1,721,092 research outputs found
Hilbert module realization of the square of white noise and the finite difference algebra
Full text linkWe develop an approach to the representations theory of the algebra of the square of white noise based on the construction of Hilbert modules. We find the unique Fock representation and show that the representation space is the usual symmetric Fock space. Although we started with one degree of freedom we end up with countably many degrees of freedom. Surprisingly, our representation turns out to have a close relation to Feinsilver's finite difference algebra. In fact, there exists a holomorphic image of the finite difference algebra in the algebra of square of white noise. Our representation restricted to this image is the Boukas representation on the finite difference Fock space. Thus we extend the Boukas representation to a bigger algebra, which is generated by creators, annihilators, and number operators
Interacting Fock space versus full Fock module
Full text linkWe present several examples where moments of creators and annihilators on an {\it interacting Fock space} may be realized as moments of creators and annihilators on a {\it full Fock module}. Motivated by this experience we answer the question, wether such a possibility exists for arbitrary interacting Fock spaces, in the affirmative sense.
Finally, we consider a subcategory of interacting Fock spaces which are embeddable into a usual Fock space. We see that a creator on the interacting Fock space is represented by an operator , where is a usual creator on the full Fock space and is an operator which does not change the number of particles. In the picture of Hilbert modules the one-particle sector is replaced by a two-sided module over an algebra which contains . Therefore, may be absorbed into the creator, so that we are concerned with a usual creator. However, this creator does not act on a Fock space, but rather on a Fock module
Squared white noise and other non-Gaussian noises as Levy processes on real Lie algebras
Full text linkIt is shown how the relations of the renormalized squared white noise defined
by Accardi, Lu, and Volovich \cite{accardi+lu+volovich99} can be realized as
factorizable current representations or L\'evy processes on the real Lie
algebra \eufrak{sl}_2. This allows to obtain its It\^o table, which turns
out to be infinite-dimensional. The linear white noise without or with number
operator is shown to be a L\'evy process on the Heisenberg-Weyl Lie algebra
or the oscillator Lie algebra. Furthermore, a joint realization of the linear
and quadratic white noise relations is constructed,
but it is proved that no such realizations exist with a vacuum that is an eigenvector of the central element and the annihilator. Classical L\'evy processes are shown to arise as components of L\'evy process on real Lie algebras and their distributions are characterized
Extending the Set of Quadratic Exponential Vectors
Full text linkWe extend the square of white noise algebra over the step functions on R to the test function space L-2(R-d) boolean AND L-infinity (R-d), and we show that in the Fock representation the exponential vectors exist for all test functions bounded by 1/2
Maximal commutative subalgebras invariant for CP-maps: (counter-)examples
No full textAvailable at http://www.worldscinet.com/idaqp/11/1104/S0219025708003269.htm
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
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
Appropriate Similarity Measures for Author Cocitation Analysis
Full text linkWe 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
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