The Lie-group method based on radial basis functions for solving nonlinear high dimensional generalized Benjamin–Bona–Mahony–Burgers equation in arbitrary domains

The aim of this paper is to introduce a new numerical method for solving the nonlinear generalized Benjamin–Bona–Mahony–Burgers (GBBMB) equation. This method is combination of group preserving scheme (GPS) with radial basis functions (RBFs), which takes advantage of two powerful methods, one as geometric numerical integration method and the other meshless method. Thus, we introduce this method as the Lie-group method based on radial basis functions (LG–RBFs). In this method, we use Kansas approach to approximate the spatial derivatives and then we apply GPS method to approximate first-order time derivative. One of the important advantages of the developed method is that it can be applied to problems on arbitrary geometry with high dimensions. To demonstrate this point, we solve nonlinear GBBMB equation on various geometric domains in one, two and three dimension spaces. The results of numerical experiments are compared with analytical solutions and the method presented in Dehghan et al. (2014) to confirm the accuracy and efficiency of the presented method

Numerical integrators based on the Magnus expansion for nonlinear dynamical systems

Explicit numerical integration algorithms up to order four based on the Magnus expansion for nonlinear non-autonomous ordinary differential equations are presented and tested on problems possessing qualitative (very often, geometric) features that is convenient to preserve under numerical discretization. The range of applications covers augmented dynamical systems, highly oscillatory problems and nonlinear non-autonomous partial differential equations of evolution previously discretized in space

Closed-form exact solutions to the density dependent Fitzhugh--Nagumo telegraph equation

We use the first integral method to construct closed-from exact solutions of the density dependent Fitzhugh–Nagumo telegraph equation. While this method is very useful for obtaining formal solutions, many of the solutions are not physically relevant. Hence, we carefully determine which of these solutions is physically useful for the problem. For standard diffusion and linear density dependent diffusion, we obtain physically meaningful exact solutions. Interestingly, the case with linear density dependence shows strong qualitative agreement the standard diffusion case. For both cases, the wave solutions result in an initial concentration which either dissipates or tends to some finite positive value for large time. While one can obtain wave solutions with general wave speeds for the standard diffusion case, when there is density dependence in diffusion, the resulting wave speeds will take specific values depending on the values of the model parameters. For stronger density dependent diffusion involving quadratic and higher order functions of the concentration, we show that the equation is not integrable, and exact solutions should not be expected for such cases

Closed-form exact solutions to the density dependent Fitzhugh--Nagumo telegraph equation

We use the first integral method to construct closed-from exact solutions of the density dependent Fitzhugh–Nagumo telegraph equation. While this method is very useful for obtaining formal solutions, many of the solutions are not physically relevant. Hence, we carefully determine which of these solutions is physically useful for the problem. For standard diffusion and linear density dependent diffusion, we obtain physically meaningful exact solutions. Interestingly, the case with linear density dependence shows strong qualitative agreement the standard diffusion case. For both cases, the wave solutions result in an initial concentration which either dissipates or tends to some finite positive value for large time. While one can obtain wave solutions with general wave speeds for the standard diffusion case, when there is density dependence in diffusion, the resulting wave speeds will take specific values depending on the values of the model parameters. For stronger density dependent diffusion involving quadratic and higher order functions of the concentration, we show that the equation is not integrable, and exact solutions should not be expected for such cases

Long-term trends of Nitrogen oxides and surface ozone concentrations in Tehran city, 2002–2011

Background and aim: Tropospheric ozone is a problem with multi aspects - hazard to human health, plant, and welfare and a key factor to climate change, air pollution and atmosphere chemistry, as well. Behavior of ozone and nitrogen oxides (NO, and NO<inf>2</inf>) concentration is highly complex and variable; therefore, their trends as short and long-term were significantly attended. Most of the studies were carried out on the behavior of pollutant concentrations in North America, Europe, and East Asia, but few studies have been conducted in west Asia. The aim of this study was to assess daily changes and long-term trend of ozone and nitrogen oxides concentrations in Tehran city, Iran from March 2002 to September 2011. Material and methods: Data were collected from 18 air quality monitoring stations. The data were sorted as daily mean of 10 years (daily changes) and annual mean for each year (long-term trend). One-sample test was used to assess the statistical significance. Results: Current findings indicated that changes of ozone, NO, and NO<inf>2</inf> concentrations are dependent from job shifts and photochemical reactions. Annual mean concentrations of ozone and NO<inf>2</inf> were gradually increased, long-term trend of ozone and NO<inf>2</inf> concentration indicated. The correlation between long term trend of ozone and NO<inf>2</inf> was significant (p < 0.05). Conclusion: The controlling program was the most important factor in long-term concentration of ozone, and nitrogen oxides, but some problems and difficulties were accounted to perform controlling program. © 2015 Motesaddi Zarandi et al

Long-term trends of Nitrogen oxides and surface ozone concentrations in Tehran city, 2002–2011

Background and aim: Tropospheric ozone is a problem with multi aspects - hazard to human health, plant, and welfare and a key factor to climate change, air pollution and atmosphere chemistry, as well. Behavior of ozone and nitrogen oxides (NO, and NO2) concentration is highly complex and variable; therefore, their trends as short and long-term were significantly attended. Most of the studies were carried out on the behavior of pollutant concentrations in North America, Europe, and East Asia, but few studies have been conducted in west Asia. The aim of this study was to assess daily changes and long-term trend of ozone and nitrogen oxides concentrations in Tehran city, Iran from March 2002 to September 2011. Material and methods: Data were collected from 18 air quality monitoring stations. The data were sorted as daily mean of 10 years (daily changes) and annual mean for each year (long-term trend). One-sample test was used to assess the statistical significance. Results: Current findings indicated that changes of ozone, NO, and NO2 concentrations are dependent from job shifts and photochemical reactions. Annual mean concentrations of ozone and NO2 were gradually increased, long-term trend of ozone and NO2 concentration indicated. The correlation between long term trend of ozone and NO2 was significant (p < 0.05). Conclusion: The controlling program was the most important factor in long-term concentration of ozone, and nitrogen oxides, but some problems and difficulties were accounted to perform controlling program. © 2015 Motesaddi Zarandi et al

Smoking Frequency and some Related Factors among High School Students of Kashan City, Iran

Aims The dramatic increase of smoking in adolescents has become one of the major challenges in most countries and it needs further consideration. The aim of this study was to determine the smoking prevalence and some related factors among high school students. Instrument & Methods This descriptive, cross-sectional study was done in 2012-13 academic year in male and female high school students of Kashan City, Iran and 328 students were selected by multi-stage random cluster sampling method. Data were collected by a researcher-made questionnaire which had three parts; demographic data, history of smoking in the family, and ways of smoking. Data analysis was done using Chi-square and ANOVA tests. Findings 19.3% (52 students) of the high school students of Kashan City, Iran, were smokers; 41 boys (20.2%) and 11 girls (8.8%). Smoking had significant relations with sex, grade and having a smoker in the family. 30.3% of the students had a cigarette smoker and 32.40% had a hookah smoker in their family. Hookah was the most prevalent tobacco product. Friends (47.8% in boys and 10.4% in girls) and then relatives (13.4% in boys and 8.2% in girls) contributed to students’ smoking. Conclusion Smoking hookah and cigarette have a high prevalence in sophomore and junior high school boys and having a smoker family member or friend is a main risk factor of start smoking in adolescents