractions may be derived from either Heine’s continued fraction for a ratio of 2φ1 functions, or other similar continued fraction expansions of ratios of 2φ1 functions. Further, by employing essentially the same methods, a new continued fraction for G(aq, b, λq)/G(a, b, λ) is derived. Finally we derive a number of new versions of some beautiful continued fraction expansions of Ramanujan for certain combinations of infinite products, with the following being an example: (−a, b; q)∞ − (a, −b; q)∞ (−a, b; q)∞ + (a, −b; q)∞ = (a − b) 1 − ab − (1 − a2)(1 − b2)q 1 − abq2 − (a − bq2)(b − aq2)q 1 − abq4 − (1 − a2q2)(1 − b2q2)q3 1 − abq6 − (a − bq4)(b − aq4)q3 1 − abq8 − ···

Emotion Regulation as the Foundation of Political Attitudes: Does Reappraisal Decrease Support for Conservative Policies?

Cognitive scientists, behavior geneticists, and political scientists have identified several ways in which emotions influence political attitudes, and psychologists have shown that emotion regulation can have an important causal effect on physiology, cognition, and subjective experience. However, no work to date explores the possibility that emotion regulation may shape political ideology and attitudes toward policies. Here, we conduct four studies that investigate the role of a particular emotion regulation strategy – reappraisal in particular. Two observational studies show that individual differences in emotion regulation styles predict variation in political orientations and support for conservative policies. In the third study, we experimentally induce disgust as the target emotion to be regulated and show that use of reappraisal reduces the experience of disgust, thereby decreasing moral concerns associated with conservatism. In the final experimental study, we show that use of reappraisal successfully attenuates the relationship between trait-level disgust sensitivity and support for conservative policies. Our findings provide the first evidence of a critical link between emotion regulation and political attitudes

Risk indicators for dental caries using the International Caries Detection and Assessment System (ICDAS)

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/73802/1/j.1600-0528.2006.00369.x.pd

Space Motions of the Dwarf Spheroidal Galaxies Draco and Sculptor based on HST Proper Motions with ~10-year Time Baseline

We present new proper motion (PM) measurements of the dwarf spheroidal galaxies (dSphs) Draco and Sculptor using multi-epoch images obtained with the Hubble Space Telescope ACS/WFC. Our PM results have uncertainties far lower than previous measurements, even made with the same instrument. The PM results for Draco and Sculptor are (mu_W,mu_N)_Dra = (-0.0562+/-0.0099,-0.1765+/-0.0100) mas/yr and (mu_W,mu_N)_Scl = (-0.0296+/-0.0209,-0.1358 +/-0.0214) mas/yr. The implied Galactocentric velocity vectors for Draco and Sculptor have radial and tangential components: (V_rad,V_tan)_Dra = (-88.6,161.4) +/- (4.4,5.6) km/s; and (V_rad,V_tan)_Scl = (72.6,200.2) +/- (1.3,10.8) km/s. We study the detailed orbital history of both Draco and Sculptor via numerical orbit integrations. Orbital periods of Draco and Sculptor are found to be 1-2 and 2-5 Gyrs, respectively, accounting for uncertainties in the MW mass. We also study the influence of the Large Magellanic Cloud (LMC) on the orbits of Draco and Sculptor. Overall, the inclusion of the LMC increases the scatter in the orbital results. Based on our calculations, Draco shows a rather wide range of orbital parameters depending on the MW mass and inclusion/exclusion of the LMC, but Sculptor's orbit is very well constrained with its most recent pericentric approach to the MW being 0.3-0.4 Gyr ago. Our new PMs imply that the orbital trajectories of both Draco and Sculptor are confined within the Disk of Satellites (DoS), better so than implied by earlier PM measurements, and likely rule out the possibility that these two galaxies were accreted together as part of a tightly bound group.Comment: 17 pages, 8 figures, 6 tables. Accepted for publication in Ap

Investigation of non-uniform airflow signal oscillation during high frequency chest compression

BACKGROUND: High frequency chest compression (HFCC) is a useful and popular therapy for clearing bronchial airways of excessive or thicker mucus. Our observation of respiratory airflow of a subject during use of HFCC showed the airflow oscillation by HFCC was strongly influenced by the nonlinearity of the respiratory system. We used a computational model-based approach to analyse the respiratory airflow during use of HFCC. METHODS: The computational model, which is based on previous physiological studies and represented by an electrical circuit analogue, was used for simulation of in vivo protocol that shows the nonlinearity of the respiratory system. Besides, airflow was measured during use of HFCC. We compared the simulation results to either the measured data or the previous research, to understand and explain the observations. RESULTS AND DISCUSSION: We could observe two important phenomena during respiration pertaining to the airflow signal oscillation generated by HFCC. The amplitudes of HFCC airflow signals varied depending on spontaneous airflow signals. We used the simulation results to investigate how the nonlinearity of airway resistance, lung capacitance, and inertance of air characterized the respiratory airflow. The simulation results indicated that lung capacitance or the inertance of air is also not a factor in the non-uniformity of HFCC airflow signals. Although not perfect, our circuit analogue model allows us to effectively simulate the nonlinear characteristics of the respiratory system. CONCLUSION: We found that the amplitudes of HFCC airflow signals behave as a function of spontaneous airflow signals. This is due to the nonlinearity of the respiratory system, particularly variations in airway resistance