264 research outputs found
Coherent states of a charged particle in a uniform magnetic field
The coherent states are constructed for a charged particle in a uniform
magnetic field based on coherent states for the circular motion which have
recently been introduced by the authors.Comment: 2 eps figure
Function reconstruction as a classical moment problem: A maximum entropy approach
We present a systematic study of the reconstruction of a non-negative
function via maximum entropy approach utilizing the information contained in a
finite number of moments of the function. For testing the efficacy of the
approach, we reconstruct a set of functions using an iterative entropy
optimization scheme, and study the convergence profile as the number of moments
is increased. We consider a wide variety of functions that include a
distribution with a sharp discontinuity, a rapidly oscillatory function, a
distribution with singularities, and finally a distribution with several spikes
and fine structure. The last example is important in the context of the
determination of the natural density of the logistic map. The convergence of
the method is studied by comparing the moments of the approximated functions
with the exact ones. Furthermore, by varying the number of moments and
iterations, we examine to what extent the features of the functions, such as
the divergence behavior at singular points within the interval, is reproduced.
The proximity of the reconstructed maximum entropy solution to the exact
solution is examined via Kullback-Leibler divergence and variation measures for
different number of moments.Comment: 20 pages, 17 figure
Lyapunov exponent and natural invariant density determination of chaotic maps: An iterative maximum entropy ansatz
We apply the maximum entropy principle to construct the natural invariant
density and Lyapunov exponent of one-dimensional chaotic maps. Using a novel
function reconstruction technique that is based on the solution of Hausdorff
moment problem via maximizing Shannon entropy, we estimate the invariant
density and the Lyapunov exponent of nonlinear maps in one-dimension from a
knowledge of finite number of moments. The accuracy and the stability of the
algorithm are illustrated by comparing our results to a number of nonlinear
maps for which the exact analytical results are available. Furthermore, we also
consider a very complex example for which no exact analytical result for
invariant density is available. A comparison of our results to those available
in the literature is also discussed.Comment: 16 pages including 6 figure
Generating Bounds for the Ground State Energy of the Infinite Quantum Lens Potential
Moment based methods have produced efficient multiscale quantization
algorithms for solving singular perturbation/strong coupling problems. One of
these, the Eigenvalue Moment Method (EMM), developed by Handy et al (Phys. Rev.
Lett.{\bf 55}, 931 (1985); ibid, {\bf 60}, 253 (1988b)), generates converging
lower and upper bounds to a specific discrete state energy, once the signature
property of the associated wavefunction is known. This method is particularly
effective for multidimensional, bosonic ground state problems, since the
corresponding wavefunction must be of uniform signature, and can be taken to be
positive. Despite this, the vast majority of problems studied have been on
unbounded domains. The important problem of an electron in an infinite quantum
lens potential defines a challenging extension of EMM to systems defined on a
compact domain. We investigate this here, and introduce novel modifications to
the conventional EMM formalism that facilitate its adaptability to the required
boundary conditions.Comment: Submitted to J. Phys.
