scholarly journals Automatic discovery of irrationality proofs and irrationality measures

2020 ◽  
pp. 1-11
Author(s):  
Doron Zeilberger ◽  
Wadim Zudilin
Keyword(s):  
Symbolic Computation ◽  
Experimental Mathematics ◽  
Automatic Discovery ◽  
Human Touch

We illustrate the power of Experimental Mathematics and Symbolic Computation to suggest irrationality proofs of natural constants, and the determination of their irrationality measures. Sometimes such proofs can be fully automated, but sometimes there is still need for a human touch.

scholarly journals Learning a gradient grammar of French liaison

2020 ◽  
Vol 8 ◽  
Author(s):  
Paul Smolensky ◽  
Eric Rosen ◽  
Matthew Goldrick
Keyword(s):  
Symbolic Computation ◽  
Learning Algorithm ◽  
General Algorithm ◽  
Complex Pattern ◽  
Symbolic Representations ◽  
Weighted Constraints ◽  
Grammatical Analysis ◽  
French Words

In certain French words, an orthgraphically-final consonant is unpronounced except, in certain environments, when it precedes a vowel. This phenomenon, liaison, shows significant interactions with several other patterns in French (including h-aspiré, schwa deletion, and the presence of other morphemes in the liaison context). We present a learning algorithm that acquires a grammar that accounts for these patterns and their interactions. The learned grammar employs Gradient Symbolic Computation (GSC), incorporating weighted constraints and partially-activated symbolic representations. Grammatical analysis in the GSC framework includes the challenging determination of the numerical strength of symbolic constituent activations (as well as constraints). Here we present the first general algorithm for learning these quantities from empirical examples: the Error-Driven Gradient Activation Readjustment (EDGAR). Smolensky and Goldrick (2016) proposed a GSC analysis, with hand-determined numerical strengths, in which liaison derives from the coalescence of partially-activated input consonants. EDGAR allows us to extend this work to a wider range of liaison phenomena by automatically determining the more comprehensive set of numerical strengths required to generate the complex pattern of overall liaison behaviour.

Computing Switching Surfaces in Optimal Control Based on Triangular Decomposition

2014 ◽  
Vol 4 (4) ◽  
pp. 345-367
Author(s):  
Xiaoliang Li ◽  
Yanli Huang ◽  
Zewei Zheng ◽  
Wanyou Cheng
Keyword(s):  
Optimal Control ◽  
Symbolic Computation ◽  
Time Optimal Control ◽  
Triangular Decomposition ◽  
Computational Tools ◽  
Computational Burden ◽  
Time Optimal ◽  
Explicit Determination ◽  
Switching Strategies

AbstractVarious algorithms for optimal control require the explicit determination of switching surfaces. However, switching strategies may be very complicated, such that the computation of switching surfaces is quite challenging. General methods are proposed here to compute switching surfaces systematically, based on algebraic computational tools such as triangular decomposition. Our methods are highly complex compared to some widely-used numerical options, but they can be made feasible for realtime applications by moving the computational burden off-line. The tutorial-style presentation is intended to introduce potentially powerful symbolic computation methods to system scientists in particular, and an illustrative example of time-optimal control is given to show the effectiveness and generality of our approach.

Galactic orbits of stars

1966 ◽  
Vol 25 ◽  
pp. 93-97
Author(s):  
Richard Woolley
Keyword(s):  
Globular Cluster ◽  
Potential Field ◽  
High Velocity ◽  
Velocity Vector ◽  
Variable Stars ◽  
The Sun ◽  
Proper Motions ◽  
Rr Lyrae ◽  
The Galaxy

It is now possible to determine proper motions of high-velocity objects in such a way as to obtain with some accuracy the velocity vector relevant to the Sun. If a potential field of the Galaxy is assumed, one can compute an actual orbit. A determination of the velocity of the globular clusterωCentauri has recently been completed at Greenwich, and it is found that the orbit is strongly retrograde in the Galaxy. Similar calculations may be made, though with less certainty, in the case of RR Lyrae variable stars.

Distance to SN 1987A and the LMC

1999 ◽  
Vol 190 ◽  
pp. 549-554
Author(s):  
Nino Panagia
Keyword(s):  
Angular Size ◽  
Large Magellanic Cloud ◽  
Magellanic Cloud ◽  
Light Curves ◽  
Distance Modulus ◽  
Absolute Size ◽  
Sn 1987A

Using the new reductions of the IUE light curves by Sonneborn et al. (1997) and an extensive set of HST images of SN 1987A we have repeated and improved Panagia et al. (1991) analysis to obtain a better determination of the distance to the supernova. In this way we have derived an absolute size of the ringRabs= (6.23 ± 0.08) x 1017cm and an angular sizeR″ = 808 ± 17 mas, which give a distance to the supernovad(SN1987A) = 51.4 ± 1.2 kpc and a distance modulusm–M(SN1987A) = 18.55 ± 0.05. Allowing for a displacement of SN 1987A position relative to the LMC center, the distance to the barycenter of the Large Magellanic Cloud is also estimated to bed(LMC) = 52.0±1.3 kpc, which corresponds to a distance modulus ofm–M(LMC) = 18.58±0.05.

International determination of the total motion of the pole

1961 ◽  
Vol 13 ◽  
pp. 29-41
Author(s):  
Wm. Markowitz
Keyword(s):  
Secular Motion ◽  
The Future

A symposium on the future of the International Latitude Service (I. L. S.) is to be held in Helsinki in July 1960. My report for the symposium consists of two parts. Part I, denoded (Mk I) was published [1] earlier in 1960 under the title “Latitude and Longitude, and the Secular Motion of the Pole”. Part II is the present paper, denoded (Mk II).

Time and Latitude in South Africa

1972 ◽  
Vol 1 ◽  
pp. 27-38
Author(s):  
J. Hers
Keyword(s):  
South Africa ◽  
Cape Town ◽  
Astronomical Observations ◽  
Royal Observatory ◽  
The Republic ◽  
Astronomical Determination ◽  
Limited Accuracy ◽  
Better Than

In South Africa the modern outlook towards time may be said to have started in 1948. Both the two major observatories, The Royal Observatory in Cape Town and the Union Observatory (now known as the Republic Observatory) in Johannesburg had, of course, been involved in the astronomical determination of time almost from their inception, and the Johannesburg Observatory has been responsible for the official time of South Africa since 1908. However the pendulum clocks then in use could not be relied on to provide an accuracy better than about 1/10 second, which was of the same order as that of the astronomical observations. It is doubtful if much use was made of even this limited accuracy outside the two observatories, and although there may – occasionally have been a demand for more accurate time, it was certainly not voiced.

Large-scale Motion of Solar Filaments

2000 ◽  
Vol 179 ◽  
pp. 205-208
Author(s):  
Pavel Ambrož ◽  
Alfred Schroll
Keyword(s):  
Magnetic Flux ◽  
Proper Motion ◽  
Time Scale ◽  
Large Scale ◽  
Accuracy Of Measurements ◽  
Solar Filaments ◽  
General Movement ◽  
Scale Motion ◽  
Velocity Scatter

AbstractPrecise measurements of heliographic position of solar filaments were used for determination of the proper motion of solar filaments on the time-scale of days. The filaments have a tendency to make a shaking or waving of the external structure and to make a general movement of whole filament body, coinciding with the transport of the magnetic flux in the photosphere. The velocity scatter of individual measured points is about one order higher than the accuracy of measurements.

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