Numerical Solutions of Matrix Differential Models using Cubic Matrix Splines II

This paper presents the non-linear generalization of a previous work on matrix differential models. It focusses on the construction of approximate solutions of first-order matrix differential equations Y'(x)=f(x,Y(x)) using matrix-cubic splines. An estimation of the approximation error, an algorithm for its implementation and illustrative examples for Sylvester and Riccati matrix differential equations are given.Comment: 14 pages; submitted to Math. Comp. Modellin

Solving a class of generalized lyapunov operator differential equations without the exponential operator function

In this paper a method for solving operator differential equations of the type X' = A + BX + XD; X(0) = Co, avoiding the operator exponential function is given . Results are applied to solve initial value problems related to Riccati type operator differential equations whose associated algebraic equation is solvable

Analytical approximate solutions and error bounds for nonsymmetric riccati matrix differential equations

AbstractIn this paper we construct analytical approximate solutions for the nonsymmetric Riccati matrix differential equation. Given an admissible error ∈ > 0, we determine an interval where we construct an approximate solution whose error is smaller than ϵ for all the points of the interval. The approximate solution is constructed in terms of matrices related to the data

Explicit solutions for non homogeneous sturm mouville operator problems

In this paper we study existence and uniqueness conditions for the solutions of Sturm-Liouville operator problems related to the operator differential equation X" - QX = F(t). Explicit solutions of the problem in terms of a square root of the operator Q are given

Exact, approximate solutions and error bounds for coupled implicit systems of partial differential equations

In this paper coupled implicit initial-boundary value systems of second order partial differential equations are considered. Given a finite domain and an admissible error ϵ an analytic approximate solution whose error is upper bounded by ϵ in the given domain is constructed in terms of the data

An algebraic approach for solving boundary value matrix problems: existence, uniqueness and closed form solution

Sin resume

A Rodrigues-type formula for Gegenbauer matrix polynomials

This paper centers on the derivation of a Rodrigues-type formula for the Gegenbauer matrix polynomial. A connection between Gegenbauer and Jacobi matrix polynomials is givenThis research has been supported by the Universitat Politecnica de Valencia under grant PAID-06-11-2020.Defez Candel, E. (2013). A Rodrigues-type formula for Gegenbauer matrix polynomials. Applied Mathematics Letters. 26:899-903. https://doi.org/10.1016/j.aml.2013.04.001S8999032

Valle, A. del (1998). Aportación Bio-bibliográfica a la Historia de la Ciencia.

Sin resume

Heat resistance of spore-forming microorganisms (Bacillus sporothermodurans, Bacillus subtilis and Geobacillus stearothermophilus) under isothermal and non-iiothermal conditions

[SPA]El principal género de microorganismos esporulados altamente resistentes al calor involucrados en el deterioro de alimentos es Bacillus. Este género causa problemas de no esterilidad en alimentos enlatados y reduce la vida comercial de muchos alimentos procesados. En este estudio se determinó la termorresistencia de Bacillus sporothermodurans IIC65, Bacillus subtilis IC9 y Geobacillus stearothermophilus T26 mediante un termorresistómetro Mastia (Conesa et al., 2009). Las determinaciones de termorresistencia se realizaron bajo condiciones isotérmicas (a 120ºC, 122,5ºC, 125ºC y 127,5ºC), bajo condiciones no isotérmicas (a velocidades de calentamiento de 1ºC/min y 20ºC/min) y bajo condiciones más complejas (tratamiento con etapas de calentamiento, mantenimiento y enfriamiento a una velocidad de calentamiento/enfriamiento de 27,5ºC/min). Los resultados mostraron que Geobacillus stearothermophilus no fue tan resistente al calor como se pensaba; Bacillus sporothermodurans y Bacillus subtilis presentaron hombros en las curvas de supervivencia y fueron más termorresistentes que lo que se predijo mediante el modelo de Weibull, mientras que Geobacillus stearothermophilus presentó colas en las curvas de supervivencia y fue menos termorresistente que lo que se predijo mediante el modelo de Weibull; y la inactivación más rápida fue lograda a una velocidad de calentamiento de 20ºC/min. Además, la inactivación que se consiguió bajo el tratamiento térmico más complejo (calentamiento-mantenimiento-enfriamiento) fue baja comparada con la inactivación que se logró a 1ºC/min y 20ºC/min para Bacillus sporothermodurans y Bacillus subtilis. [ENG]The main genus of heat-resistant spore-forming bacteria involved in food spoilage is Bacillus. Mostly, heat-resistant spore-forming Bacillus cause non-sterility problems in canned food and reduce the shelf life of many processed foods. In this study the heat resistance of Bacillus sporothermodurans IIC65, Bacillus subtilis IC9 and Geobacillus stearothermophilus T26 was determined by a thermoresistometer Mastia (Conesa et al., 2009) under isothermal conditions at 120ºC, 122.5ºC, 125ºC and 127.5ºC, non-isothermal conditions at heating rates of 1ºC/min and 20ºC/min and under more complex conditions (heating, holding and cooling periods) at a heating/cooling rate of 27.5ºC/min. The results showed that Geobacillus stearothermophilus was not as heat resistant as is thought; Bacillus sporothermodurans and Bacillus subtilis presented shoulders in their survival curves and they were always more heat resistant than predicted by Weibull model while Geobacillus stearothermophilus presented tail phenomena and it was always less heat resistant than predicted by Weibull model; and the fastest inactivation was achieved at a heating rate of 20ºC/min. In addition, the inactivation achieved under a complex thermal treatment (heating-holding-cooling) was low compared to that achieved at 1ºC/min and 20ºC/min for Bacillus sporothermodurans and Bacillus subtilis.Escuela Técnica superior de Ingeniería AgronómicaUniversidad Politécnica de Cartagen