74 research outputs found
Wilson function transforms related to Racah coefficients
The irreducible -representations of the Lie algebra consist of
discrete series representations, principal unitary series and complementary
series. We calculate Racah coefficients for tensor product representations that
consist of at least two discrete series representations. We use the explicit
expressions for the Clebsch-Gordan coefficients as hypergeometric functions to
find explicit expressions for the Racah coefficients. The Racah coefficients
are Wilson polynomials and Wilson functions. This leads to natural
interpretations of the Wilson function transforms. As an application several
sum and integral identities are obtained involving Wilson polynomials and
Wilson functions. We also compute Racah coefficients for U_q(\su(1,1)), which
turn out to be Askey-Wilson functions and Askey-Wilson polynomials.Comment: 48 page
Quantum Field Theory on the Noncommutative Plane with Symmetry
We study properties of a scalar quantum field theory on the two-dimensional
noncommutative plane with quantum symmetry. We start from the
consideration of a firstly quantized quantum particle on the noncommutative
plane. Then we define quantum fields depending on noncommutative coordinates
and construct a field theoretical action using the -invariant measure
on the noncommutative plane. With the help of the partial wave decomposition we
show that this quantum field theory can be considered as a second quantization
of the particle theory on the noncommutative plane and that this field theory
has (contrary to the common belief) even more severe ultraviolet divergences
than its counterpart on the usual commutative plane. Finally, we introduce the
symmetry transformations of physical states on noncommutative spaces and
discuss them in detail for the case of the quantum group.Comment: LaTeX, 26 page
Covariant q-differential operators and unitary highest weight representations for U_q su(n,n)
We investigate a one-parameter family of quantum Harish-Chandra modules of
U_q sl(2n). This family is an analog of the holomorphic discrete series of
representations of the group SU(n,n) for the quantum group U_q su(n, n). We
introduce a q-analog of "the wave" operator (a determinant-type differential
operator) and prove certain covariance property of its powers. This result is
applied to the study of some quotients of the above-mentioned quantum
Harish-Chandra modules. We also prove an analog of a known result by J.Faraut
and A.Koranyi on the expansion of reproducing kernels which determines the
analytic continuation of the holomorphic discrete series.Comment: 26 page
Skin lesions suspected of malignancy:an increasing burden on general practice
BACKGROUND: Skin cancer is believed to impose a heavy burden on healthcare services, but the burden of skin lesions suspected of malignancy on primary healthcare has never been evaluated. Therefore the aim of this study was to determine the demand for care in general practice due to these suspected skin lesions (i.e. lesions that are suspected of malignancy by either the patient or the GP). METHODS: Registry study based on data (2001–2010) from the Registration Network Groningen. This is a general practice registration network in the northern part of the Netherlands with an average annual population of approximately 30,000 patients. All patient contacts are coded according to the International Classification of Primary Care (ICPC). Consultations for skin lesions suspected of malignancy were selected according to the assigned ICPC codes. Subsequently, the number of consultations per year and the annual percent change in number of contacts (using the JoinPoint regression program) were calculated and analysed. Additionally, the percentage of patients referred to secondary care or receiving minor surgery within one year after the first contact were calculated. RESULTS: From 2001 onwards we found an annual increase in demand for care due to skin lesions suspected of malignancy of 7.3% (p < 0.01) and in 2010 the benign:malignant ratio was 10:1. In total 13.0% of the patients were referred and after 2006, minor surgery was performed on 31.2% of the patients. Most surgeries and referrals took place within 30 days. CONCLUSIONS: Suspected skin lesions impose an increasing burden on primary healthcare and most likely on healthcare costs as well. General practitioners should therefore be trained in diagnosing skin lesions suspected of malignancy, as a high diagnostic accuracy can save lives in the case of melanoma, and may also prevent unnecessary, costly, excisions and referrals to secondary healthcare
Quantum planes and quantum cylinders from Poisson homogeneous spaces
Quantum planes and a new quantum cylinder are obtained as quantization of
Poisson homogeneous spaces of two different Poisson structures on classical
Euclidean group E(2).Comment: 13 pages, plain Tex, no figure
The exponential map for representations of
For the quantum group and the corresponding quantum algebra
Fronsdal and Galindo explicitly constructed the so-called
universal -matrix. In a previous paper we showed how this universal
-matrix can be used to exponentiate representations from the quantum algebra
to get representations (left comodules) for the quantum group. Here, further
properties of the universal -matrix are illustrated. In particular, it is
shown how to obtain comodules of the quantum algebra by exponentiating modules
of the quantum group. Also the relation with the universal -matrix is
discussed.Comment: LaTeX-file, 7 pages. Submitted for the Proceedings of the 4th
International Colloquium ``Quantum Groups and Integrable Systems,'' Prague,
22-24 June 199
Free q-Schrodinger Equation from Homogeneous Spaces of the 2-dim Euclidean Quantum Group
After a preliminary review of the definition and the general properties of
the homogeneous spaces of quantum groups, the quantum hyperboloid qH and the
quantum plane qP are determined as homogeneous spaces of Fq(E(2)). The
canonical action of Eq(2) is used to define a natural q-analog of the free
Schro"dinger equation, that is studied in the momentum and angular momentum
bases. In the first case the eigenfunctions are factorized in terms of products
of two q-exponentials. In the second case we determine the eigenstates of the
unitary representation, which, in the qP case, are given in terms of Hahn-Exton
functions. Introducing the universal T-matrix for Eq(2) we prove that the
Hahn-Exton as well as Jackson q-Bessel functions are also obtained as matrix
elements of T, thus giving the correct extension to quantum groups of well
known methods in harmonic analysis.Comment: 19 pages, plain tex, revised version with added materia
Fermat-linked relations for the Boubaker polynomial sequences via Riordan matrices analysis
The Boubaker polynomials are investigated in this paper. Using Riordan
matrices analysis, a sequence of relations outlining the relations with
Chebyshev and Fermat polynomials have been obtained. The obtained expressions
are a meaningful supply to recent applied physics studies using the Boubaker
polynomials expansion scheme (BPES).Comment: 12 pages, LaTe
On the Two q-Analogue Logarithmic Functions
There is a simple, multi-sheet Riemann surface associated with e_q(z)'s
inverse function ln_q(w) for 0< q < 1. A principal sheet for ln_q(w) can be
defined. However, the topology of the Riemann surface for ln_q(w) changes each
time "q" increases above the collision point of a pair of the turning points of
e_q(x). There is also a power series representation for ln_q(1+w). An
infinite-product representation for e_q(z) is used to obtain the ordinary
natural logarithm ln{e_q(z)} and the values of sum rules for the zeros "z_i" of
e_q(z). For |z|<|z_1|, e_q(z)=exp{b(z)} where b(z) is a simple, explicit power
series in terms of values of these sum rules. The values of the sum rules for
the q-trigonometric functions, sin_q(z) and cos_q(z), are q-deformations of the
usual Bernoulli numbers.Comment: This is the final version to appear in J.Phys.A: Math. & General.
Some explict formulas added, and to update the reference
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