Some notes to extend the study on random non-autonomous second order linear differential equations appearing in Mathematical Modeling

The objective of this paper is to complete certain issues from our recent contribution [J. Calatayud, J.-C. Cort\'es, M. Jornet, L. Villafuerte, Random non-autonomous second order linear differential equations: mean square analytic solutions and their statistical properties, Advances in Difference Equations, 2018:392, 1--29 (2018)]. We restate the main theorem therein that deals with the homogeneous case, so that the hypotheses are clearer and also easier to check in applications. Another novelty is that we tackle the non-homogeneous equation with a theorem of existence of mean square analytic solution and a numerical example. We also prove the uniqueness of mean square solution via an habitual Lipschitz condition that extends the classical Picard Theorem to mean square calculus. In this manner, the study on general random non-autonomous second order linear differential equations with analytic data processes is completely resolved. Finally, we relate our exposition based on random power series with polynomial chaos expansions and the random differential transform method, being the latter a reformulation of our random Fr\"obenius method.Comment: 15 pages, 0 figures, 2 table

Analysis of the random heat equation via approximate density functions

[EN] In this paper we study the randomized heat equation with homogeneous boundary conditions. The diffusion coefficient is assumed to be a random variable and the initial condition is treated as a stochastic process. The solution of this randomized partial differential equation problem is a stochastic process, which is given by a random series obtained via the classical method of separation of variables. Any stochastic process is determined by its finite-dimensional joint distributions. In this paper, the goal is to obtain approximations to the probability density function of the solution (the first finite-dimensional distributions) under mild conditions. Since the solution is expressed as a random series, we perform approximations to its probability density function. Several illustrative examples are shown.This work has been supported by the Spanish Ministerio de Economia, Industria y Competitividad (MINECO), the Agencia Estatal de Investigacion (AEI) and Fondo Europeo de Desarrollo Regional (FEDER UE) grant MTM2017-89664-P.Calatayud, J.; Cortés, J. (2021). Analysis of the random heat equation via approximate density functions. Romanian Reports in Physics. 73(2):1-10. http://hdl.handle.net/10251/181144S11073

