Mean square solution of Bessel differential equation with uncertainties

[EN] This paper deals with the study of a Bessel-type differential equation where input parameters (coefficient and initial conditions) are assumed to be random variables. Using the so-called Lp-random calculus and assuming moment conditions on the random variables in the equation, a mean square convergent generalized power series solution is constructed. As a result of this convergence, the sequences of the mean and standard deviation obtained from the truncated power series solution are convergent as well. The results obtained in the random framework extend their deterministic counterpart. The theory is illustrated in two examples in which several distributions on the random inputs are assumed. Finally, we show through examples that the proposed method is computationally faster than Monte Carlo method.This work has been partially supported by the Spanish Ministerio de Economía y Competitividad grant MTM2013-41765-P and by the European Union in the FP7-PEOPLE-2012-ITN Program under Grant Agreement No. 304617 (FP7 Marie Curie Action, Project Multi-ITN STRIKE-Novel Methods in Computational Finance) and Mexican Conacyt.Cortés, J.; Jódar Sánchez, LA.; Villafuerte, L. (2017). Mean square solution of Bessel differential equation with uncertainties. Journal of Computational and Applied Mathematics. 309:383-395. https://doi.org/10.1016/j.cam.2016.01.034S38339530

Social, Cultural and Behavioral Determinants of Health among Hawaii Filipinos: The Filipino Healthy Communities Project

Background/Purpose: Filipinos are Hawaii’s largest immigrant group and second largest ethnic group. The Hawaii Filipino Health Communities Project was initiated by the Hawaii State Department of Health, because of the high rates of heart disease and stroke mortality, and other behavioral risks seen among Hawaii’s Filipino population (i.e. high smoking rates among Filipino men). The project sought to gather Filipino community members’ perspectives on why such chronic disease health disparities exist for Filipinos, and identify solutions to address them. Methods: The project gathered information from both immigrant and local Filipinos throughout the state, using community engagement methods of interviews with community leaders (n=20) and community-based focus groups (n=20 groups with 130 participants), Results: Filipino community members were aware of, and community leaders well-versed in, the behavioral, cultural, and social determinants of health in their communities. However, being aware of such determinants of health has yet not resulted in changed behavior in the overall Filipino community (i.e. improved diet, increased physical activity, or better access to healthcare). Conclusion: More outreach is needed with Filipinos, along with interventions to combat health disparities in chronic disease, such as increased smoking cessation and creative ways to eat healthier and increase physical activit

Solving linear and quadratic random matrix differential equations: A mean square approach

[EN] In this paper linear and Riccati random matrix differential equations are solved taking advantage of the so called L-p-random calculus. Uncertainty is assumed in coefficients and initial conditions. Existence of the solution in the L-p-random sense as well as its construction are addressed. Numerical examples illustrate the computation of the expectation and variance functions of the solution stochastic process. (C) 2016 Elsevier Inc. All rights reserved.This work has been partially supported by the Spanish Ministerio de Economia y Competitividad grant MTM2013-41765-P and by the European Union in the FP7-PEOPLE-2012-ITN Program under Grant Agreement no. 304617 (FP7 Marie Curie Action, Project Multi-ITN STRIKE-Novel Methods in Computational Finance).Casabán Bartual, MC.; Cortés López, JC.; Jódar Sánchez, LA. (2016). Solving linear and quadratic random matrix differential equations: A mean square approach. Applied Mathematical Modelling. 40(21-22):9362-9377. https://doi.org/10.1016/j.apm.2016.06.017S936293774021-2

Random Hermite differential equations: Mean square power series solutions and statistical properties

This paper deals with the construction of random power series solution of second order linear differential equations of Hermite containing uncertainty through its coefficients and initial conditions. Under appropriate hypotheses on the data, we establish that the constructed random power series solution is mean square convergent. We provide conditions in order to obtain random polynomial solutions and, as a consequence, random Hermite polynomial are introduced. Also, the main statistical functions of the approximate stochastic process solution generated by truncation of the exact power series solution are given. Finally, we apply the proposed technique to several illustrative examples comparing the numerical results with respect to those provided by other available approaches including Monte Carlo simulation. © 2011 Elsevier Inc. All rights reserved.This work has been partially supported by the Spanish M.C.Y.T. and FEDER grants MTM2009-08587, DPI2010-20891-C02-01 as well as the Universitat Politecnica de Valencia grant PAID-06-09 (Ref. 2588).Calbo Sanjuán, G.; Cortés López, JC.; Jódar Sánchez, LA. (2011). Random Hermite differential equations: Mean square power series solutions and statistical properties. Applied Mathematics and Computation. 218(7):3654-3666. https://doi.org/10.1016/j.amc.2011.09.008S36543666218

