ABSTRACT The purpose of this study is to investigate the importance of emphasizing multiple representations instruction and its effect on students’ images of the definite integral. The data were collected from three sections of an... more
ABSTRACT The purpose of this study is to investigate the importance of emphasizing multiple representations instruction and its effect on students’ images of the definite integral. The data were collected from three sections of an undergraduate calculus I course. The students in the treatment group, received an in-depth instruction of multiple representations of the definite integral. The two other sections served as control groups and did not receive such instruction. The data were collected from a pretest and a posttest. Participants for this study were 96 first-year calculus students, who had just finished studying the concept of differentiation and had started the integral concept. Results of this study revealed that students who received an in-depth multiple representations instruction showed higher levels of comprehension of the definite integral concept.
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q-ROPFLS, including numeric and linguistic data, has a wide range of applications in handling uncertain information. This article aims to investigate q-ROPFL correlation coefficient based on the proposed information energy and covariance... more
q-ROPFLS, including numeric and linguistic data, has a wide range of applications in handling uncertain information. This article aims to investigate q-ROPFL correlation coefficient based on the proposed information energy and covariance formulas. Moreover, considering that different q-ROPFL elements may have varying criteria weights, the weighted correlation coefficient is further explored. Some desirable characteristics of the presented correlation coefficients are also discussed and proven. In addition, some theoretical development is provided, including the concept of composition matrix, correlation matrix, and equivalent correlation matrix via the proposed correlation coefficients. Then, a clustering algorithm is expanded where data is expressed in q-ROPFL form with unknown weight information and is explained through an illustrative example. Besides, detailed parameter analysis and comparative study are performed with the existing approaches to reveal the effectiveness of the f...
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In this article, we present a one-step hybrid block method for approximating the solutions of second-order fuzzy initial value problems. We prove the stability and convergence results of the method and present several examples to... more
In this article, we present a one-step hybrid block method for approximating the solutions of second-order fuzzy initial value problems. We prove the stability and convergence results of the method and present several examples to illustrate the efficiency and accuracy of the proposed method. The numerical results are compared with the existing ones in the literature.
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In this paper, the new iterative transform method and the homotopy perturbation transform method was used to solve fractional-order Equal-Width equations with the help of Caputo-Fabrizio. This method combines the Laplace transform with... more
In this paper, the new iterative transform method and the homotopy perturbation transform method was used to solve fractional-order Equal-Width equations with the help of Caputo-Fabrizio. This method combines the Laplace transform with the new iterative transform method and the homotopy perturbation method. The approximate results are calculated in the series form with easily computable components. The fractional Equal-Width equations play an essential role in describe hydromagnetic waves in cold plasma. Our object is to study the nonlinear behaviour of the plasma system and highlight the critical points. The techniques are very reliable, effective, and efficient, which can solve a wide range of problems arising in engineering and sciences.
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Abstract.In this paper, we have considered an analytical solution of the time-fractional wave equation with the help of the double Laplace transform. With the proposed technique the exact solution is obtained. The method is very simple... more
Abstract.In this paper, we have considered an analytical solution of the time-fractional wave equation with the help of the double Laplace transform. With the proposed technique the exact solution is obtained. The method is very simple and easy. For an application, an example is provide.
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We study the solution of fractional Fredholm integrodifferential equation. A modified version of the fractional power series method (RPS) is presented to extract an approximate solution of the model. The RPS method is a combination of the... more
We study the solution of fractional Fredholm integrodifferential equation. A modified version of the fractional power series method (RPS) is presented to extract an approximate solution of the model. The RPS method is a combination of the generalized fractional Taylor series and the residual functions. To show the efficiency of the proposed method, numerical results are presented.
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A new Tau method is presented for the two dimensional Poisson equation Comparison of the results for the test problemu(x,y)=sin(4πx)sin(4πy)with those computed by Haidvogel and Zang, using the matrix diagonalization method, and Dang-Vu... more
A new Tau method is presented for the two dimensional Poisson equation Comparison of the results for the test problemu(x,y)=sin(4πx)sin(4πy)with those computed by Haidvogel and Zang, using the matrix diagonalization method, and Dang-Vu and Delcarte, using the Chebyshev collocation method, indicates that our method would be more accurate.
