1,721,549 research outputs found
A diluted version of the problem of the existence of the Hofstadter sequence
No full textWe investigate the conditions on an integer sequence f(n)f(n), n is an element of N, with f(1) = 0, such that the sequence q(n), computed recursively via q(n) = q(n-q(n-1)) + f(n), with q(1) = 1, exists. We prove that f(n) is 'slow', that is, f(n+1) - f(n) is an element of {0,1}, n >= 1, is a sufficient but not necessary condition for the existence of sequence q. Sequences q defined in this way typically display non-trivial dynamics: in particular, they are generally aperiodic with no obvious patterns. We discuss and illustrate this behavior with some examples
Bifurcation phenomena and attractive periodic solutions in the saturating inductor circuit
No full textIn this paper, we investigate bifurcation phenomena, such as those of the periodic solutions, for the 'unperturbed' nonlinear system G(x)x+beta x=0, with G(x) = (alpha +x(2))/ (1 + x(2)) and alpha > 1, beta > 0, when we add the two competing terms -f(t) + gamma x, with f(t) a time-periodic analytic 'forcing' function and gamma > 0 the dissipative parameter. The resulting differential equation G(x)x+beta x+yx-f(t) = 0 describes approximately an electronic system known as the saturating inductor circuit. For any periodic orbit of the unperturbed system, we provide conditions which give rise to the appearance of subharmonic solutions. Furthermore, we show that other bifurcation phenomena arise as there is a periodic solution with the same period as the forcing function f (t) which branches off the origin when the perturbation is switched on. We also show that such a solution, which encircles the origin, attracts the entire phase space when the dissipative parameter becomes large enough. We then compute numerically the basins of attraction of the attractive periodic solutions by choosing specific examples of the forcing function f (t), which are dictated by experience. We provide evidence showing that all the dynamics of the saturating inductor circuit is organized by the persistent subharmonic solutions and by the periodic solution around the origin
The high-order Euler method and the spin-orbit model
No full textWe present an algorithm for the rapid numerical integration of smooth, time-periodic differential equations with small nonlinearity, particularly suited to problems with small dissipation. The emphasis is on speed without compromising accuracy and we envisage applications in problems where integration over long time scales is required; for instance, orbit probability estimation via Monte Carlo simulation. We demonstrate the effectiveness of our algorithm by applying it to the spin-orbit problem, for which we have derived analytical results for comparison with those that we obtain numerically. Among other tests, we carry out a careful comparison of our numerical results with the analytically predicted set of periodic orbits that exists for given parameters. Further tests concern the long-term behaviour of solutions moving towards the quasi-periodic attractor, and capture probabilities for the periodic attractors computed from the formula of Goldreich and Peale. We implement the algorithm in standard double precision arithmetic and show that this is adequate to obtain an
excellent measure of agreement between analytical predictions and the proposed fast algorithm
Periodic attractors for the varactor equation
No full textWe consider a class of differential equations, x + yx + x(2p) = f(wt), with p is an element of N and omega is an element of R-d, describing one-dimensional dissipative systems subject to a periodic forcing. For p = 1 the equation describes a resistor-inductor-varactor circuit, hence the name 'varactor equation'. We concentrate on the limit cycle described by the trajectory with the same period as the forcing; numerically, for g large enough, it appears to attract all trajectories which remain bounded in phase space. We find estimates for the basin of attraction of this limit cycle, which are good for large values of g. Also, we show that the results extend to the case of quasi-periodic forcing, provided the frequency vector omega satisfies a Diophantine condition - for instance, the Bryuno or the standard Diophantine condition
Going Beyond Counting First Authors in Author Co-citation Analysis
Get PDFThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Variations on the Author
Get PDF“Variations on the Author” discusses two of Eduardo Coutinho’s recent films (Um Dia na Vida, from 2010, and Últimas Conversas, posthumously released in 2015) and their contribution to the general question of documentary authorship. The director’s filmography is characterized by a consistent yet self-effacing form of authorial self-inscription: Coutinho often features as an interviewer that rather than express opinions propels discourses; an interviewer that is good at listening. This mode of self-inscription characterizes him as an author who is not expressive but who is nonetheless markedly present on the screen. In Um Dia na Vida, however, Coutinho is completely absent form the image, while Últimas Conversas, on the contrary, includes a confessional prologue that moves the director from the margins to the center of his films. This article examines the ways in which these works stand out in the filmography of a director who offers new insights into the notion of cinematic authorship
Appropriate Similarity Measures for Author Cocitation Analysis
Get PDFWe provide a number of new insights into the methodological discussion about author cocitation analysis. We first argue that the use of the Pearson correlation for measuring the similarity between authors’ cocitation profiles is not very satisfactory. We then discuss what kind of similarity measures may be used as an alternative to the Pearson correlation. We consider three similarity measures in particular. One is the well-known cosine. The other two similarity measures have not been used before in the bibliometric literature. Finally, we show by means of an example that our findings have a high practical relevance.information science;Pearson correlation;cosine;similarity measure;author cocitation analysis
Dispelling the Myths Behind First-author Citation Counts
Get PDFWe conducted a full-scale evaluative citation analysis study of scholars in the XML research field to explore just how different from each other author rankings resulting from different citation counting methods actually are, and to demonstrate the capability of emerging data and tools on the Web in supporting more realistic citation counting methods. Our results contest some common arguments for the continued
use of first-author citation counts in the evaluation of scholars, such as high correlations between author rankings by first-author citation counts and other citation
counting methods, and high costs of using more realistic citation counting methods that are not well-supported by the ISI databases. It is argued that increasingly available digital full text research papers make it possible for citation analysis studies to go beyond what the ISI databases have directly supported and to employ more
sophisticated methods
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