Photo-induced luminescence

The present paper is a critical review dealing with the characteristics, reaction mechanisms and photoproducts, instrumentation and analytical applications of the photo-induced either chemiluminescence or fluorescence. Special attention is paid to the determination of pesticides by continuous-flow methodologies. The paper is divided into several sections covering the most relevant published papers.Catalá Icardo, M.; Martínez Calatayud, JM. (2008). Photo-induced luminescence. Critical Reviews in Analytical Chemistry. 38(2):118-130. doi:10.1080/10408340802039609S118130382Lukasiewicz, R. J., & Fitzgerald, J. M. (1973). Digital integration method for fluorimetric studies of photochemically unstable compounds. Analytical Chemistry, 45(3), 511-517. doi:10.1021/ac60325a002Aaron, J. J., Villafranca, J. E., White, V. R., & Fitzgerald, J. M. (1976). A Quantitative Photochemical-Fluorimetric Method for Measurement of Nonfluorescent Vitamin K1. Applied Spectroscopy, 30(2), 159-162. doi:10.1366/000370276774456408Coly, A., & Aaron, J.-J. (1998). Fluorimetric analysis of pesticides: Methods, recent developments and applications. Talanta, 46(5), 815-843. doi:10.1016/s0039-9140(97)00366-4Aaron, J.-J., & Coly, A. (2000). Luminescence methods in pesticide analysis. Applications to the environment. Analusis, 28(8), 699-709. doi:10.1051/analusis:2000280699Catalá Icardo, M., Garcı́a Mateo, J. V., & Martı́nez Calatayud, J. (2002). Multicommutation as a powerful new analytical tool. TrAC Trends in Analytical Chemistry, 21(5), 366-378. doi:10.1016/s0165-9936(02)00505-8Coly, A. (1999). Photochemically-induced fluorescence determination of sulfonylurea herbicides using micellar media. Talanta, 49(1), 107-117. doi:10.1016/s0039-9140(98)00349-xWerkhoven-Goewie, C. E., Boon, W. M., Praat, A. J. J., Frei, R. W., Brinkman, U. A. T., & Little, C. J. (1982). Preconcentration and LC analysis of chlorophenols, using a styrene-divinyl-benzene copolymeric sorbent and photochemical reaction detection. Chromatographia, 16(1), 53-59. doi:10.1007/bf02258869Scholten, A. H. M. T., Welling, P. L. M., Brinkman, U. A. T., & Frei, R. W. (1980). Use of PTFE coils in post-column photochemical reactors for liquid chromatograph — application to pharmaceuticals. Journal of Chromatography A, 199, 239-248. doi:10.1016/s0021-9673(01)91376-7Batley, G. E. (1984). Use of Teflon components in photochemical reactors. Analytical Chemistry, 56(12), 2261-2262. doi:10.1021/ac00276a066Engelhardt, H., & Neue, U. D. (1982). Reaction detector with three dimensional coiled open tubes in HPLC. Chromatographia, 15(7), 403-408. doi:10.1007/bf02261598Coly, A., & Aaron, J.-J. (1994). Photochemical–spectrofluorimetric method for the determination of several aromatic insecticides. The Analyst, 119(6), 1205-1209. doi:10.1039/an9941901205ALBERTGARCIA, J., ICARDO, M., & CALATAYUD, J. (2006). Analytical strategy photodegradation/chemiluminescence/continuous-flow multicommutation methodology for the determination of the herbicide Propanil. Talanta, 69(3), 608-614. doi:10.1016/j.talanta.2005.10.044Coly, A., & Aaron, J.-J. (1998). Cyclodextrin-enhanced fluorescence and photochemically-induced fluorescence determination of five aromatic pesticides in water. Analytica Chimica Acta, 360(1-3), 129-141. doi:10.1016/s0003-2670(97)00721-6Poulsen, J. B., Birks, K. S., Gandelman, M. S., & Birks, J. W. (1986). Crocheted PTFE reactors for post-column photochemistry in HPLC. Chromatographia, 22(7-12), 231-234. doi:10.1007/bf02268764Martínez Calatayud, J. 1988.Flow Injection Analysis of Pharmaceuticals. Automation in the Laboratory, 458London, UK: Taylor and Francis Ltd.Palomeque, M., Garcı́a Bautista, J. ., Catalá Icardo, M., Garcı́a Mateo, J. ., & Martı́nez Calatayud, J. (2004). Photochemical-chemiluminometric determination of aldicarb in a fully automated multicommutation based flow-assembly. Analytica Chimica Acta, 512(1), 149-156. doi:10.1016/j.aca.2004.02.031Chivulescu, A., Catalá-Icardo, M., Garcı́a Mateo, J. ., & Martı́nez Calatayud, J. (2004). New flow-multicommutation method for the photo-chemiluminometric determination of the carbamate pesticide asulam. Analytica Chimica Acta, 519(1), 113-120. doi:10.1016/j.aca.2004.05.046PAWLICOVÁ, Z., ALBERT-GARCÍA, J. R., SAHUQUILLO, I., GARCÍA MATEO, J. V., CATALÁ ICARDO, M., & MARTÍNEZ CALATAYUD, J. (2006). Chemiluminescent Determination of the Pesticide Bromoxynil by On-line Photodegradation in a Flow-Injection System. Analytical Sciences, 22(1), 29-34. doi:10.2116/analsci.22.29Mervartová, K., Calatayud, J. M., & Icardo, M. C. (2005). A Fully Automated Assembly Using Solenoid Valves for the Photodegradation and Chemiluminometric Determination of the Herbicide Chlorsulfuron. Analytical Letters, 38(1), 179-194. doi:10.1081/al-200043477Coly, A., & Aaron, J.-J. (1999). Sensitive and rapid flow injection analysis of sulfonylurea herbicides in water with micellar-enhanced photochemically induced fluorescence detection. Analytica Chimica Acta, 392(2-3), 255-264. doi:10.1016/s0003-2670(99)00229-9Garcı́a-Campaña, A. M., Aaron, J.