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Gautschi proposed a method for computing incomplete beta functions I x ( a , b ) using Miller’s algorithm with a three-term recurrence relation and showed a computation program in ALGOL. In this paper, first, Miller’s algorithm using the recurrence relation satisfied by f k ( x ) = I x ( a + k , b ) is described. Next, another solution that is first-order independent of f k ( x ) of the recurrence relation is given, and its general solution can be expressed as a linear sum of these. Using this general solution, an error analysis for the function I x ( a , b ) is performed for the first time. The relative error of the function values is then expressed in a new formula to a trend of the error behavior. Also, Miller’s algorithm with a normalizing sum is explained and its error analysis is performed. Since Miller’s algorithm requires a predefined number of iterations of the recurrence relation, it is necessary to repeat the computation of the recurrence relation with increasing number of iterations until the required accuracy will be met. Therefore, in this paper, we apply Deuflhard’s algorithm, which can automatically obtain the function value with the required accuracy. This algorithm requires far fewer iterations than Gautschi’s algorithm to obtain the same accuracy.

Between the genesis of computer science in the 1960s and the advent of the World Wide Web around 1990, computer science evolved in significant ways. The author has termed this period the \"second age of computer science.\" This book describes its evolution in the form of several interconnected parallel histories.

A well-known and successful algorithm to compute the singular value decomposition (SVD) of a matrix was published by Golub and Reinsch ( Numer. Math. 14:403–420, 1970 ), together with an implementation in Algol. We give an updated implementation in extended double precision arithmetic in the C programming language. Extended double precision is native for Intel x86 processors and provides improved accuracy at full hardware speed. The complete program for computing the SVD is listed. Additionally, a comprehensive explanation of the original algorithm of Golub and Reinsch ( Numer. Math. 14:403–420, 1970 ) is given at an elementary level without referring to the more general results of Francis ( Comput. J. 4:265–271, 1961 , 1962 ).

We present the first pulsation analysis of four totally eclipsing Algol systems S Cnc, SS Cet, TW And, and VW Cyg using the latest data available from Kepler (K2), and TESS databases. Based on the characteristics observed they are classified to be oscillating eclipsing Algol binaries with primary components having γ Dor type pulsations. The photometric solutions were derived for five Algols including TT Hya using Wilson-Devinney code (v2015), and the absolute parameters of all Algols in study were computed. The period variation study was also conducted using the O-C diagram and the variation is correlated either to mass loss or mass transfer or presence of third body in these systems. All the available IUE high and low resolution spectra for S Cnc, TT Hya as well as VBT and LAMOST spectra for SS Cet were used to measure the equivalent widths of prominent lines, and their significance is presented. Based on the photometric, spectroscopic, period variation, and pulsation studies the evolutionary scenario of all the five Algols is discussed using Teff - Luminosity, q-r and q-p diagrams.

Several computer programs that can implement the Out-of-Kilter algorithm have been written. To date programs have been written in Fortran, Algol, Pascal, Basic, C++ and Matlab. According to the knowledge of the author, a program to do this in R has not yet been written. The R program written in this article can solve both the maximum flow and minimum cost-maximum flow problems. Since the Out-of-Kilter algorithm has a network flow as input, it can also be used to solve the flow in any problem whose information can be presented in the form of a network flow. This includes among others the transportation problem, the assignment problem, the shortest route problem and the caterer problem.

The semantics of programming languages tend to be discussed with high levels of formality; much of the previous research—both philosophical and historical—has investigated them from this perspective. In this paper, I draw on the philosophical and cognitive theories of metaphor and use the early work of Adriaan van Wijngaarden as a historical case study to explore the conceptual and discursive surroundings of semantics. I investigate the relationships between the texts of semantics, the abstract entities they denote, and the metaphors, analogies, and illustrative language used to accompany or explain the same. This serves to further understanding of the historical developments of work in this area, the nature of programming languages and their semantics, and the importance of the communicative methods used in dissemination and education of computer science.

