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Algebra and graphs
Published in Allan Bonnick, Automotive Science and Mathematics, 2008
An expression such as 5x−5y has two terms and 5 is common to both of them. 5 is therefore a common factor. A factor is defined as a common part of two or more terms that make up an algebraic expression. The expression 5x−5y can be written as 5(x−y), and the factors of the expression are 5 and (x−y).
Algebra
Published in John Bird, Bird's Engineering Mathematics, 2021
The laws of precedence which apply to arithmetic also apply to algebraic expressions. The order is Brackets, Of, Division, Multiplication, Addition and Subtraction (i.e. BODMAS).
Algebra 1
Published in Surinder S. Virdi, Advanced Construction Mathematics, 2019
If two or more terms in an algebraic expression have a common factor, then the factors may be used to rewrite the expression. The common factors could be numbers, symbols or a combination of the two. The process is the reverse of removing brackets, as shown in example 2.5.
Supporting the development of preservice teachers’ mathematical connection skills in a teacher education programme
Published in International Journal of Mathematical Education in Science and Technology, 2023
Özge Dışbudak-Kuru, Mine Işıksal-Bostan
As shown in Table 5, PST28 used symbolic and picture representations in teaching the multiplication of an algebraic expression by a natural number. However, she could have used concrete manipulatives such as algebra tiles and technological tools such as GeoGebra to provide more concrete experiences to the students. For this reason, her lesson plan was coded at Level 1 under this component. If PSTs use various representations as much as possible ways to teach the concept, then their lesson plans were coded at Level 2 under his component. The analysis of the lesson plans showed that five PSTs’ initial lesson plans and 16 PSTs’ revised lesson plans were coded at Level 2 with respect to using multiple representations component. As an illustrative, excerpts from PST13’s lesson plan are shown in Table 6.
A new fitness function in genetic programming for classification of imbalanced data
Published in Journal of Experimental & Theoretical Artificial Intelligence, 2022
The distance for all training data samples is calculated, and this classification distance is used to estimate how close the GP-Program (classifier) prediction is. Finally, we sum up these values for this estimation, and the objective will be to generate a classifier that gives predictions as close to expected class values. A GP Program represents algebraic expression. So depending on the expression, its value may be very large. The difference between this absolute value and the expected class value is calculated. Again this calculated value may be very large in some cases. When we sum up these values, this summation nullifies even some correctly or near correct predictions. Therefore, this calculated value for individual data samples prediction needs to be bounded. To bound these classification distance values, we apply the hyperbolic tangent function on each classification distance before summation. For example, Figure 4 shows a hyperbolic tangent plot in which the X-axis shows different numeric values and the Y-axis represents the corresponding hyperbolic tangent value. Thus, the application of hyperbolic tangent values bound the individual classification distance between −1 and +1.
Effects of large aromatic precursors on soot formation in turbulent non-premixed sooting jet flames
Published in Combustion Theory and Modelling, 2019
This leads to a different, but equivalent formulation of the presumed PDF and the resulting convolution [29], The new PDF, , is modelled using a presumed PDF approach [36–38], in which a beta distribution is used for the mixture fraction, Z, based on its mean and variance and a Delta Dirac distribution is used for Λ and Θ. The resulting form of the presumed PDF is In the above equation, the filtered mixture fraction variance, , is modelled by an algebraic expression [39,40]. Combining the above equations and assuming a unique inversion between (Z, C) and (Λ, Θ), the filtered thermochemical quantities can be finally written as, where is the flamelet library established using flamelet solutions convoluted with the presumed subfilter PDF.