-J., & Bosque-Sendra, J. M. (2001). Micellar-enhanced photochemically induced fluorescence detection of chlorophenoxyacid herbicides. Flow injection analysis of mecoprop and 2,4-dichlorophenoxyacetic acid. Talanta, 55(3), 531-539. doi:10.1016/s0039-9140(01)00470-2Parrilla�V�zquez, P., Gil�Garc�a, M. D., Barranco�Mart�nez, D., & Mart�nez�Galera, M. (2005). Application of coupled-column liquid chromatography combined with post-column photochemically induced fluorimetry derivatization and fluorescence detection to the determination of pyrethroid insecticides in vegetable samples. Analytical and Bioanalytical Chemistry, 381(6), 1217-1225. doi:10.1007/s00216-004-3043-xIrace-Guigand, S., Leverend, E., Seye, M. D. G., & Aaron, J. J. (2005). A new on-line micellar-enhanced photochemically-induced fluorescence method for determination of phenylurea herbicide residues in water. Luminescence, 20(3), 138-142. doi:10.1002/bio.817Liu, L., & Guo, Q.-X. (2002). Journal of Inclusion Phenomena and Macrocyclic Chemistry, 42(1/2), 1-14. doi:10.1023/a:1014520830813Frankewich, R. P., Thimmaiah, K. N., & Hinze, W. L. (1991). Evaluation of the relative effectiveness of different water-soluble .beta.-cyclodextrin media to function as fluorescence enhancement agents. Analytical Chemistry, 63(24), 2924-2933. doi:10.1021/ac00024a023Patel, B. M., Moye, H. A., & Weinberger, R. (1991). Postcolumn formation of fluorophores from nitrogenous pesticides by UV photolysis. Talanta, 38(8), 913-922. doi:10.1016/0039-9140(91)80272-2Torrents, A., Anderson, B. G., Bilboulian, S., Johnson, W. E., & Hapeman, C. J. (1997). Atrazine Photolysis:  Mechanistic Investigations of Direct and Nitrate-Mediated Hydroxy Radical Processes and the Influence of Dissolved Organic Carbon from the Chesapeake Bay. Environmental Science & Technology, 31(5), 1476-1482. doi:10.1021/es9607289Dogliotti, L., & Hayon, E. (1967). Flash photolysis of per[oxydi]sulfate ions in aqueous solutions. The sulfate and ozonide radical anions. The Journal of Physical Chemistry, 71(8), 2511-2516. doi:10.1021/j100867a019Pérez-Ruiz, T. (2001). Flow injection determination of methamidophos using online photo-oxidation and fluorimetric detection. Talanta, 54(5), 989-995. doi:10.1016/s0039-9140(01)00369-1Pérez-Ruiz, T., Martínez-Lozano, C., Tomás, V., & Martín, J. (2002). FLOW INJECTION SPECTROFLUORIMETRIC DETERMINATION OF MALATHION IN ENVIRONMENTAL SAMPLES USING ON-LINE PHOTOOXIDATION. Analytical Letters, 35(7), 1239-1250. doi:10.1081/al-120005976Pérez-Ruiz, T., Martínez-Lozano, C., Tomás, V., & Martín, J. (2002). Fluorimetric determination of arsanilic acid by flow-injection analysis using on-line photo-oxidation. Analytical and Bioanalytical Chemistry, 372(2), 387-390. doi:10.1007/s00216-001-1173-yPérez-Ruiz, T., Martı́nez-Lozano, C., Tomás, V., & Martı́n, J. (2001). Flow-injection fluorimetric method for the determination of dimethylarsinic acid using on-line photo-oxidation. Analytica Chimica Acta, 447(1-2), 229-235. doi:10.1016/s0003-2670(01)01299-5Baird, C. 1995.Environmental Chemistry, 509–510. New York: W. H. Freeman and Company.Bauer, R., & Fallmann, H. (1997). The Photo-Fenton Oxidation — A cheap and efficient wastewater treatment method. Research on Chemical Intermediates, 23(4), 341-354. doi:10.1163/156856797x00565Huston, P. L., & Pignatello, J. J. (1999). Degradation of selected pesticide active ingredients and commercial formulations in water by the photo-assisted Fenton reaction. Water Research, 33(5), 1238-1246. doi:10.1016/s0043-1354(98)00330-3CATASTINI, C., SARAKHA, M., MAILHOT, G., & BOLTE, M. (2002). Iron (III) aquacomplexes as effective photocatalysts for the degradation of pesticides in homogeneous aqueous solutions. The Science of The Total Environment, 298(1-3), 219-228. doi:10.1016/s0048-9697(02)00219-xZepp, R. G., Schlotzhauer, P. F., & Sink, R. M. (1985). Photosensitized transformations involving electronic energy transfer in natural waters: role of humic substances. Environmental Science & Technology, 19(1), 74-81. doi:10.1021/es00131a008Pérez-Ruiz, T., Lozano, C. M., Tomás, V., & Martı́n, J. (2003). Flow injection chemiluminescence determination of carbaryl using photolytic decomposition and photogenerated tris (2,2′-bipyridyl)ruthenium(III). Analytica Chimica Acta, 476(1), 141-148. doi:10.1016/s0003-2670(02)01355-7Pérez-Ruiz, T., Martínez-Lozano, C., Tomás, V., & Martín, J. (2002). Chemiluminescence determination of carbofuran and promecarb by flow injection analysis using two photochemical reactions. The Analyst, 127(11), 1526-1530. doi:10.1039/b207460pMiles, C. J., & Moye, H. A. (1988). Postcolumn photolysis of pesticides for fluorometric determination by high-performance liquid chromatography. Analytical Chemistry, 60(3), 220-226. doi:10.1021/ac00154a007Soto-Chinchilla, J. J., Garcı́a-Campaña, A. M., Gámiz-Gracia, L., Cuadros-Rodrı́guez, L., & Vidal, J. L. M. (2004). Determination of a N-methylcarbamate pesticide in environmental samples based on the application of photodecomposition and peroxyoxalate chemiluminescent detection. Analytica Chimica Acta, 524(1-2), 235-240. doi:10.1016/j.aca.2004.05.084And, S. T., & Aaron, J. J. (1987). Fluorimetric Determination of Non-Fluorescent Dinitroaniline Derivative Herbicides, Using