A stellar corona mapped Our knowledge of the morphology and time evolution of stellar coronae is based almost entirely on observations of the Sun. Now observations of the close binary system Algol (Beta Persei) in the constellation of Perseus have provided the first detailed time-lapse images of the magnetosphere of a star other than the Sun. Algol consists of a radio bright K subgiant star in a very close and rapid orbit with a main sequence B8 star. Theory predicts that the coronal plasma should be confined in a magnetic loop structure: the observations reveal a large coronal loop, about one subgiant diameter in height, which is rather larger than predicted, with its base straddling the subgiant and its apex oriented towards the B8 star. The close binary Algol system contains a radio-bright KIV sub-giant star in a very close and rapid orbit with a main sequence B8 star. Evidence points to the existence of an extended, complex coronal magnetosphere originating at the cooler K subgiant, but the detailed morphology of the subgiant's corona and its possible interaction with its companion are unknown. Multi-epoch radio imaging of the Algol system now reveals a large coronal loop suggestive of a persistent asymmetric magnetic field structure aligned between the two stars. The close binary Algol system contains a radio-bright KIV subgiant star in a very close (0.062 astronomical units) and rapid (2.86 day) orbit with a main sequence B8 star. Because the rotation periods of the two stars are tidally locked to the orbital period, the rapid rotation drives a magnetic dynamo. A large body of evidence points to the existence of an extended, complex coronal magnetosphere originating at the cooler K subgiant 1 , 2 , 3 , 4 . The detailed morphology of the subgiant's corona and its possible interaction with its companion are unknown, though theory predicts that the coronal plasma should be confined in a magnetic loop structure 5 , as seen on the Sun. Here we report multi-epoch radio imaging of the Algol system, in which we see a large, persistent coronal loop approximately one subgiant diameter in height, whose base is straddling the subgiant and whose apex is oriented towards the B8 star. This suggests that a persistent asymmetric magnetic field structure is aligned between the two stars. The loop is larger than anticipated theoretically 6 , 7 , but the size may be the result of a magnetic interaction between the two stars.

There probably has never been such a controversial programming language as Algol. In the early 1960s the disciplinary success of the so-called Algol project in helping to forge the discipline of computer science was not matched by a significant adoption of the Algol language, in any of its three versions. This contrast is even more striking when considering the contemporary success of IBM’s Fortran, a language that, like Algol, was also conceived for scientific computation, but unlike Algol, initially only available for IBM computers. Through extensive archival research, this article shows how the relentless pursuit of a still better language that came to dominate the agenda of the Algol project brought to the fore the tension between the research-driven dimension of the project and the goal of developing a reliable programming language. Such a strong research-oriented agenda increased IBM’s doubts about a project that the firm already felt little urge to support. Yet IBM did not want to appear as obstructing the development of either Algol or Cobol, even if these “common languages” posed a clear risk to the firm’s marketing model. The US Department of Defense’s endorsement of Cobol and the rising popularity of Algol in Europe convinced IBM to push for the use of Fortran in Western Europe in order to protect the domestic market. IBM’s action in support of Fortran reminds us of the power imbalances that have shaped computer science.

We present a review of the latest results of studies of the class of mass-accreting pulsating components of semi-detached eclipsing binaries known as oEA stars. The application of the techniques of asteroseismology to this class of stars unlocks new pathways for gaining a deeper understanding of the short-term evolution and magnetic activity of binary stars. We report the discovery of 49 new pulsating components of eclipsing binaries, based on data from NASA’s TESS space telescope. Recent observational results on the pulsation characteristics of these stars are summarized. The effects of the interaction of the magnetic and spot activity of the Roche-lobe-filling component of a system with the pulsations of the mass-accreting component are discussed.

The current consensus is that at least half of the OB stars are formed in binary or multiple star systems. The evolution of OB stars is greatly influenced by whether the stars begin as close binaries, and the evolution of the binary systems depend on whether the mass transfer is conservative or nonconservative. FUV/NUV spectropolarimetry is poised to answer the latter question. This paper discusses how the Polstar spectropolarimetry mission can characterize the degree of nonconservative mass transfer that occurs at various stages of binary evolution, from the initial mass reversal to the late Algol phase, and quantify its amount. The proposed instrument combines spectroscopic and polarimetric capabilities, where the spectroscopy can resolve Doppler shifts in UV resonance lines with 10 km/s precision, and polarimetry can resolve linear polarization with 10−3 precision or better. The spectroscopy will identify absorption by mass streams and other plasmas seen in projection against the stellar disk as a function of orbital phase, as well as scattering from extended splash structures, including jets. The polarimetry tracks the light coming from material not seen against the stellar disk, allowing the geometry of the scattering to be tracked, resolving ambiguities left by the spectroscopy and light-curve information. For example, nonconservative mass streams ejected in the polar direction will produce polarization of the opposite sign from conservative transfer accreting in the orbital plane. Time domain coverage over a range of phases of the binary orbit are well supported by the Polstar observing strategy. Special attention will be given to the epochs of enhanced systemic mass loss that have been identified from IUE observations (pre-mass reversal and tangential gas stream impact). We show how the history of systemic mass and angular momentum loss/gain episodes can be inferred via ensemble evolution through the r–q diagram. Combining the above elements will significantly improve our understanding of the mass transfer process and the amount of mass that can escape from the system, an important channel for changing the final mass and ultimate supernova of a large number of massive stars found in binaries at close enough separation to undergo interaction.