Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 15

# Search results for: J. Olivares

##### 15 Hypergeometric Solutions to Linear Nonhomogeneous Fractional Equations with Spherical Bessel Functions of the First Kind

Authors: Pablo Martin, Jorge Olivares, Fernando Maass

Abstract:

The use of fractional derivatives to different problems in Engineering and Physics has been increasing in the last decade. For this reason, we have here considered partial derivatives when the integral is a spherical Bessel function of the first kind in both regular and modified ones simple initial conditions have been also considered. In this way, the solution has been found as a combination of hypergeometric functions. The case of a general rational value for α of the fractional derivative α has been solved in a general way for alpha between zero and two. The modified spherical Bessel functions of the first kind have been also considered and how to go from the regular case to the modified one will be also shown. Downloads 158
##### 14 Nonhomogeneous Linear Second Order Differential Equations and Resonance through Geogebra Program

Authors: F. Maass, P. Martin, J. Olivares

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The aim of this work is the application of the program GeoGebra in teaching the study of nonhomogeneous linear second order differential equations with constant coefficients. Different kind of functions or forces will be considered in the right hand side of the differential equations, in particular, the emphasis will be placed in the case of trigonometrical functions producing the resonance phenomena. In order to obtain this, the frequencies of the trigonometrical functions will be changed. Once the resonances appear, these have to be correlationated with the roots of the second order algebraic equation determined by the coefficients of the differential equation. In this way, the physics and engineering students will understand resonance effects and its consequences in the simplest way. A large variety of examples will be shown, using different kind of functions for the nonhomogeneous part of the differential equations. Downloads 150
##### 13 Educatronic Prototype for Learning Geometry, Based on a Multitouch Surface

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This paper presents a didactic model and a tool as educational resources to support the learning of geometry; they focus on topics difficult to understand. The target population is elementary school students. The tool is based on a collaborative educational approach using multi-touch devices. The proposal is based on the challenges found in the instructional design and prototype implementation. Traditionally, elementary students have had many problems assimilating mathematical topics; this new Educatronic prototype facilitates the learning experience using exercises and they were tested with different children demonstrating the benefits of the prototype by improving their mathematical skills. Downloads 242
##### 12 Linear fractional differential equations for second kind modified Bessel functions

Authors: Jorge Olivares, Fernando Maass, Pablo Martin

Abstract:

Fractional derivatives have been considered recently as a way to solve different problems in Engineering. In this way, second kind modified Bessel functions are considered here. The order α fractional differential equations of second kind Bessel functions, Kᵥ(x), are studied with simple initial conditions. The Laplace transform and Caputo definition of fractional derivatives are considered. Solutions have been found for ν=1/3, 1/2, 2/3, -1/3, -1/2 and (-2/3). In these cases, the solutions are the sum of two hypergeometric functions. The α fractional derivatives have been for α=1/3, 1/2 and 2/3, and the above values of ν. No convergence has been found for the integer values of ν Furthermore when α has been considered as a rational found m/p, no general solution has been found. Clearly, this case is more difficult to treat than those of first kind Bessel Function. Downloads 244
##### 11 Nonhomogeneous Linear Fractional Differential Equations Will Bessel Functions of the First Kind Giving Hypergeometric Functions Solutions

Authors: Fernando Maass, Pablo Martin, Jorge Olivares

Abstract:

Fractional derivatives have become very important in several areas of Engineering, however, the solutions of simple differential equations are not known. Here we are considering the simplest first order nonhomogeneous differential equations with Bessel regular functions of the first kind, in this way the solutions have been found which are hypergeometric solutions for any fractional derivative of order α, where α is rational number α=m/p, between zero and one. The way to find this result is by using Laplace transform and the Caputo definitions of fractional derivatives. This method is for values longer than one. However for α entire number the hypergeometric functions are Kumer type, no integer values of alpha, the hypergeometric function is more complicated is type ₂F₃(a,b,c, t2/2). The argument of the hypergeometric changes sign when we go from the regular Bessel functions to the modified Bessel functions of the first kind, however it integer seems that using precise values of α and considering no integers values of α, a solution can be obtained in terms of two hypergeometric functions. Further research is required for future papers in order to obtain the general solution for any rational value of α. Downloads 112
##### 10 Formative Assessment in an Introductory Python Programming Course