the Photoreduction of Anthraquinone - 2, 6-Disulfonate. Analytical Letters, 20(12), 1995-2009. doi:10.1080/00032718708078040Miles, C. J., & Anson Moye, H. (1987). High performance liquid chromatography with post-column photolysis of pesticides for generation of fluorophores. Chromatographia, 24(1), 628-632. doi:10.1007/bf02688556Patel, B. M., Moye, H. A., & Weinberger, R. (1990). Formation of fluorophores from nitrogenous pesticides by photolysis and reaction with OPA-2-mercaptoethanol for fluorescence detection in liquid chromatography. Journal of Agricultural and Food Chemistry, 38(1), 126-134. doi:10.1021/jf00091a027Durand, G., Barceló, D., Albaigés, J., & Mansour, M. (1990). Utilisation of liquid chromatography in aquatic photodegradation studies of pesticides: A comparison between distilled water and seawater. Chromatographia, 29(3-4), 120-124. doi:10.1007/bf02268696Rosen, J. D., Strusz, R. F., & Still, C. C. (1969). Photolysis of phenylurea herbicides. Journal of Agricultural and Food Chemistry, 17(2), 206-207. doi:10.1021/jf60162a046Lay, J. P., Klein, W., & Korte, F. (1975). Beiträge zur ökologischen Chemie C. Chemosphere, 4(3), 161-168. doi:10.1016/0045-6535(75)90094-6Tanaka, F. S., Hoffer, B. L., & Wien, R. G. (1985). Detection of halogenated biphenyls from sunlight photolysis of chlorinated herbicides in aqueous solution. Pesticide Science, 16(3), 265-270. doi:10.1002/ps.2780160309Pelizzetti, E., Maurino, V., Minero, C., Carlin, V., Tosato, M. L., Pramauro, E., & Zerbinati, O. (1990). Photocatalytic degradation of atrazine and other s-triazine herbicides. Environmental Science & Technology, 24(10), 1559-1565. doi:10.1021/es00080a016Chukwudebe, A., March, R. B., Othman, M., & Fukuto, T. R. (1989). Formation of trialkyl phosphorothioate esters from organophosphorus insecticides after exposure to either ultraviolet light or sunlight. Journal of Agricultural and Food Chemistry, 37(2), 539-545. doi:10.1021/jf00086a058Durand, G., De Bertrand, N., & Barceló, D. (1991). Applications of thermospray liquid chromatography-mass spectrometry in photochemical studies of pesticides in water. Journal of Chromatography A, 554(1-2), 233-250. doi:10.1016/s0021-9673(01)88453-3WOLFE, N., ZEPP, R., & PARIS, D. (1978). Carbaryl, propham and chlorpropham: A comparison of the rates of hydrolysis and photolysis with the rate of biolysis. Water Research, 12(8), 565-571. doi:10.1016/0043-1354(78)90134-3Samanidou, V., Fytianos, K., Pfister, G., & Bahadir, M. (1988). Photochemical decomposition of carbamate pesticides in natural waters of northern Greece. Science of The Total Environment, 76(1), 85-92. doi:10.1016/0048-9697(88)90287-2Konstantinou, I. K., Sakkas, V. A., & Albanis, T. A. (2001). Photocatalytic degradation of the herbicides propanil and molinate over aqueous TiO2 suspensions: identification of intermediates and the reaction pathway. Applied Catalysis B: Environmental, 34(3), 227-239. doi:10.1016/s0926-3373(01)00218-1Machado, F., Collin, L., & Boule, P. (1995). Photolysis of bromoxynil (3,5-dibromo-4-hydroxybenzonitrile) in aqueous solution. Pesticide Science, 45(2), 107-110. doi:10.1002/ps.2780450203Boule, P., Guyon, C., & Lemaire, J. (1982). Photochemistry and environment IV- Photochemical behaviour of monochlorophenols in dilute aqueous solution. Chemosphere, 11(12), 1179-1188. doi:10.1016/0045-6535(82)90031-5Almansa Lopez, E. (2003). Simultaneous quantification of chlorophenoxyacid herbicides based on time-resolved photochemical derivatization to induce fluorescence in micellar medium. Talanta, 60(2-3), 355-367. doi:10.1016/s0039-9140(03)00109-7Garcia, L. F., Eremin, S., & Aaron, J.-J. (1996). Flow-Injection Analysis of Chlorophenoxyacid Herbicides using Photochemically Induced Fluorescence Detectiona. Analytical Letters, 29(8), 1447-1461. doi:10.1080/00032719608001493Lahuerta Zamora, L., Fuster Mestre, Y., Duart, M. J., Antón Fos, G. M., García Doménech, R., Gálvez Álvarez, J., & Martínez Calatayud, J. (2001). Prediction of the Chemiluminescent Behavior of Pharmaceuticals and Pesticides. Analytical Chemistry, 73(17), 4301-4306. doi:10.1021/ac010133iGómez-Taylor Corominas, B. (2003). Prediction of the chemiluminescent behaviour of phenols and polyphenols. Talanta, 60(2-3), 623-628. doi:10.1016/s0039-9140(03)00105-xPolo Martí, E., Catalá Icardo, M., Lahuerta Zamora, L., Antón Fos, G. M., & Martínez Calatayud, J. (2004). Theoretical prediction of the chemiluminescence behaviour of the ergot alkaloids. Analytica Chimica Acta, 527(2), 177-186. doi:10.1016/j.aca.2004.07.026P�rez-Ruiz, T., Mart�nez-Lozano, C., Tom�s, V., Sanz, A., & Garre, R. (2003). Flow Injection Spectrophotometric Determination of Ferbam Based on a Photochemical Reaction. Microchimica Acta, 142(4), 231-235. doi:10.1007/s00604-003-0027-zRoda, A., Rauch, P., Ferri, E., Girotti, S., Ghini, S., Carrea, G., & Bovara, R. (1994). Chemiluminescent flow sensor for the determination of Paraoxon and Aldicarb pesticides. 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Density function of random differential equations via finite difference schemes: a theoretical analysis of a random diffusion-reaction Poisson-type problem

