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Basics of Motor Design
Published in Richard E. Neapolitan, Kwang Hee Nam, AC Motor Control and Electrical Vehicle Applications, 2018
Richard E. Neapolitan, Kwang Hee Nam
Consider 18 slot–8 pole motor running at 600 rpm. Note that the electrical frequency is fe=40 $ f_e=40 $ Hz. For r¯=4 $ \bar{r}=4 $ , then k=|0.5×4+18|/4=5 $ k=|0.5\times 4 + 18|/4=5 $ is an odd integer. Thus, vibration is excited at frequency fex=2×5×40=400 $ f_{ex}=2\times 5 \times 40= 400 $ Hz.
Combinatorics
Published in B. V. Senthil Kumar, Hemen Dutta, Discrete Mathematical Structures, 2019
B. V. Senthil Kumar, Hemen Dutta
Solution.(i) The sum of two even integers or of two odd integers is even. Consider the subsets {1, 3, 5, 7, 9} and {2, 4, 6, 8} of S as pigeonholes. Hence, n = 3.(ii) Consider the five subsets {1, 6}, {2, 7}, {3, 8}, {4, 9}, {5} of S as pigeonholes. Then, n = 6 will guarantee that two integers will belong to one of the subsets and their difference will be 5.
Exploring Mathematical Statements
Published in John D. Ross, Kendall C. Richards, Introductory Analysis, 2020
John D. Ross, Kendall C. Richards
Universal quantifiers are typically statements that claim all objects of a certain type will satisfy a certain property. Examples include: All integers are positive.All prime numbers are odd.Every perfect square is also a perfect cube.
Global stabilisation for a class of upper-triangular nonlinear systems with unmodelled dynamics and time-delay
Published in International Journal of Control, 2020
Weihai Zhang, Ling-Rong Xue, Zhen-Guo Liu, Zong-Yao Sun
In this paper, we consider the nonlinear time-delay system where denotes the unmeasurable state and denotes the measurable state of the system. is the system input. is an odd integer. The time-varying delay is bounded and with δ being a known constant. For , is the unknown control coefficient and satisfies , where ε and are positive constants. The initial date , where is a given continuous function. For , is the continuous function. For system (2), we introduce the following assumptions.
A Review on Static Reconfiguration Techniques of Solar PV to Mitigate Mismatch Loss and Minimize Partial Shading Effect
Published in IETE Journal of Research, 2021
Kanjune Akshay Bapurao, Suresh Mikkili, Praveen Kumar Bonthagorla
Magic square is classified into three types: Odd MS (n = 3, 5, 7, 9 …): where n is odd.Doubly Even (n = 4, 8, 12, 16): It consists of a square, where n is divisible by 4.Singly even (n = 2, 6, 10, 14, 18): It consists of a square which is divisible by 2 but not by 4.