China
Africa
Explore chapters and articles related to this topic
Introduction
Published in Georgios A. Drosopoulos, Georgios E. Stavroulakis, Nonlinear Mechanics for Composite Heterogeneous Structures, 2022
Georgios A. Drosopoulos, Georgios E. Stavroulakis
Some basic calculations with matrices are now presented. Addition takes place for matrices with the same dimensions and is provided by the sum of the corresponding elements of each matrix, as denoted by equation (1.18). It is noted that addition of matrices possesses the commutative property, thus A+B=B+A.
Compressive Sensing for Wireless Sensor Networks
Published in Fei Hu, Qi Hao, Intelligent Sensor Networks, 2012
Mohammadreza Mahmudimanesh, Abdelmajid Khelil, Neeraj Suri
The accumulation is actually taking place by adding vectors of the same size across the WSN. Therefore, it can be done by any order since the addition is a commutative operation. This property of CS measurement has a very important advantage. Due to the commutative property of addition, accumulation can be done in any order. Therefore, the same approach as discussed earlier can be applied to a star topology, chain topology, or more complex tree topologies. As long as the tree routing is applied, accumulation can be done over many levels. Thus, we can extend the very simple topology in Figure 16.4 to a multi-hop WSN depicted in 16.5.
Fast Matrix Computations
Published in Vijay K. Madisetti, The Digital Signal Processing Handbook, 2017
A vital feature of Equation 10.2 is that it is noncommutative, i.e., it does not depend on the commutative property of multiplication. This can be seen easily by noting that each of the mi are the product of a linear combination of the elements of A by a linear combination of the elements of B, in that order, so that it is never necessary to use, say a2,2b2,1 = b2,1a2,2. We note there exist commutative algorithms for 2 × 2 matrix multiplication that require even fewer operations, but they are of little practical use.
Performance of second-grade elementary school students on counting, place value understanding, and addition operation in natural numbers
Published in International Journal of Mathematical Education in Science and Technology, 2022
Osman Birgin, Ramazan Gürbüz, Kafiye Zeynep Memiş
It is also indicated in some studies that deficiencies in counting skills slow down the processing speed for solving math problems as well as prevent the development of automaticity skills in arithmetic (Bull & Johnston, 1997; Cumming & Elkins, 1999; Gebhardt et al., 2012). Processing speed means the ability to solve mathematical problems quickly and accurately within a specific time limit, and automaticity refers to the ability to perform mental computations in arithmetic operations (i.e. addition, subtraction, multiplication, and division) without using finger counting (Cumming & Elkins, 1999; Kaufmann et al., 2011). For this reason, students who have difficulties in number concepts and counting skills may skip some numbers while counting; repeat the same number more than once; and/or use undeveloped counting strategies such as finger counting (Bull & Johnston, 1997). Moreover, these students cannot comprehend the commutative property of addition and multiplication as well as count number strings incorrectly and have difficulty in learning the concept of place value (Geary et al., 2000). Thus, it is suggested in the results of previous research that number knowledge and counting skills have a serious impact on later mathematics performance and arithmetic skills.
Fairness in penalty shootouts: Is it worth using dynamic sequences?
Published in Journal of Sports Sciences, 2022
László Csató, Dóra Gréta Petróczy
Assume that the two rules differ in the probability of the th round. Hence the shooting order of the teams in the th round is different under the two mechanisms, for the Catch-up and for the Behind-first. If the scores of the teams differ at the beginning of the th round, then the team lagging behind has the probability of scoring, and the other team has the probability of scoring. The commutative property of multiplication implies that the probability of the th round is independent of the shooting order, which contradicts the assumption above. To conclude, the teams should be tied at the beginning of the th round and their shooting order should be different under the two mechanisms.
The power of their ideas: leveraging teachers’ mathematical ideas in professional development
Published in International Journal of Mathematical Education in Science and Technology, 2022
In the first example provided, the commutative property of addition over the integers was explored. For many of the participating teachers, this led to new mathematical understandings since many had only considered this property over the whole numbers. In the second example, a teacher was deliberately selected whose solution incorporated the transitive property of equality; a powerful property that teachers had been exposed to, but lacked understanding of. Inspired by the teacher’s final equation, we proceeded to collectively examine order of operations. This was worthy of consideration since many teachers teach PEMDAS in a manner that can lead to miscalculations (Dupree, 2016). An intentional strategy here was to take advantage of participating teachers’ mathematical ideas to organically push their thinking to consider ideas that most certainly could support their instruction.