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We introduce a simple and efficient series solution for a class of nonlinear fractional differential equations of Caputo's type. The new approach is a modified form of the well-known Taylor series expansion where we overcome the... more
We introduce a simple and efficient series solution for a class of nonlinear fractional differential equations of Caputo's type. The new approach is a modified form of the well-known Taylor series expansion where we overcome the difficulty of computing iterated fractional derivatives, which do not compute in general. The terms of the series are determined sequentially with explicit formula, where only integer derivatives have to be computed. The efficiency of the new algorithm is illustrated through several examples. Comparison with other series methods such as the Adomian decomposition method and the homotopy perturbation method is made to indicate the efficiency of the new approach. The algorithm can be implemented for a wide class of fractional differential equations with different types of fractional derivatives.
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In this paper, we study a class of second-order delay fractional differential equations with a variable-order Caputo derivative. This type of equation is an extension to ordinary delay equations which are used in the modeling of several... more
In this paper, we study a class of second-order delay fractional differential equations with a variable-order Caputo derivative. This type of equation is an extension to ordinary delay equations which are used in the modeling of several biological systems such as population dynamics, epidemiology, and immunology. Usually, fractional differential equations are difficult to solve analytically, and with fractional derivatives of variable-order, they become more challenging. Therefore, the need for reliable numerical techniques is worth investigating. To solve this type of equation, we derive a new approach based on the operational matrix. We use the shifted Chebyshev polynomials of the second kind as the basis for the approximate solutions. A convergence analysis is discussed and the uniform convergence of the approximate solutions is proven. Several examples are discussed to illustrate the efficiency of the presented approach. The computed errors, figures, and tables show that the app...
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With lack of student motivation, there will be a little or no real learning in the class and this directly effects student achievement and test scores. Some students are naturally motivated to learn, but many students are not motivated,... more
With lack of student motivation, there will be a little or no real learning in the class and this directly effects student achievement and test scores. Some students are naturally motivated to learn, but many students are not motivated, they do care little about learning and need their instructors to motivate them. Thus, motivating students is part of the instructor's job. It's a tough task to motivate students and make them have more attention and enthusiasm. As a part of this research, a questionnaire has been distributed among a sample of 155 students out of 1502 students from Foundation Program at Qatar University. The questionnaire helped us to determine some methods to motivate the students and encourage them to study such as variety of teaching activities, encouraging students to participate during the lectures, creating intense competition between the students, using instructional technology, not using grades as a threat and respecting the students and treating them ...
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Stratified double median ranked set sampling (SDMRSS) method is suggested for estimating the population mean. The SDMRSS is compared with the simple random sampling (SRS), stratified simple random sampling (SSRS), and stratified ranked... more
Stratified double median ranked set sampling (SDMRSS) method is suggested for estimating the population mean. The SDMRSS is compared with the simple random sampling (SRS), stratified simple random sampling (SSRS), and stratified ranked set sampling (SRSS). It is shown that SDMRSS estimator is an unbiased of the population mean and more efficient than SRS, SSRS, and SRSS. Also, by SDMRSS, we can increase the efficiency of mean estimator for specific value of the sample size. SDMRSS is applied on real life examples, and the results of the example agreed the theoretical results.
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Weakness of students in mathematics is a very old problem, discovering the source of this weakness is not an easy mission and needs to check the curriculum, teaching methods, learning process, assessment methods and using the technology... more
Weakness of students in mathematics is a very old problem, discovering the source of this weakness is not an easy mission and needs to check the curriculum, teaching methods, learning process, assessment methods and using the technology in teaching mathematics. In addition, Mathematics is a vertically structured field, secondary stage depends on preparatory stage which depends also on primary stage. Determining the source of weakness depends on the outcomes of each stage by using international tests to be fair with all stages including the first year University students. In this paper, Authors used four international tests to discriminate the level of students and to investigate their actual performance in the levels; grade 4, grade 8 and first year University students and the end of secondary stage. These international tests are TIMSS for grades 4 and 8, PISA for grade 10, and ACT and ACCUPLACER for first year University students. It is found that the problem starts after grade 8 s...
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The present paper deals with a connection between quantum quadratic operators (QQOs) and quasi QQOs on 𝕄2(ℂ). We show that QQOs and quasi QQOs on 𝕄2(ℂ) coincide in the class of Volterra type of operators. To establish this result, we... more
The present paper deals with a connection between quantum quadratic operators (QQOs) and quasi QQOs on 𝕄2(ℂ). We show that QQOs and quasi QQOs on 𝕄2(ℂ) coincide in the class of Volterra type of operators. To establish this result, we first describe these two kind of operators on the commutative part of 𝕄2(ℂ). Furthermore, in the last section, we introduce a quantum analogue of Volterra operators and provide concrete examples of such kind of operators. It is established that the considered examples also satisfy quasiness condition as well. The obtained results will allow to produce (with explicit conditions) a class of unital, but not trace-preserving positive maps of 𝕄2(ℂ).