Solving the random diffusion model in an infinite medium: A mean square approach

[EN] This paper deals with the construction of an analytic-numerical mean square solution of the random diffusion model in an infinite medium. The well-known Fourier transform method, which is used to solve this problem in the deterministic case, is extended to the random framework. Mean square operational rules to the Fourier transform of a stochastic process are developed and stated. The main statistical moments of the stochastic process solution are also computed. Finally, some illustrative numerical examples are included.This work has been partially supported by the Ministerio de Economia y Competitividad grant: DPI2010-20891-c0-01, and Universitat Politecnica de Valencia grant: PAID06-11-2070.Casabán, M.; Company Rossi, R.; Cortés, J.; Jódar Sánchez, LA. (2014). Solving the random diffusion model in an infinite medium: A mean square approach. Applied Mathematical Modelling. 38(24):5922-5933. https://doi.org/10.1016/j.apm.2014.04.063S59225933382

A mean square chain rule and its application in solving the random Chebyshev differential equation

[EN] In this paper a new version of the chain rule for calculat- ing the mean square derivative of a second-order stochastic process is proven. This random operational calculus rule is applied to construct a rigorous mean square solution of the random Chebyshev differential equation (r.C.d.e.) assuming mild moment hypotheses on the random variables that appear as coefficients and initial conditions of the cor- responding initial value problem. Such solution is represented through a mean square random power series. Moreover, reliable approximations for the mean and standard deviation functions to the solution stochastic process of the r.C.d.e. are given. Several examples, that illustrate the theoretical results, are included.This work was completed with the support of our TEX-pert.Cortés, J.; Villafuerte, L.; Burgos-Simon, C. (2017). A mean square chain rule and its application in solving the random Chebyshev differential equation. Mediterranean Journal of Mathematics. 14(1):14-35. https://doi.org/10.1007/s00009-017-0853-6S1435141Calbo, G., Cortés, J.C., Jódar, L., Villafuerte, L.: Analytic stochastic process solutions of second-order random differential equations. Appl. Math. Lett. 23(12), 1421–1424 (2010). doi: 10.1016/j.aml.2010.07.011El-Tawil, M.A., El-Sohaly, M.: Mean square numerical methods for initial value random differential equations. Open J. Discret. Math. 1(1), 164–171 (2011). doi: 10.4236/ojdm.2011.12009Khodabin, M., Maleknejad, K., Rostami, K., Nouri, M.: Numerical solution of stochastic differential equations by second order Runge Kutta methods. Math. Comp. Model. 59(9–10), 1910–1920 (2010). doi: 10.1016/j.mcm.2011.01.018Santos, L.T., Dorini, F.A., Cunha, M.C.C.: The probability density function to the random linear transport equation. Appl. Math. Comput. 216(5), 1524–1530 (2010). doi: 10.1016/j.amc.2010.03.001González Parra, G., Chen-Charpentier, B.M., Arenas, A.J.: Polynomial Chaos for random fractional order differential equations. Appl. Math. Comput. 226(1), 123–130 (2014). doi: 10.1016/j.amc.2013.10.51El-Beltagy, M.A., El-Tawil, M.A.: Toward a solution of a class of non-linear stochastic perturbed PDEs using automated WHEP algorithm. Appl. Math. Model. 37(12–13), 7174–7192 (2013). doi: 10.1016/j.apm.2013.01.038Nouri, K., Ranjbar, H.: Mean square convergence of the numerical solution of random differential equations. Mediterran. J. Math. 12(3), 1123–1140 (2015). doi: 10.1007/s00009-014-0452-8Villafuerte, L., Braumann, C.A., Cortés, J.C., Jódar, L.: Random differential operational calculus: theory and applications. Comp. Math. Appl. 59(1), 115–125 (2010). doi: 10.1016/j.camwa.2009.08.061Øksendal, B.: Stochastic differential equations: an introduction with applications, 6th edn. Springer, Berlin (2007)Soong, T.T.: Random differential equations in science and engineering. Academic Press, New York (1973)Wong, B., Hajek, B.: Stochastic processes in engineering systems. Springer Verlag, New York (1985)Arnold, L.: Stochastic differential equations. Theory and applications. John Wiley, New York (1974)Cortés, J.C., Jódar, L., Camacho, J., Villafuerte, L.: Random Airy type differential equations: mean square exact and numerical solutions. Comput. Math. Appl. 60(5), 1237–1244 (2010). doi: 10.1016/j.camwa.2010.05.046Calbo, G., Cortés, J.C., Jódar, L.: Random Hermite differential equations: mean square power series solutions and statistical properties. Appl. Math. Comp. 218(7), 3654–3666 (2011). doi: 10.1016/j.amc.2011.09.008Calbo, G., Cortés, J.C., Jódar, L., Villafuerte, L.: Solving the random Legendre differential equation: Mean square power series solution and its statistical functions. Comp. Math. Appl. 61(9), 2782–2792 (2010). doi: 10.1016/j.camwa.2011.03.045Cortés, J.C., Jódar, L., Company, R., Villafuerte, L.: Laguerre random polynomials: definition, differential and statistical properties. Utilit. Math. 98, 283–293 (2015)Cortés, J.C., Jódar, L., Villafuerte, L.: Mean square solution of Bessel differential equation with uncertainties. J. Comp. Appl. Math. 309, 383–395 (2017). doi: 10.1016/j.cam.2016.01.034Golmankhaneh, A.K., Porghoveh, N.A., Baleanu, D.: Mean square solutions of second-order random differential equations by using homotopy analysis method. Romanian Reports Physics 65(2), 1237–1244 (2013)Khalaf, S.L.: Mean square solutions of second-order random differential equations by using homotopy perturbation method. Int. Math. Forum 6(48), 2361–2370 (2011)Khudair, A.R., Ameen, A.A., Khalaf, S.L.: Mean square solutions of second-order random differential equations by using Adomian decomposition method. Appl. Math. Sci. 5(49), 2521–2535 (2011)Agarwal, R.P., O’Regan, D.: Ordinary and partial differential equations. Springer, New York (2009

