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Full-Text Articles in Physical Sciences and Mathematics
Biorthogonal-Wavelet-Based Method For Numerical Solution Of Volterra Integral Equations, Mutaz Mohammad
Biorthogonal-Wavelet-Based Method For Numerical Solution Of Volterra Integral Equations, Mutaz Mohammad
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© 2019 by the authors. Framelets theory has been well studied in many applications in image processing, data recovery and computational analysis due to the key properties of framelets such as sparse representation and accuracy in coefficients recovery in the area of numerical and computational theory. This work is devoted to shedding some light on the benefits of using such framelets in the area of numerical computations of integral equations. We introduce a new numerical method for solving Volterra integral equations. It is based on pseudo-spline quasi-affine tight framelet systems generated via the oblique extension principles. The resulting system is …
A Numerical Solution Of Fredholm Integral Equations Of The Second Kind Based On Tight Framelets Generated By The Oblique Extension Principle, Mutaz Mohammad
A Numerical Solution Of Fredholm Integral Equations Of The Second Kind Based On Tight Framelets Generated By The Oblique Extension Principle, Mutaz Mohammad
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© 2019 by the authors. In this paper, we present a new computational method for solving linear Fredholm integral equations of the second kind, which is based on the use of B-spline quasi-affine tight framelet systems generated by the unitary and oblique extension principles. We convert the integral equation to a system of linear equations. We provide an example of the construction of quasi-affine tight framelet systems. We also give some numerical evidence to illustrate our method. The numerical results confirm that the method is efficient, very effective and accurate.
Meanings, Dimensions, And Categories Of Mathematics Teacher Beliefs: A Navigation Through The Literature, Shashidhar Belbase
Meanings, Dimensions, And Categories Of Mathematics Teacher Beliefs: A Navigation Through The Literature, Shashidhar Belbase
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This paper aimed to discuss the meanings, dimensions, and categories of teacher beliefs about teaching and learning mathematics. I reviewed the relevant literature about teacher beliefs in general, beliefs about mathematics, and beliefs about mathematics teaching and learning in particular. Based on the review of the literature, I outlined the meanings of teacher beliefs and conceptualized three dimensions of teacher beliefs "“ affective dimension, cognitive dimension, and pedagogical dimension. Then, I discussed three viewpoints to observe teacher beliefs "“ relational, institutional, and praxis lenses. I utilized these lenses to categorize belief constructs into three classes of beliefs about mathematics, teaching …