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This paper begins with some concept of formative assessment and the relationship with learning objective: contents objectives, processes objectives, and metacognitive objectives. Two methodologies are describes Evidence-Based teaching and Question Drive Instruction. To do formative assessments in larges classes a Classroom Response System (CRS) is needed. But most of CRS use only Multiple Choice Questions (MCQ), True/False question, or text entry; however, this is insufficient to formative assessment. To do that a new CRS, call FAMA was developed. FAMA support six types of questions: Choice, Order, Inline choice, Text entry, Associated, and Slider. An experiment participated in 149 students from four engineering careers. For results, Kendall's Range Correlation Analysis and descriptive analysis was done. In conclusion, there is a strong relation between contents question, process questions (ask in formative assessment without a score) and metacognitive questions, asked in summative assessment. As future work, the lecturer can do personalized teaching, because knows the behavior of all students in each formative assessment Downloads 47
##### 9 Levels of Reflection in Engineers EFL Learners: The Path to Content and Language Integrated Learning Implementation in Chilean Higher Education

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This study takes part of a major project based on implementing a CLIL program (Content and Language Integrated Learning) at Universidad Técnica Federico Santa María, a leading Chilean tertiary Institution. It aims at examining the relationship between the development of Reflective Processes (RP) and Cognitive Academic Language Proficiency (CALP) in weekly learning logs written by faculty members, participants of an initial professional development online course on English for Academic Purposes (EAP). Such course was designed with a genre-based approach, and consists of multiple tasks directed to academic writing proficiency. The results of this analysis will be described and classified in a scale of key indicators that represent both the Reflective Processes and the advances in CALP, and that also consider linguistic proficiency and task progression. Such indicators will evidence affordances and constrains of using a genre-based approach in an EFL Engineering CLIL program implementation at tertiary level in Chile, and will serve as the starting point to the design of a professional development course directed to teaching methodologies in a CLIL EFL environment in Engineering education at Universidad Técnica Federico Santa María.

Keywords: EFL, EAL, genre, CLIL, engineering

##### 8 High Accuracy Analytic Approximation for Special Functions Applied to Bessel Functions J₀(x) and Its Zeros

Authors: Fernando Maass, Pablo Martin, Jorge Olivares

Abstract:

The Bessel function J₀(x) is very important in Electrodynamics and Physics, as well as its zeros. In this work, a method to obtain high accuracy approximation is presented through an application to that function. In most of the applications of this function, the values of the zeros are very important. In this work, analytic approximations for this function have been obtained valid for all positive values of the variable x, which have high accuracy for the function as well as for the zeros. The approximation is determined by the simultaneous used of the power series and asymptotic expansion. The structure of the approximation is a combination of two rational functions with elementary functions as trigonometric and fractional powers. Here us in Pade method, rational functions are used, but now there combined with elementary functions us fractional powers hyperbolic or trigonometric functions, and others. The reason of this is that now power series of the exact function are used, but together with the asymptotic expansion, which usually includes fractional powers trigonometric functions and other type of elementary functions. The approximation must be a bridge between both expansions, and this can not be accomplished using only with rational functions. In the simplest approximation using 4 parameters the maximum absolute error is less than 0.006 at x ∼ 4.9. In this case also the maximum relative error for the zeros is less than 0.003 which is for the second zero, but that value decreases rapidly for the other zeros. The same kind of behaviour happens for the relative error of the maximum and minimum of the functions. Approximations with higher accuracy and more parameters will be also shown. All the approximations are valid for any positive value of x, and they can be calculated easily. Downloads 171
##### 7 High Accuracy Analytic Approximations for Modified Bessel Functions I₀(x)

Authors: Pablo Martin, Jorge Olivares, Fernando Maass

Abstract:

A method to obtain analytic approximations for special function of interest in engineering and physics is described here. Each approximate function will be valid for every positive value of the variable and accuracy will be high and increasing with the number of parameters to determine. The general technique will be shown through an application to the modified Bessel function of order zero, I₀(x). The form and the calculation of the parameters are performed with the simultaneous use of the power series and asymptotic expansion. As in Padé method rational functions are used, but now they are combined with other elementary functions as; fractional powers, hyperbolic, trigonometric and exponential functions, and others. The elementary function is determined, considering that the approximate function should be a bridge between the power series and the asymptotic expansion. In the case of the I₀(x) function two analytic approximations have been already determined. The simplest one is (1+x²/4)⁻¹/⁴(1+0.24273x²) cosh(x)/(1+0.43023x²). The parameters of I₀(x) were determined using the leading term of the asymptotic expansion and two coefficients of the power series, and the maximum relative error is 0.05. In a second case, two terms of the asymptotic expansion were used and 4 of the power series and the maximum relative error is 0.001 at x≈9.5. Approximations with much higher accuracy will be also shown. In conclusion a new technique is described to obtain analytic approximations to some functions of interest in sciences, such that they have a high accuracy, they are valid for every positive value of the variable, they can be integrated and differentiated as the usual, functions, and furthermore they can be calculated easily even with a regular pocket calculator. Downloads 175
##### 6 Kinetic Study of Physical Quality Changes on Jumbo Squid (Dosidicus gigas) Slices during Application High-Pressure Impregnation

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This study presents the simultaneous application of high hydrostatic pressure (HHP) and osmotic dehydration of jumbo squid (Dosidicus gigas) slice. Diffusion coefficients for both components water and solids were improved by the process pressure, being influenced by pressure level. The working conditions were different pressures such as 100, 250, 400 MPa and pressure atmospheric (0.1 MPa) for time intervals from 30 to 300 seconds and a 15% NaCl concentration. The mathematical expressions used for mass transfer simulations both water and salt were those corresponding to Newton, Henderson and Pabis, Page and Weibull models, where the Weibull and Henderson-Pabis models presented the best fitted to the water and salt experimental data, respectively. The values for water diffusivity coefficients varied from 1.62 to 8.10x10⁻⁹ m²/s whereas that for salt varied among 14.18 to 36.07x10⁻⁹ m²/s for selected conditions. Finally, as to quality parameters studied under the range of experimental conditions studied, the treatment at 250 MPa yielded on the samples a minimum hardness, whereas springiness, cohesiveness and chewiness at 100, 250 and 400 MPa treatments presented statistical differences regarding to unpressurized samples. The colour parameters L* (lightness) increased, however, but b* (yellowish) and a* (reddish) parameters decreased when increasing pressure level. This way, samples presented a brighter aspect and a mildly cooked appearance. The results presented in this study can support the enormous potential of hydrostatic pressure application as a technique important for compounds impregnation under high pressure. Downloads 270
##### 5 Kinetics of Phytochemicals and Antioxidant Activity during Thermal Treatment of Cape Gooseberry (Physalis peruviana L)

Abstract:

Cape gooseberry, the fruit of the plant Physalis peruviana L. has gained interest in research given its contents of promising health-promoting compounds like contents. The presence of carotenoids, ascorbic acid, minerals, polyphenols, vitamins and antioxidants. This project aims to study thermal stability of β-carotene, ascorbic acid, catechin and epicatechin and antioxidant activity in the matrix of the Cape Gooseberry. Fruits were obtained from a Colombian field in Cundinamarca. Ripeness stage was 4 (According to NTC 4580, corresponding to mature stage) at the moment of the experiment. The fruits have been subjected to temperatures of 40, 60, 80, 100 and 120°C for several times. β-Carotene, ascorbic acid, catechin and epicatechin content were assessed with HPLC and antioxidant activity with the DPPH method. β-Carotene was stable upon 100°C, and showed some degradation at 120°C. The same behavior was observed for epicatechin. Catechin increased during treatment at 40°C, at 60°C it remained stable and it showed degradation at 80°C, 100°C and 120°C that could be described by a second order kinetic model. Ascorbic acid was the most heat-sensitive of the analyzed compounds. It showed degradation at all studied temperatures, and could be described by a first order model. The activation energy for ascorbic acid degradation in cape gooseberry was 46.0 kJ/mol and its degradation rate coefficient at 100 °C was 6.53 x 10-3 s-1. The antioxidant activity declined for all studied temperatures. Results from this study showed that cape gooseberry is an important source of different health-promoting compounds and some of them are stable to heat. That makes this fruit a suitable raw material for processed products such as jam, juices and dehydrated fruit, giving the consumer a good intake of these compounds. Downloads 382
##### 4 Exploring the Development of Communicative Skills in English Teaching Students: A Phenomenological Study During Online Instruction

