1,721,024 research outputs found
Solutions for certain classes of the Riccati differential equation
No full textWe derive some analytic closed-form solutions for a class of Riccati equations y'(x) - lambda(0)(x) y(x) +/- y(2)(x) = +/- s(0)(x) where lambda(0)( x), s(0)( x) are C-infinity- functions. We show that if delta(n) = lambda(n)s(n-1) - lambda(n-1)s(n) = 0, where lambda(n) = lambda(')(n-1) + s(n-1) + lambda(0)lambda(n-1) and s(n) = s(n-1)(')+ s(0)lambda(k-1) , n = 1, 2, ... , then the Riccati equation has a solution given by y( x) = -/+ s(n-1)(x)/ lambda(n-1)(x). Extension to the generalized Riccati equation y'(x) + P(x) y(x) + Q(x) y(2)(x) = R(x) is also investigated
Asymptotic iteration method for the inverse power potentials
No full textThe asymptotic iteration method (AIM) is used to accurately calculate the eigenvalues of the Schrödinger equation with the potential ()=−−, ∈(0,1), in arbitrary dimensions. The recently studied case, =1/2, is discussed in detail where we give a reason for non-polynomial solutions. Using AIM sequences, we develop a method to compute the coefficients of the series solution in this case. AIM applications for =1/3,=1/4 and =2/3 are also discussed
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe 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
Generalized quantum isotonic nonlinear oscillator in d dimensions
No full text81Q60; 2735228Source type: Electronic(1)http://dx.doi.org/10.1088/1751-8113/43/46/46530
Soft and hard confinement of a two-electron quantum system
No full textA model physical problem is studied in which a system of two electrons is subject either to soft
confinement by means of attractive oscillator potentials or by entrapment within an impenetrable
spherical box of finite radius R. When hard confinement is present the oscillators can be switched
off. Exact analytical solutions are found for special parameter sets, and highly accurate numerical
solutions (18 decimal places) are obtained for general cases. Some interesting degeneracy questions
are discussed at length
Physical applications of second-order linear differential equations that admit polynomial solutions
No full text34A05 (34A30); 2726694Source type: Electronic(1)http://dx.doi.org/10.1088/1751-8113/43/41/41520
Variations on the Author
Full text link“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
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