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Modular Arithmetic
Published in Khaleel Ahmad, M. N. Doja, Nur Izura Udzir, Manu Pratap Singh, Emerging Security Algorithms and Techniques, 2019
Thus, the mathematical operations of the above integers can be performed as follows. Addition: It states that the addition of two integers is always an integer. 2 + 5 = 7 −7 + 4 = −3 Subtraction: It states that the subtraction of two integers is again an integer. 6 − 4 = 2 Multiplication: It states that multiplying two integers always results in an integer. Division: It states that dividing (/, ÷) integers with other integers always results in an integer.
Numeric Data in Memory
Published in Julio Sanchez, Maria P. Canton, Software Solutions for Engineers and Scientists, 2018
Julio Sanchez, Maria P. Canton
The integers are the set of whole numbers, which can be positive or negative. The integer digits are located one storage unit apart and do not have a decimal point. The computer storage of unsigned integers is in a straightforward binary encoding. Since the smallest addressable unit of storage in the PC is one byte, the CPU logic pads with leading zeros numbers that are smaller than one byte. Figure 2.1 is a representation of an integer number stored electronically in a computer cell.
Synchronization for Markovian master-slave neural networks: an event-triggered impulsive approach
Published in International Journal of Systems Science, 2023
Yumei Zhou, Yuru Guo, Chang Liu, Hui Peng, Hongxia Rao
The symbols , , , and denote the non-negative integers, positive integers, the real number set, the n dimension vectors, and the dimensional real matrices, respectively. stands for the probability of a stochastic variable. is the Euclidean norm. , and stand for a transpose, largest eigenvalue and smallest eigenvalue of a matrix Q, respectively, and Q>0 implies the matrix is positive definite. A index * means a symmetric element in a matrix. I is the identity matrix.
A note on scheduling on uniform parallel machines with unavailability constraints
Published in International Journal of Production Research, 2021
Dehua Xu, Limin Xu, Zhijun Xu, Xianyu Yu
This issue indicates that variables in the original model are not well-defined either. As variables have a close relationship with variables , in order to make these variables well-defined, here we resort to (i.e. the total processing time of the jobs assigned to be processed on machine i) and (i.e. the total processing time of the jobs assigned to be processed on machine i but before the unavailable period of machine i). Let ε be a positive real number that is sufficiently small and set ε to 1 if are integers. Specifically, we have the following two constraint sets. Note that we always have according to (8) for . It is easy to see that if and only if , where . This coincides with the definition of , where .
Topological pressure for an iterated function system
Published in Dynamical Systems, 2021
In this section, we recall the WLLZ's topological entropy [20] which is different from Bi ś's [2] and Bufetov's [4]. At first, we introduce some basic notions. Let be the set of non-negative integers, let be the set of positive integers, and let be the set of all real number, respectively. Let be a metric space and let . Then , , , and denote the closure of A, the interior of A, the complement of A, the diameter of A and the cardinality of A, respectively. Let . For , let . Let For , let Let be an iterated function system. The is called an invariant subset of if for all .