Abstract:

This research explored whether the context of online instruction has influenced the development of first-year English-teaching students' communication skills, being these speaking and listening. The theoretical basis finds its niche in the need to bridge the gap in knowledge about the Chilean online educational context and the development of English communicative skills. An interpretative paradigm and a phenomenological design were implemented in this study. Twenty- two first-year students and two teachers from an English teaching training program participated in the study. The students' ages ranged from 18 to 26 years of age, and the teachers' years of experience ranged from 5 to 13 years in the program. For data collection purposes, semi- structured interviews were applied to both students and teachers. Interview questions were based on the initial conceptualization of the central phenomenon. Observations, field notes, and focus groups with the students are also part of the data collection process. Data analysis considered two-cycle methods. The first included descriptive coding for field notes, initial coding for interviews, and creating a codebook. The second cycle included axial coding for both field notes and interviews. After data analysis, the findings show that students perceived online classes as instances in which active communication cannot always occur. In addition, changes made to the curricula as a consequence of the COVID-19 pandemic have affected students' speaking and listening skills. Downloads 11
##### 3 Kinetic Modelling of Drying Process of Jumbo Squid (Dosidicus Gigas) Slices Subjected to an Osmotic Pretreatment under High Pressure

Abstract:

This research presents the simultaneous application of high hydrostatic pressure (HHP) and osmotic dehydration (DO) as a pretreatment to hot –air drying of jumbo squid (Dosidicus gigas) cubes. The drying time was reduced to 2 hours at 60ºC and 5 hours at 40°C as compared to the jumbo squid samples untreated. This one was due to osmotic pressure under high-pressure treatment where increased salt saturation what caused an increasing water loss. Thus, a more reduced time during convective drying was reached, and so water effective diffusion in drying would play an important role in this research. Different working conditions such as pressure (350-550 MPa), pressure time (5-10 min), salt concentration, NaCl (10 y 15%) and drying temperature (40-60ºC) were optimized according to kinetic parameters of each mathematical model. The models used for drying experimental curves were those corresponding to Weibull, Page and Logarithmic models, however, the latest one was the best fitted to the experimental data. The values for water effective diffusivity varied from 4.82 to 6.59x10-9 m2/s for the 16 curves (DO+HHP) whereas the control samples obtained a value of 1.76 and 5.16×10-9 m2/s, for 40 and 60°C, respectively. On the other hand, quality characteristics such as color, texture, non-enzymatic browning, water holding capacity (WHC) and rehydration capacity (RC) were assessed. The L* (lightness) color parameter increased, however, b * (yellowish) and a* (reddish) parameters decreased for the DO+HHP treated samples, indicating treatment prevents sample browning. The texture parameters such as hardness and elasticity decreased, but chewiness increased with treatment, which resulted in a product with a higher tenderness and less firmness compared to the untreated sample. Finally, WHC and RC values of the most treatments increased owing to a minor damage in tissue cellular compared to untreated samples. Therefore, a knowledge regarding to the drying kinetic as well as quality characteristics of dried jumbo squid samples subjected to a pretreatment of osmotic dehydration under high hydrostatic pressure is extremely important to an industrial level so that the drying process can be successful at different pretreatment conditions and/or variable processes. Downloads 164

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