Discrete Darboux transformation for discrete polynomials of hypergeometric type

Darboux Transformation, well known in second order differential operator theory, is applied here to the difference equation satisfied by the discrete hypergeometric polynomials(Charlier, Meixner-Krawchuk, Hahn)

Quantum Structure of Space Near a Black Hole Horizon

We describe a midi-superspace quantization scheme for generic single horizon black holes in which only the spatial diffeomorphisms are fixed. The remaining Hamiltonian constraint yields an infinite set of decoupled eigenvalue equations: one at each spatial point. The corresponding operator at each point is the product of the outgoing and ingoing null convergences, and describes the scale invariant quantum mechanics of a particle moving in an attractive $1/X^2$ potential. The variable $X$ that is analoguous to particle position is the square root of the conformal mode of the metric. We quantize the theory via Bohr quantization, which by construction turns the Hamiltonian constraint eigenvalue equation into a finite difference equation. The resulting spectrum gives rise to a discrete spatial topology exterior to the horizon. The spectrum approaches the continuum in the asymptotic region.Comment: References added and typos corrected. 21 pages, 1 figur

Reheating induced by competing decay modes

We address the problem of studying the decay of the inflaton field $\phi$ to another scalar field $\chi$ through parametric resonance in the case of a coupling that involves several decay modes. This amounts to the presence of extra harmonic terms in the perturbation of the $\chi$ field dynamics. For the case of two frequencies we compute the geometry of the resonance regions, which is significantly altered due to the presence of non-cuspidal resonance regions associated to higher harmonics and to the emergence of instability `pockets'. We discuss the effect of this change in the efficiency of the energy transfer process for the simplest case of a coupling given by a combination of the two interaction terms of homogeneous degree usually considered in the literature. We find that the presence of higher harmonics has limited cosmological implications.Comment: 14 pages, 4 figures Added references. Corrected typo

Early childhood respiratory tract infections according to parental subfertility and conception by assisted reproductive technologies.

STUDY QUESTION Are children conceived by ART or born to subfertile parents more susceptible to upper or lower respiratory tract infections (URTI, LRTI)? SUMMARY ANSWER ART-conceived children had a higher frequency of and risk of hospitalization for respiratory infections up to age 3, which was only partly explained by parental subfertility. WHAT IS KNOWN ALREADY Some studies report increased risks of infections in children conceived by ART. Results for URTIs and LRTIs are inconclusive, and the contribution of underlying parental subfertility remains unclear. STUDY DESIGN, SIZE, DURATION We included 84 102 singletons of the Norwegian Mother, Father and Child Cohort Study (MoBa) born between 1999 and 2009. Mothers reported time-to-pregnancy at recruitment and child history of, frequency of and hospitalization for, respiratory infections when the child was 6, 18 and 36 months old by questionnaires. Subfertility was defined as having taken 12 or more months to conceive. The Medical Birth Registry of Norway (MBRN) provided information on ART. URTI included throat and ear infections, while LRTI included bronchitis, bronchiolitis, respiratory syncytial virus and pneumonia. PARTICIPANTS/MATERIALS, SETTING, METHODS We used log-binomial regression to estimate risk ratios (RR) and 95% CI of any respiratory tract infection and hospitalization, and negative-binomial regression to calculate incidence rate ratios (IRR) and 95% CI for number of infections. We compared children conceived by ART, and naturally conceived children of subfertile parents, to children of fertile parents (<12 months to conceive) while adjusting for maternal age, education, BMI and smoking during pregnancy and previous livebirths. We accounted for dependency between children born to the same mother. MAIN RESULTS AND THE ROLE OF CHANCE A total of 7334 (8.7%) singletons were naturally conceived by subfertile parents and 1901 (2.3%) were conceived by ART. Between age 0 and 36 months, 41 609 (49.5%) of children experienced any URTI, 15 542 (18.5%) any LRTI and 4134 (4.9%) were hospitalized due to LRTI. Up to age 3, children conceived by ART had higher frequencies of URTI (adjusted IRR (aIRR) 1.16; 95% CI 1.05-1.28) and hospitalizations due to LRTI (adjusted RR (aRR) 1.25; 95% CI 1.02-1.53), which was not seen for children of subfertile parents. Children conceived by ART were not at higher risks of respiratory infections up to age 18 months; only at age 19-36 months, they had increased risk of any LRTI (aRR 1.16; 95% CI 1.01-1.33), increased frequency of LRTIs (IRR 1.22; 95% CI 1.02-1.47) and a higher risk of hospitalization for LRTI (aRR 1.35; 95% CI 1.01-1.80). They also had an increased frequency of URTIs (aIRR; 1.19; 95% CI 1.07-1.33). Children of subfertile parents only had a higher risk of LRTIs (aRR 1.09; 95% CI 1.01-1.17) at age 19-36 months. LIMITATIONS, REASONS FOR CAUTION Self-reported time-to-pregnancy and respiratory tract infections by parents could lead to misclassification. Both the initial participation rate and loss to follow up in the MoBa limits generalizability to the general Norwegian population. WIDER IMPLICATIONS OF THE FINDINGS ART-conceived children might be more susceptible to respiratory tract infections in early childhood. This appears to be only partly explained by underlying parental subfertility. Exactly what aspects related to the ART procedure might be reflected in these associations need to be further investigated. STUDY FUNDING/COMPETING INTEREST(S) Funding was received from the Swiss National Science Foundation (P2BEP3_191798), the Research Council of Norway (no. 262700), and the European Research Council (no. 947684). All authors declare no conflict of interest. TRIAL REGISTRATION NUMBER N/A

