This dissertation focuses on the development of adaptive time-stepping and high-order parallel stages exponential Runge–Kutta methods for discretizing stiff partial differential equations (PDEs). The design of exponential Runge–Kutta methods relies heavily on the existing stiff order conditions available in the literature, primarily up to order 5. It is well-known that constructing higher-order efficient methods that strictly satisfy all the stiff order conditions is challenging. Typically, methods up to order 5 have been derived by relaxing one or more order conditions, depending on the desired accuracy level. Our approach will be based on a comprehensive investigation of these conditions. We will derive novel and efficient exponential Runge–Kutta schemes of orders up to 5, which not only fulfill the stiff order conditions in a strict sense but also support the implementation of variable step sizes. Furthermore, we develop the first-ever sixth-order exponential Runge–Kutta schemes by leveraging the exponential B-series theory. Notably, all the newly derived schemes allow the efficient computation of multiple stages, either simultaneously or in parallel. To establish the convergence properties of the proposed methods, we perform an analysis within an abstract Banach space in the context of semigroup theory. Our numerical experiments are given on parabolic PDEs to confirm the accuracy and efficiency of the newly constructed methods.

El comportamiento agresivo en el ámbito educativo viene siendo foco de estudio en numerosas investigaciones que tienen como objetivo descubrir las variables implicadas a nivel social, personal y escolar. En este estudio se pretende establecer un modelo predictivo entre el comportamiento agresivo y diferentes variables psicoeducativas tales como la personalidad, las atribuciones académicas, el rechazo escolar y el rendimiento académico. La investigación se ha llevado a cabo con 501 estudiantes de edades comprendidas entre los 8 y los 12 años ((M = 10,08, DE = 1,31) escolarizados en los niveles de 3º a 6º de Educación Primaria, de cinco centros educativos públicos y concertados de la provincia de Alicante, de los cuales 234 son chicos (46.7%) y 267 chicas (53.3%). Los instrumentos empleados para medir cada variable han sido: Aggression Questionaire (comportamiento agresivo), School Refusal Assessment Scale-Revised-Children (rechazo escolar), Sydney Attribution Scale (atribuciones académicas), Cuestionario «Big Five» de personalidad para niños y adolescentes (personalidad) y las calificaciones escolares (rendimiento académico). Bajo la aprobación, permiso y consentimiento del Equipo directivo y de las familias, la aplicación de estos instrumentos se llevó a cabo de forma colectiva en las aulas, con una presentación de las pruebas aleatoria en cada uno de los grupos. Para el análisis de los datos se han empleado diferentes pruebas estadísticas tales como la prueba Z de diferencia de proporciones, el análisis de varianza (ANOVA), prueba t de diferencia de medias para muestras independientes, el índice d propuesto por Cohen (1988) y la prueba de regresión logística por pasos de Wald. Los resultados obtenidos confirman varias hipótesis planteadas en el estudio y se concluye que quienes puntúan más alto en comportamiento agresivo se caracterizan por un mayor nivel de extroversión, atribuir su fracaso académico a causas internas y tener mayores probabilidades de suspender. La multidimensionalidad del comportamiento agresivo y su repercusión a nivel académico, social y personal evidencia la necesidad de actuar en base a la coeducación, la educación emocional, la individualidad y el desarrollo íntegro de los niños y niñas para superar problemas educativos y garantizar la vida en sociedad.

Purpose: We investigated the associations of early onset polysubstance use prior to age 18 with the prevalence of bronchitis among U.S. adults and tested whether the associations differ by gender. Methods: A total of 77,950 adults, of them 2,653 with bronchitis in the past year, were from the combined 2013 and 2014 National Survey on Drug Use and Health data. The variable cluster analysis was used to classify nine variables about substance use prior to age 18 (cigarettes, cigars, smokeless tobacco, marijuana, cocaine, heroin, methamphetamines, ecstasy, and phencyclidine). Weighted multivariate logistic regression analysis (MLR) was used to examine the associations with bronchitis. Results: Nine variables were divided into two clusters: early onset poly tobacco use (three tobacco use variables) and early onset poly drug use (six drug use variables). The overall prevalence of bronchitis was 3.8% (5.1% for females and 2.3% for males). MLR analysis showed that being female, elderly (ages 65 and above), obese, and early onset poly tobacco use were associated with increased odds of bronchitis (p < 0.05). Gender-stratified analyses showed that early-onset poly tobacco use was significantly associated with bronchitis only in males, whereas early onset poly drug use was associated with bronchitis only in females. Moreover, obesity and tobacco use in the past year revealed associations with bronchitis regardless of gender. Conclusions: Obesity, early onset poly tobacco use prior to age 18, and tobacco use in the past year were positively associated with bronchitis; furthermore, the associations of early onset polysubstance use with bronchitis differed by gender, which indicated that gender differences should be considered in developing effective prevention strategies.

The aim of the thesis was to design a house that minor changes can be easily adapted to the changed situation. House may very well be a ONE-GENERATION after adjustment becomes a two-generation. The house is designed as a lightweight wooden construction with steel elements. As part of the thesis is resolved interior element, and a kitchen island. It is designed as a place for cooking with Sink area. The whole is topped with Corian and has a built-in fireplace insert.

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Surveys ordinarily ask questions in an ordinal scale and often result in missing data. We suggest a regression based technique for imputing missing ordinal data. Multilevel cumulative logit model was used with an assumption that observed responses of certain key variables can serve as covariate in predicting missing item responses of an ordinal variable. Individual predicted probabilities at each response level were obtained. Average individual predicted probabilities for each response level were used to randomly impute the missing responses using a uniform distribution. Finally, likelihood ratio chi square statistics was used to compare the imputed and observed distributions. Two other forms of multiple imputation algorithms were performed for comparison. Performance of our imputation technique was comparable to other 2 established algorithms. Our method being simpler does not involve any complex algorithms and with further research can potentially be used as an imputation technique for missing ordinal variables.

In this work, the effectiveness of multi-objective design optimization using metamodeling techniques and an internal state variable (ISV) plasticity damage material model as a design tool is demonstrated. Multi-objective design optimization, metamodeling, and ISV plasticity damage material models are brought together to provide a design tool capable of meeting the stringent structural design requirements of today and of the future. The process of implementing this tool are laid out, and two case studies using multi-objective design optimization were carried out. The first was the optimization of a Chevrolet Equinox rear subframe. The optimized subframe was 12% lighter and met design requirements not achieved by the heavier initial design. The second case was the optimization of a Formula SAE front upright. The optimized upright meets all the design constraints and is 22% lighter.