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We introduce a new family of N -dimensional quantum superintegrable model consisting of double singular oscillators of type (n, N −n). The special cases (2, 2) and (4, 4) were previously identified as the duals of 3-and 5-dimensional deformed Kepler-Coulomb systems with u(1) and su(2) monopoles respectively. The models are multiseparable and their wave functions are obtained in (n, N − n) doublehyperspherical coordinates. We obtain the integrals of motion and construct the finitely generated polynomial algebra that is the direct sum of a quadratic algebra Q(3) involving three generators, so(n), so(N − n) (i.e. Q(3) ⊕ so(n) ⊕ so (N − n) ). The structure constants of the quadratic algebra themselves involve the Casimir operators of the two Lie algebras so(n) and so(N − n). Moreover, we obtain the finite dimensional unitary representations (unirreps) of the quadratic algebra and present an algebraic derivation of the degenerate energy spectrum of the superintegrable model.

We introduce a new superintegrable Kepler-Coulomb system with non-central terms in N -dimensional Euclidean space. We show this system is multiseparable and allows separation of variables in hyperspherical and hyperparabolic coordinates. We present the wave function in terms of special functions. We give a algebraic derivation of spectrum of the superintegrable system. We show how the so(N + 1) symmetry algebra of the N -dimensional Kepler-Coulomb system is deformed to a quadratic algebra with only 3 generators and structure constants involving a Casimir operator of so(N − 1) Lie algebra. We construct the quadratic algebra and the Casimir operator. We show this algebra can be realized in terms of deformed oscillator and obtain the structure function which yields the energy spectrum.

Tuberculosis is a public health problem in Bangladesh. This cross-sectional study was conducted to assess knowledge of TB patients about symptoms, ways of transmission and treatment of tuberculosis, and their perception of the illness. Between March and August 2008, 762 adult TB patients were interviewed at selected DOTS centre of Dhaka city. Male and female distribution was 55.6% and 44.4%, respectively. One quarter of them were illiterate, and more than half had extended family and live in a congested situation. Night fever was the most common symptom known (89.9%), and 56% were aware that it could spread through sneezing/coughing. Television was mentioned as a source of information about TB. The majority expressed a helping attitude towards other TB patients. Although most of them were positive about getting family support, 46.6% mentioned discrimination of separate utensils for food or drink. About 50.5% expressed increased sadness, 39.8% had fear of loss of job/wedges, and 21.4% felt socially neglected. Along with drug treatment the psychosocial reactions of TB patients should be addressed at DOTS centers for better control of the disease.

By applying the recurrence approach and coupling constant metamorphosis, we construct higher order integrals of motion for the Stackel equivalents of the N -dimensional superintegrable Kepler-Coulomb model with non-central terms and the double singular oscillators of type (n, N − n). We show how the integrals of motion generate higher rank cubic algebra C(3)⊕L 1 ⊕L 2 with structure constants involving Casimir operators of the Lie algebras L 1 and L 2 . The realizations of the cubic algebras in terms of deformed oscillators enable us to construct finite dimensional unitary representations and derive the degenerate energy spectra of the corresponding superintegrable systems.

Second order superintegrable systems in conformally flat spaces. IV. The classical 3D Stäckel transform and 3D classification theory J. Math. Phys. 47, 043514 (2006) We introduce a Hartmann system in the generalized Taub-NUT space with Abelian monopole interaction. This quantum system includes well known Kaluza-Klein monopole and MIC-Zwanziger monopole as special cases. It is shown that the corresponding Schrödinger equation of the Hamiltonian is separable in both spherical and parabolic coordinates. We obtain the integrals of motion of this superintegrable model and construct the quadratic algebra and Casimir operator. This algebra can be realized in terms of a deformed oscillator algebra and has finite dimensional unitary representations (unirreps) which provide energy spectra of the system. This result coincides with the physical spectra obtained from the separation of variables. Published by AIP Publishing. [http://dx

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We revisit the MIC-harmonic oscillator in flat space with monopole interaction and derive the polynomial algebra satisfied by the integrals of motion and its energy spectrum using the ad hoc recurrence approach. We introduce a superintegrable monopole system in a generalized Taub-Newman-Unti-Tamburino (NUT) space. The Schrödinger equation of this model is solved in spherical coordinates in the framework of Stäckel transformation. It is shown that wave functions of the quantum system can be expressed in terms of the product of Laguerre and Jacobi polynomials. We construct ladder and shift operators based on the corresponding wave functions and obtain the recurrence formulas. By applying these recurrence relations, we construct higher order algebraically independent integrals of motion. We show that the integrals form a polynomial algebra. We construct the structure functions of the polynomial algebra and obtain the degenerate energy spectra of the model. Published by AIP Publishing.