Vector Continued Fractions using a Generalised Inverse
A real vector space combined with an inverse for vectors is sufficient to
define a vector continued fraction whose parameters consist of vector shifts
and changes of scale. The choice of sign for different components of the vector
inverse permits construction of vector analogues of the Jacobi continued
fraction. These vector Jacobi fractions are related to vector and scalar-valued
polynomial functions of the vectors, which satisfy recurrence relations similar
to those of orthogonal polynomials. The vector Jacobi fraction has strong
convergence properties which are demonstrated analytically, and illustrated
numerically.Comment: Published form - minor change
Inverting the Sachs-Wolfe Formula: an Inverse Problem Arising in Early-Universe Cosmology
The (ordinary) Sachs-Wolfe effect relates primordial matter perturbations to
the temperature variations in the cosmic microwave background
radiation; can be observed in all directions around us. A standard
but idealised model of this effect leads to an infinite set of moment-like
equations: the integral of with respect to k ()
is equal to a given constant, , for . Here, P is the
power spectrum of the primordial density variations, is a spherical
Bessel function and y is a positive constant. It is shown how to solve these
equations exactly for ~. The same solution can be recovered, in
principle, if the first ~m equations are discarded. Comparisons with classical
moment problems (where is replaced by ) are made.Comment: In Press Inverse Problems 1999, 15 pages, 0 figures, Late
Symptomatic hypogammaglobulinemia in infancy and childhood – clinical outcome and in vitro immune responses
BACKGROUND: Symptomatic hypogammaglobulinemia in infancy and childhood (SHIC), may be an early manifestation of a primary immunodeficiency or a maturational delay in the normal production of immunoglobulins (Ig). We aimed to evaluate the natural course of SHIC and correlate in vitro lymphoproliferative and secretory responses with recovery of immunoglobulin values and clinical resolution. METHODS: Children, older than 1 year of age, referred to our specialist clinic because of recurrent infections and serum immunoglobulin (Ig) levels 2 SD below the mean for age, were followed for a period of 8 years. Patient with any known familial, clinical or laboratory evidence of cellular immunodeficiency or other immunodeficiency syndromes were excluded from this cohort. Evaluation at 6- to 12-months intervals continued up to 1 year after resolution of symptoms. In a subgroup of patients, in vitro lymphocyte proliferation and Ig secretion in response to mitogens was performed. RESULTS: 32 children, 24 (75%) males, 8 (25%) females, mean age 3.4 years fulfilled the inclusion criteria. Clinical presentation: ENT infections 69%, respiratory 81%, diarrhea 12.5%. During follow-up, 17 (53%) normalized serum Ig levels and were diagnosed as transient hypogammaglobulinemia of infancy (THGI). THGI patients did not differ clinically or demographically from non-transient patients, both having a benign clinical outcome. In vitro Ig secretory responses, were lower in hypogammaglobulinemic, compared to normal children and did not normalize concomitantly with serum Ig's in THGI patients. CONCLUSIONS: The majority of children with SHIC in the first decade of life have THGI. Resolution of symptoms as well as normalization of Ig values may be delayed, but overall the clinical outcome is good and the clinical course benign
Pertussis infection in fully vaccinated children in day-care centers, Israel.
We tested 46 fully vaccinated children in two day-care centers in Israel who were exposed to a fatal case of pertussis infection. Only two of five children who tested positive for Bordetella pertussis met the World Health Organization's case definition for pertussis. Vaccinated children may be asymptomatic reservoirs for infection
Densities of States, Moments, and Maximally Broken Time-Reversal Symmetry
Power moments, modified moments, and optimized moments are powerful tools for
solving microscopic models of macroscopic systems; however the expansion of the
density of states as a continued fraction does not converge to the macroscopic
limit point-wise in energy with increasing numbers of moments. In this work the
moment problem is further constrained by minimal lifetimes or maximal breaking
of time-reversal symmetry, to yield approximate densities of states with
point-wise macroscopic limits. This is applied numerically to models with one
and two finite bands with various singularities, as well as to a model with
infinite band-width, and the results are compared with the maximum entropy
approximation where possible.Comment: Accepted for publication in Physical Review
Hypercomplex polynomials, vietoris’ rational numbers and a related integer numbers sequence
This paper aims to give new insights into homogeneous hypercomplex Appell polynomials through the study of some interesting arithmetical properties of their coefficients. Here Appell polynomials are introduced as constituting a hypercomplex generalized geometric series whose fundamental role sometimes seems to have been neglected. Surprisingly, in the simplest non-commutative case their rational coefficient sequence reduces to a coefficient sequence S used in a celebrated theorem on positive trigonometric sums by Vietoris (Sitzungsber Österr Akad Wiss 167:125–135, 1958). For S a generating function is obtained which allows to derive an interesting relation to a result deduced by Askey and Steinig (Trans AMS 187(1):295–307, 1974) about some trigonometric series. The further study of S is concerned with a sequence of integers leading to its irreducible representation and its relation to central binomial coefficients.The work of the first and third authors was supported by Portuguese funds through the CIDMA - Center for Research and Development in Mathematics and Applications, and the Portuguese Foundation for Science and Technology (“FCT-Fundação para a Ciência e Tecnologia”), within project PEstOE/MAT/UI4106/2013. The work of the second author was supported by Portuguese funds through the CMAT - Centre of Mathematics and FCT within the Project UID/MAT/00013/2013.info:eu-repo/semantics/publishedVersio
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