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Matrices
Published in James R. Kirkwood, Bessie H. Kirkwood, Linear Algebra, 2020
James R. Kirkwood, Bessie H. Kirkwood
In the real numbers, every non-zero number has a multiplicative inverse. For example, the multiplicative inverse of 2 is ½ because2×½=1,
Modular Arithmetic
Published in Khaleel Ahmad, M. N. Doja, Nur Izura Udzir, Manu Pratap Singh, Emerging Security Algorithms and Techniques, 2019
In mathematics, when we multiply two numbers and their sum is 1, the number we multiply to a given number is called its multiplicative inverse, e.g., a × 1/a = 1 or a·1/a, where 1/a is the multiplicative inverse of a (Barua, 2017).
Introduction
Published in Vlad P. Shmerko, Svetlana N. Yanushkevich, Sergey Edward Lyshevski, Computer Arithmetics for Nanoelectronics, 2018
Vlad P. Shmerko, Svetlana N. Yanushkevich, Sergey Edward Lyshevski
Example 11.9 The set {0,1,2} with addition and multiplication modulo 3 is a field. There is an identity 0 with respect to modulo 3 addition, and identity 1 with respect to modulo 3 multiplication. Every element has a unique additive inverse, and every element other than 0 has a multiplicative inverse.
Cognitive instructional principles in elementary mathematics classrooms: a case of teaching inverse relations
Published in International Journal of Mathematical Education in Science and Technology, 2021
Meixia Ding, Ryan Hassler, Xiaobao Li
As indicated by Table 2, teachers in G1 and G2 taught additive inverse lessons, while teachers in G3 and G4 taught multiplicative inverse lessons. Both part-whole and comparison word problems were included because these are major problem structures (Ng & Lee, 2009) that can be used to facilitate inverse relations (Carpenter et al., 1999). Lesson topics included fact family, finding the missing number, using inverse operations to compute (or check), initial unknown problems, comparison word problems (e.g. find the difference, find the large/small quantity), and two-step word problems where the solutions steps indicate inverse relations. These topics were recommended by the literature (e.g. Baroody, 1999; Baroody et al., 2009; Carpenter et al., 2003; Ding 2016; Nunes et al., 2009; Resnick et al., 1987; Torbeyns et al., 2009) and available in both textbooks.
Discrete-time interval optimal control problem
Published in International Journal of Control, 2019
J. R. Campos, E. Assunção, G. N. Silva, W. A. Lodwick, M. C. M. Teixeira
The interval arithmetic proposed by Moore (1966) implies that, given two elements A, B ∈ KnC and , the usual interval arithmetic operations are defined by A*B = {a*b| a ∈ A, b ∈ B} where * ∈ { +, −, ×, ÷} and sA = {sa| a ∈ A}. However, these operations do not possess the desired properties such as additive inverse, multiplicative inverse or distributive law and still it generates overestimation (Chalco-Cano, Mizukoshi, Román-Flores, & Flores-Franulic, 2009). The SLCIA (Chalco-Cano et al., 2014) addresses some of these limitations; it yields a richer algebraic structure. In addition, several concepts of interval analysis have been developed using SLCIA (Huamán, 2014; Leal, 2015) such as interval difference equations and the admissible intervals sets.
A lightweight authentication scheme for telecare medical information system
Published in Connection Science, 2021
Lijun Xiao, Songyou Xie, Dezhi Han, Wei Liang, Jun Guo, Wen-Kuang Chou
Table 6 shows the computational complexity of the proposed scheme and other relevant schemes (Farash et al., 2016; Li et al., 2018; Salem & Amin, 2020). The scheme Farash et al. (2016) uses the hash function and scalar multiplication. The scheme Li et al. (2018) uses the hash function and Chebyshev chaotic map algorithm. The scheme Salem and Amin (2020) uses the hash function, modular exponentiation, modular multiplication and multiplicative inverse. The scheme in this article uses PUF, PRNG and scalar multiplication algorithms. Compared with the hash function, PUF has a lower implementation cost, so the scheme in this article also has advantages in implementation cost compared with other schemes.