A nilpotent IP polynomial multiple recurrence theorem

We generalize the IP-polynomial Szemer\'edi theorem due to Bergelson and McCutcheon and the nilpotent Szemer\'edi theorem due to Leibman. Important tools in our proof include a generalization of Leibman's result that polynomial mappings into a nilpotent group form a group and a multiparameter version of the nilpotent Hales-Jewett theorem due to Bergelson and Leibman.Comment: v4: switch to TeXlive 2016 and biblate

Constraining ^(26)Al+p resonances using ^(26)Al(^3He,d)^(27)Si

The ^(26)Al(^3He,d)^(27)Si reaction was measured from 0°≤θ_(c.m.)≤35° at E(^3He)=20 MeV using a quadrupole-dipole-dipole-dipole magnetic spectrometer. States in ^(27)Si were observed above the background at 7652 and 7741 keV and upper limits were set for the state at 7592 keV. Implications for the ^(26)Al(p,γ)^(27)Si stellar reaction rate are discussed

Convergence of the Magnus series

The Magnus series is an infinite series which arises in the study of linear ordinary differential equations. If the series converges, then the matrix exponential of the sum equals the fundamental solution of the differential equation. The question considered in this paper is: When does the series converge? The main result establishes a sufficient condition for convergence, which improves on several earlier results.Comment: 11 pages; v2: added justification for conjecture, minor clarifications and correction

Quantum Transport in a Nanosize Silicon-on-Insulator Metal-Oxide-Semiconductor

An approach is developed for the determination of the current flowing through a nanosize silicon-on-insulator (SOI) metal-oxide-semiconductor field-effect transistors (MOSFET). The quantum mechanical features of the electron transport are extracted from the numerical solution of the quantum Liouville equation in the Wigner function representation. Accounting for electron scattering due to ionized impurities, acoustic phonons and surface roughness at the Si/SiO2 interface, device characteristics are obtained as a function of a channel length. From the Wigner function distributions, the coexistence of the diffusive and the ballistic transport naturally emerges. It is shown that the scattering mechanisms tend to reduce the ballistic component of the transport. The ballistic component increases with decreasing the channel length.Comment: 21 pages, 8 figures, E-mail addresses: [email protected]

A new class of coherent states with Meixner-Pollaczek polynomials for the Gol'dman-Krivchenkov Hamiltonian

A class of generalized coherent states with a new type of the identity resolution are constructed by replacing the labeling parameter zn/n! of the canonical coherent states by Meixner-Pollaczek polynomials with specific parameters. The constructed coherent states belong to the state Hilbert space of the Gol'dman-Krivchenkov Hamiltonian.Comment: 10 pages, Submitte

Periodic Quasi - Exactly Solvable Models

Various quasi-exact solvability conditions, involving the parameters of the periodic associated Lam{\'e} potential, are shown to emerge naturally in the quantum Hamilton-Jacobi approach. It is found that, the intrinsic nonlinearity of the Riccati type quantum Hamilton-Jacobi equation is primarily responsible for the surprisingly large number of allowed solvability conditions in the associated Lam{\'e} case. We also study the singularity structure of the quantum momentum function, which yields the band edge eigenvalues and eigenfunctions.Comment: 11 pages, 5 table