Microstructural and high-temperature impedance spectroscopy study of Ba6MNb9O30 (M=Ga, Sc, In) relaxor dielectric ceramics with tetragonal tungsten bronze structure

The authors would like to thank to the following funding organisations: the Royal Society for providing a research fellowship (F.D.M.), EPSRC for providing the PhD student grant (A.R.) and Roberto Rocca Education Program for providing an additional fellowship (A.R.).This work reports on the microstructural and high-temperature impedance spectroscopy study of a family of dielectric ceramics Ba6MNb9O30 (M=Ga, Sc, In) of tetragonal tungsten bronze (TTB) structure with relaxor properties. For Ba6GaNb9O30 and Ba6InNb9O30 pellets, the SEM images have revealed good, dense internal microstructures, with well-bonded grains and only discrete porosity; in contrast Ba6ScNb9O30 pellets had a poorer microstructure, with many small and poorly-bonded grains gathered in agglomerates, resulting in significant continuous porosity and poorly defined grain boundary regions. The electroactive regions were characterised by the bulk and grain boundaries capacitances and resistances, while their contribution to the electrical conduction process was estimated by determining activation energies from the temperature (Arrhenius) dependence of both electric conductivities and time constants. For Ga and In analogues the electronic conductivity are dominated by the bulk response, while for Sc analogue, the poorly defined grain boundaries give a bulk-like response, mixing with the main bulk contribution.PostprintPeer reviewe

Treatment of Community-Acquired Pneumonia in Immunocompromised Adults:A Consensus Statement Regarding Initial Strategies

Background Community-acquired pneumonia (CAP) guidelines have improved the treatment and outcomes of patients with CAP, primarily by standardization of initial empirical therapy. But current society-published guidelines exclude immunocompromised patients. Research Question There is no consensus regarding the initial treatment of immunocompromised patients with suspected CAP. Study Design and Methods This consensus document was created by a multidisciplinary panel of 45 physicians with experience in the treatment of CAP in immunocompromised patients. The Delphi survey methodology was used to reach consensus. Results The panel focused on 21 questions addressing initial management strategies. The panel achieved consensus in defining the population, site of care, likely pathogens, microbiologic workup, general principles of empirical therapy, and empirical therapy for specific pathogens. Interpretation This document offers general suggestions for the initial treatment of the immunocompromised patient who arrives at the hospital with pneumonia