[EN] A computational approach to approximate the probability density function of random differential equations is based on transformation of random variables and finite difference schemes. The theoretical analysis of this computational method has not been performed in the extant literature. In this paper, we deal with a particular random differential equation: a random diffusion-reaction Poisson-type problem of the form , , with boundary conditions , . Here, alpha, A and B are random variables and is a stochastic process. The term is a stochastic process that solves the random problem in the sample path sense. Via a finite difference scheme, we approximate with a sequence of stochastic processes in both the almost sure and senses. This allows us to find mild conditions under which the probability density function of can be approximated. Illustrative examples are included.This work has been supported by the Spanish Ministerio de Economia y Competitividad grant MTM2017-89664-P. Marc Jornet acknowledges the doctorate scholarship granted by Programa de Ayudas de Investigacion y Desarrollo (PAID), Universitat Politecnica de Valencia.Calatayud, J.; Cortés, J.; Díaz, J.; Jornet, M. (2020). Density function of random differential equations via finite difference schemes: a theoretical analysis of a random diffusion-reaction Poisson-type problem. Stochastics: An International Journal of Probability and Stochastic Processes (Online). 92(4):627-641. https://doi.org/10.1080/17442508.2019.1645849S627641924Berman, A., & Plemmons, R. J. (1994). Nonnegative Matrices in the Mathematical Sciences. doi:10.1137/1.9781611971262Brezis, H. (2011). Functional Analysis, Sobolev Spaces and Partial Differential Equations. doi:10.1007/978-0-387-70914-7Dorini, F. A., Cecconello, M. S., & Dorini, L. B. (2016). On the logistic equation subject to uncertainties in the environmental carrying capacity and initial population density. Communications in Nonlinear Science and Numerical Simulation, 33, 160-173. doi:10.1016/j.cnsns.2015.09.009Hussein, A., & Selim, M. M. (2012). Solution of the stochastic radiative transfer equation with Rayleigh scattering using RVT technique. Applied Mathematics and Computation, 218(13), 7193-7203. doi:10.1016/j.amc.2011.12.088Jost, J. (2007). Partial Differential Equations. Graduate Texts in Mathematics. doi:10.1007/978-0-387-49319-0Kallianpur, G. (1980). Stochastic Filtering Theory. Stochastic Modelling and Applied Probability. doi:10.1007/978-1-4757-6592-2Lord, G. J., Powell, C. E., & Shardlow, T. (2009). An Introduction to Computational Stochastic PDEs. doi:10.1017/cbo9781139017329Strand, J. . (1970). Random ordinary differential equations. Journal of Differential Equations, 7(3), 538-553. doi:10.1016/0022-0396(70)90100-2Villafuerte, L., Braumann, C. A., Cortés, J.-C., & Jódar, L. (2010). Random differential operational calculus: Theory and applications. Computers & Mathematics with Applications, 59(1), 115-125. doi:10.1016/j.camwa.2009.08.061Williams, D. (1991). Probability with Martingales. doi:10.1017/cbo978051181365