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This study investigated the effects of the flipped classroom and peer instructional pedagogical models on students' achievements in Calculus for Business courses. One hundred eight students participated in the study and were divided... more
This study investigated the effects of the flipped classroom and peer instructional pedagogical models on students' achievements in Calculus for Business courses. One hundred eight students participated in the study and were divided into three groups. The Control group (35) was taught according to the traditional model; the first experimental group was taught according to the flipped classroom model (36); and the second experimental group was taught according to both the flipped classroom and the peer instruction models (37). Students in the experimental groups watched recorded lecture videos on Blackboard and solved an online pre-assignment before coming to class. A quasi-experimental design was implemented and two research instruments were designed and used; a pre- and post-tests. All the participants took a pre- test during the first week of the semester and completed a post-test after the treatment during the fourteenth week. The results of this study showed that students’ ...
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In this paper, the method of lower and upper solutions is extended to deal with certain nonlinear fractional boundary value problem of order 3 < δ ≤ 4. Two well-defined monotone sequences of lower and upper solutions which converge... more
In this paper, the method of lower and upper solutions is extended to deal with certain nonlinear fractional boundary value problem of order 3 < δ ≤ 4. Two well-defined monotone sequences of lower and upper solutions which converge uniformly to actual solution of the problem are presented. The convergence of these sequences is verified numerically through one example and a result on the existence of positive solutions is obtained.
The purpose of this study is to investigate the importance of emphasizing multiple representations instruction and its effect on students’ images of the definite integral. The data were collected from three sections of an undergraduate... more
The purpose of this study is to investigate the importance of emphasizing multiple representations instruction and its effect on students’ images of the definite integral. The data were collected from three sections of an undergraduate calculus I course. The students in the treatment group, received an in-depth instruction of multiple representations of the definite integral. The two other sections served as control groups and did not receive such instruction. The data were collected from a pretest and a posttest. Participants for this study were 96 first-year calculus students, who had just finished studying the concept of differentiation and had started the integral concept. Results of this study revealed that students who received an in-depth multiple representations instruction showed higher levels of comprehension of the definite integral concept.
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In this paper, we discuss the solvability of a class of multiterm initial value problems involving the Caputo–Fabrizio fractional derivative via the Laplace transform. We derive necessary and sufficient conditions to guarantee the... more
In this paper, we discuss the solvability of a class of multiterm initial value problems involving the Caputo–Fabrizio fractional derivative via the Laplace transform. We derive necessary and sufficient conditions to guarantee the existence of solutions to the problem. We also obtain the solutions in closed forms. We present two examples to illustrate the validity of the obtained results.
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In this research, the well-known non-linear Lane–Emden–Fowler (LEF) equations are approximated by developing a nature-inspired stochastic computational intelligence algorithm. A trial solution of the model is formulated as an artificial... more
In this research, the well-known non-linear Lane–Emden–Fowler (LEF) equations are approximated by developing a nature-inspired stochastic computational intelligence algorithm. A trial solution of the model is formulated as an artificial feed-forward neural network model containing unknown adjustable parameters. From the LEF equation and its initial conditions, an energy function is constructed that is used in the algorithm for the optimisation of the networks in an unsupervised way. The proposed scheme is tested successfully by applying it on various test cases of initial value problems of LEF equations. The reliability and effectiveness of the scheme are validated through comprehensive statistical analysis. The obtained numerical results are in a good agreement with their corresponding exact solutions, which confirms the enhancement made by the proposed approach.
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In this work, we are concerned with presenting a novel study on the generalized reaction Duffing model involving two actions on the time coordinate: fractional time derivative and multiple pantograph time delays. The modified fractional... more
In this work, we are concerned with presenting a novel study on the generalized reaction Duffing model involving two actions on the time coordinate: fractional time derivative and multiple pantograph time delays. The modified fractional Maclaurin series is suggested to suit and treat the presence of these time actions. Graphical analysis in support of the impact of fractional order and delay parameters on the dynamics of the Duffing model is performed. One of the findings that has been drawn in this research is to give a reasonable description of one of the cases of physical meaning of fractional derivative.