Jacobi-Predictor-Corrector Approach for the Fractional Ordinary Differential Equations

We present a novel numerical method, called {\tt Jacobi-predictor-corrector approach}, for the numerical solution of fractional ordinary differential equations based on the polynomial interpolation and the Gauss-Lobatto quadrature w.r.t. the Jacobi-weight function $\omega(s)=(1-s)^{\alpha-1}(1+s)^0$. This method has the computational cost O(N) and the convergent order $IN$, where $N$ and $IN$ are, respectively, the total computational steps and the number of used interpolating points. The detailed error analysis is performed, and the extensive numerical experiments confirm the theoretical results and show the robustness of this method.Comment: 24 pages, 5 figure

Absolute calibration of Analog Detectors using Stimulated Parametric Down Conversion

Spontaneous parametric down conversion has been largely exploited as a tool for absolute calibration of photon counting detectors, photomultiplier tubes or avalanche photodiodes working in Geiger regime. In this work we investigate the extension of this technique from very low photon flux of photon counting regime to the absolute calibration of analog photodetectors at higher photon flux. Moving toward higher photon rate, i.e. at high gain regime, with the spontaneous parametric down conversion shows intrinsic limitations of the method, while the stimulated parametric down conversion process, where a seed beam properly injected into the crystal in order to increase the photon generation rate in the conjugate arm, allows us to work around this problem. A preliminary uncertainty budget is discussed

Direct participation in and indirect exposure to the occupy central movement and depressive symptoms: a longitudinal study of Hong Kong adults

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Generalized Phase Space Representation of Operators

Introducing asymmetry into the Weyl representation of operators leads to a variety of phase space representations and new symbols. Specific generalizations of the Husimi and the Glauber-Sudarshan symbols are explicitly derivedComment: latex, 8 pages, expanded version accepted by J. Phys.

Direct mode summation for the Casimir energy of a solid ball

The Casimir energy of a solid ball placed in an infinite medium is calculated by a direct frequency summation using the contour integration. It is assumed that the permittivity and permeability of the ball and medium satisfy the condition $\epsilon_1 \mu_1=\epsilon_2\mu_2$. Upon deriving the general expression for the Casimir energy, a dilute compact ball is considered $(\epsilon_1 -\epsilon_2)^2/(\epsilon_1+\epsilon_2)^2\ll 1$. In this case the calculations are carried out which are of the first order in $\xi ^2$ and take account of the five terms in the Debye expansion of the Bessel functions involved. The implication of the obtained results to the attempts of explaining the sonoluminescence via the Casimir effect is shortly discussed.Comment: REVTeX, 7 pages, no figures and tables, treatment of a dilute dielectric ball is revised, new references are adde

Quantum States of Topologically Massive Electrodynamics and Gravity

The free quantum states of topologically massive electrodynamics and gravity in 2+1 dimensions, are explicitly found. It is shown that in both theories the states are described by infrared-regular polarization tensors containing a regularization phase which depends on the spin. This is done by explicitly realizing the quantum algebra on a functional Hilbert space and by finding the Wightman function to define the scalar product on such a Hilbert space. The physical properties of the states are analyzed defining creation and annihilation operators. For both theories, a canonical and covariant quantization procedure is developed. The higher order derivatives in the gravitational lagrangian are treated by means of a preliminary Dirac procedure. The closure of the Poincar\'e algebra is guaranteed by the infrared-finiteness of the states which is related to the spin of the excitations through the regularization phase. Such a phase may have interesting physical consequences.Comment: 21 page, latex, no figure

Maintaining Vaccine Delivery Following the Introduction of the Rotavirus and Pneumococcal Vaccines in Thailand

Although the substantial burdens of rotavirus and pneumococcal disease have motivated many countries to consider introducing the rotavirus vaccine (RV) and heptavalent pneumococcal conjugate vaccine (PCV-7) to their National Immunization Programs (EPIs), these new vaccines could affect the countries' vaccine supply chains (i.e., the series of steps required to get a vaccine from their manufacturers to patients). We developed detailed computational models of the Trang Province, Thailand, vaccine supply chain to simulate introducing various RV and PCV-7 vaccine presentations and their combinations. Our results showed that the volumes of these new vaccines in addition to current routine vaccines could meet and even exceed (1) the refrigerator space at the provincial district and sub-district levels and (2) the transport cold space at district and sub-district levels preventing other vaccines from being available to patients who arrive to be immunized. Besides the smallest RV presentation (17.1 cm3/dose), all other vaccine introduction scenarios required added storage capacity at the provincial level (range: 20 L–1151 L per month) for the three largest formulations, and district level (range: 1 L–124 L per month) across all introduction scenarios. Similarly, with the exception of the two smallest RV presentation (17.1 cm3/dose), added transport capacity was required at both district and sub-district levels. Added transport capacity required across introduction scenarios from the provincial to district levels ranged from 1 L–187 L, and district to sub-district levels ranged from 1 L–13 L per shipment. Finally, only the smallest RV vaccine presentation (17.1 cm3/dose) had no appreciable effect on vaccine availability at sub-districts. All other RV and PCV-7 vaccines were too large for the current supply chain to handle without modifications such as increasing storage or transport capacity. Introducing these new vaccines to Thailand could have dynamic effects on the availability of all vaccines that may not be initially apparent to decision-makers

Localization in Strongly Chaotic Systems

We show that, in the semiclassical limit and whenever the elements of the Hamiltonian matrix are random enough, the eigenvectors of strongly chaotic time-independent systems in ordered bases can on average be exponentially localized across the energy shell and decay faster than exponentially outside the energy shell. Typically however, matrix elements are strongly correlated leading to deviations from such behavior.Comment: RevTeX, 5 pages + 3 postscript figures, submitted to Phys. Rev. Let