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® Fundamentals
Published in William Bober, ® Essentials, 2017
For Arithmetic Statements that contain several Arithmetic Operators and parentheses, there is a specific order that is used in evaluating the arithmetic expression. First, the Arithmetic Logic Unit, going from left to right, searches for parentheses, if it finds them, it will carry out the operations inside all the parentheses in the following order: exponentiation, multiplication and division, and addition and subtraction. It then returns to the beginning of the arithmetic statement and carries out the operations in the same order listed above.
The method of fundamental solutions for scattering of electromagnetic waves by a chiral object
Published in Applicable Analysis, 2023
E. S. Athanasiadou, I. Arkoudis
For the regularity properties of the tangential components of chiral vector potentials and on the surface S as well as the analysis of the transmission problem, the following operators are needed: for A = L, R. We will refer to and as left and right circularly polarized magnetic dipole operator and for and as left and right circularly polarized electric dipole operator, respectively. As it is stated in [27,29–31], these operators satisfy the following properties: are bounded and if is a bounded domain or smoother, then they are compact for A = L, R. In paper [27], it has been proved that are compact and are bounded. It is noted that the corresponding properties for Hölder spaces and can be found in book [25] and in paper [32]. The corresponding properties for Sobolev spaces can be found in [20,21].
Finite-time fault-tolerant consensus for leader-following multi-agent systems with semi-Markov switching topologies
Published in International Journal of Control, 2022
Kun-Zhong Miao, Jian-Ning Li, Yang-Jie Chen, Sen Xu
On both sides of the formula (13), the left and right multiplication matrices and are defined, respectively. Then the following related variables are defined: then we can concluded that: According to the linear transformation expansion of formula , it can be deduced that: where Then use Shur complement Lemma to get (31), and the value and can be solved, then the controller gains can obtain, , the system can achieve fault-tolerant consensus under the consensus protocol.
Performance evaluation of MIMO DFT-Spread WR-OFDM system for spectrum efficiency and power efficiency
Published in Journal of Information and Telecommunication, 2022
The time-domain windowing technique is a popular method for reducing out-of-band emissions (OOBE) in the OFDM system. It reduces OOBE by multiplying the left and right end segments of the OFDM symbol to improve spectral characteristics. Conventional OOBE reducing techniques, such as f-OFDM, FBMC, UFMC, require plenty of multiplication, increasing the complexity of the transmitter. In contrast, the time-domain windowing technique needs single multiplication only which is effective in reducing complexity than the conventional techniques. In this paper, the Tukey window function is performed that can be defined as follows (Hossain & Ryu, 2021): where denotes Tukey window coefficients, and is the cosine fraction. This window function is utilized for left and right segments of the OFDM symbol by multiplication operations. Figure 5 shows the symbol formation and the windowing technique of the proposed method. The proposed scheme time-domain symbol length is N + CP, precisely the same as the conventional OFDM system.