Manifestaciones esqueléticas en la homocistinuria: a propósito de un caso

Se presenta el caso de una niña de 13 años con homocistinuria en la que se describen las alteraciones esqueléticas, haciendo especial énfasis en las encontradas en el raquis, donde además de osteoporosis, ensanchamientos discales no uniformes y las alteraciones morfológicas de los somas vertebrales, existe una disminución de la distancia interpedicular en el raquis lumbar bajo. Se señalan los síntomas y signos radiológicos que son importantes para el diagnóstico diferencial con la enfermedad de Marfan.The skeletal alterations of a 13-year-old girl with homocystinuria are described emphasizing those found at the spine. Osteoporosis, non-uniform widening of the intervertebral discs, morphological changes in the vertebral bodies and decrease in the distance between both pedicles in the lumbar spine were the most significant findings. A rationale of symptoms and radiological signs for differential diagnosis with Marfan syndrome is presented and discussed

Errores conceptuales en los modelos atómicos cuánticos

SUMMARY We analyze how the basic concepts about atomic models are introduced into the Spanish educational system. We considered the textbooks most currently used in the educational levels from 8th EGB to the 1st University level. We finally discuss the possible sources of misconceptions

Device for data-acquisition from transient signals: kinetic considerations

This paper reports on the evaluation and testing of a home-made device. Data-acquisition, treatment of transient signals and the hardware and software involved are discussed. Some practical aspects are developed in order to power the autonomy of procedures using the device. Kinetic and multi-signal calculations are considered in order to cover the actual tendencies in continuous-flow analysis. Somepractical advantages versus the use of classical chart recorders or commercial computerized-instrument devices are pointed out