1,720,961 research outputs found
Factorization of the Non-Normal Hamiltonian of Reggeon Field Theory in Bargmann Space
No full textIn this paper, we present a “non-linear” factorization of a family of non-normal operators arising from Gribov’s theory of the following form: Hλ′,μ,λ=λ′A*2A2+μA*A+iλA*(A+A*)A, where the quartic Pomeron coupling λ′, the Pomeron intercept μ and the triple Pomeron coupling λ are real parameters, and i2=−1. A* and A are, respectively, the usual creation and annihilation operators of the one-dimensional harmonic oscillator obeying the canonical commutation relation [A,A*]=I. In Bargmann representation, we have A⟷ddz and A*⟷z, z=x+iy. It follows that Hλ′,μ,λ can be written in the following form: Hλ′,μ,λ=p(z)d2dz2+q(z)ddz, where p(z)=λ′z2+iλz and q(z)=iλz2+μz. This operator is an operator of the Heun type where the Heun operator is defined by H=p(z)d2dz2+q(z)ddz+v(z), where p(z) is a cubic complex polynomial, q(z) and v(z) are polynomials of degree at most 2 and 1, respectively, which are given. For z=−iy, Hλ′,μ,λ takes the following form: Hλ′,μ,λ=−a(y)d2dy2+b(y)ddz, with a(y)=y(λ−λ′y) and b(y)=y(λy+μ). We introduce the change of variable y=λ2λ′(1−cos(θ)), θ∈[0,π] to obtain the main result of transforming Hλ′,μ,λ into a product of two first-order operators: H˜λ′,μ,λ=λ′(ddθ+α(θ))(−ddθ+α(θ)), with α(θ) being explicitly determined
On a Chaotic Weighted Shift zpdp+1/dzp+1 of Order p in Bargmann Space
Get PDFThis paper is devoted to the study of the chaotic properties of some specific backward
shift unbounded operators Hp=A*pAP+1; p=0,1,… realized as differential operators in Bargmann space, where A and A* are the standard Bose annihilation and creation operators such that [A,A*]=I
On the Complete Indeterminacy and the Chaoticity of the Generalized Heun Operator in Bargmann Space
No full textIn 1998, we gave a complete scattering analysis of the cubic Heun operator H=a∗(a+a∗)a acting on Bargmann space, where a and a∗ are the standard Bose annihilation and creation operators satisfying the commutation relation [a,a∗]=I. We used the boundary conditions at infinity to give a description of all maximal dissipative extensions in Bargmann space of the minimal Heun’s operator H. The characteristic functions of the dissipative extensions were computed, and some completeness theorems were obtained for the system of generalized eigenvectors of this operator. In this paper, we study the deficiency numbers of the generalized Heun’s operator Hp,m=a∗p(am+a∗m)ap;(p,m=1,2,…) acting on Bargmann space. In particular, here we find some conditions on the parameters p and m such that Hp,m is completely indeterminate. It follows from these conditions that Hp,m is entirely of minimal type. Then, we show that Hp,m and Hp,m+H∗p,m (where H∗p,m is the adjoint of Hp,m) are connected to the chaotic operators
An Elementary Construction on Nonlinear Coherent States Associated to Generalized Bargmann Spaces
Get PDFConsider the space 2(ℂ,()), where ()=−||2⋀ is the
Gaussian measure, and its generalized Bargmann subspaces which are the null
kernels of the operator Δ=−2/+(/)−;
=0,1,…. In this work, we present an other construction of following the Hermite functions
which allows us to define a family of generalized Bargmann transform which maps isometrically into 2(ℝ). The generalized coherent states ∣⟩ associated to are constructed and some properties of them are given
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
A short note on the chaoticity of a weight shift on concrete orthonormal basis associated to some Fock-Bargmann space
No full textVariations 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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