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Mathematical Review
Published in Simant Ranjan Upreti, Optimal Control for Chemical Engineers, 2016
Given a conditional statement A → B, the satisfaction of A causes B. Condition A is known as the sufficient condition. Its satisfaction is sufficient to cause the outcome B, which in turn is called the necessary condition. Outcome B is necessary for condition A to have been true. Put differently, if B did not happen, then neither did A. Using for negation, ¬B→¬A Thus, if the glass did not crack, then you did not drop it for sure.
From Multipole Methods to Photonic Crystal Device Modeling
Published in Kiyotoshi Yasumoto, Electromagnetic Theory and Applications for Photonic Crystals, 2018
Lindsay C. Botten, Ross C. McPhedran, C. Martijn de Sterke, Nicolae A. Nicorovici, Ara A. Asatryan, Geoffrey H. Smith, Timothy N. Langtry, Thomas P. White, David P. Fussell, Boris T. Kuhlmey
In addition to its intuitive and tractable qualities, the Bloch mode method is also computationally easy to implement — with our particular implementation comprising a combination of Mathematica [90] functions and Fortran — with the applications suite implemented in the former, thus exploiting the excellent programming language and numerical linear algebra library, and with the multipole based grating scattering matrices (that define the transfer matrix) being implemented in the latter, with the two linked together using the MathLink toolkit [90]. While scattering matrices can be computed using a variety of techniques, the multipole method has been central to most of the applications that we have studied. The sole proviso for its use is that adjacent layers do not interpenetrate, thus allowing the use of plane wave expansions of fields at matching interfaces. This requirement, strictly speaking, is a sufficient but not a necessary condition. Provided that the extent of the interpenetration is not too severe, plane wave expansions are still valid on the matching interfaces — a situation that is directly related to the Rayleigh controversy of diffraction grating theory [91] concerning the validity of plane wave representations for outgoing fields within the grooves of diffraction gratings. For noninterpenetrating cylinder gratings, however, the multipole technique is arguably the preferred method as the formulation is analytically elegant and structurally embodies key properties such as reciprocity and energy conservation analytically within the formulation. These properties may be verified effectively to within machine precision and are analytically inherited by the Bloch mode method making it both analytically tractable and easy to validate numerically. Nevertheless, in those circumstances when the multipole methods can no longer be used, a range of alternative techniques including differential, integral, and finite element methods may be employed.
Structure of finite dimensional exact estimation algebra on state dimension 3 and linear rank 2*
Published in International Journal of Control, 2023
Xiaopei Jiao, Stephen S.-T. Yau
However, for exact estimation algebra with nonmaximal rank, structure of estimation algebra and property of Riccati equations are still open problems. In this paper, first we develop some useful tools of underdetermined PDE. Next, we study the structure of exact estimation algebra. We establish a sufficient and necessary condition for estimation algebra to be finite dimensional. Importantly, it is different from maximal rank case that in non-maximal rank estimation algebra, η needs not to be a degree 2 polynomial and can be a polynomial of any degree . Third, for Riccati-type equation, estimates have been done from the viewpoints of both classical solution and weak solution respectively. We obtain the growth rate of classical solution. For a crucial step of weak solution analysis, it requires a detail analysis of the influence of η. Finally, finite dimensional filters are constructed successfully.
Low-cost Non-superconducting DC-fault Current Limiter for the Enhancement of Low-voltage Ride Through Capability of Doubly Fed Induction Generator
Published in IETE Technical Review, 2020
Subhendu Sekhar Sahoo, P. M. Tripathi, Kalyan Chatterjee
The emerging practice of wind energy system (WES) generated different research movement in vast technical areas. Previously, the wind energy generation system was allowed to disconnect from the grid on the occurrence of a fault [1], but the separation of the wind energy conversion system creates a discontinuity in power generation. A necessary condition is set which needs to be satisfied by the WES for grid connection. This code for grid connectivity is termed as a grid code requirement. The voltage dip due to fault results into over current in rotor circuit which claims the damage of back to back converter and rotor winding. Another fault-related issues are also discussed in this paper. These issues demand the disconnection of the wind turbine from the grid for safety and stability purpose. But disconnection leads to the collapse of the whole grid, hence, it needs to be aborted. The disconnection issue as defined by different grid companies is called as grid code. For grid connectivity, the WES needs to satisfy grid code requirement for which the design engineer needs to adapt some control strategies for satisfying grid connectivity and operation of WES.
Exploring the determinants affecting the usage of blockchain-based remittance services: an empirical study on the banking sector
Published in Behaviour & Information Technology, 2023
Muhammad Mansoor, Amir Zaib Abbasi, Ghazanfar Ali Abbasi, Sheraz Ahmad, Yujong Hwang
During the full-scale qualitative comparative analysis (fsQCA), this research carried out a necessary condition analysis (NCA) to assess whether or not the distinct effect of each antecedent condition is required for the desired conclusion. If a situation that may cause something is always present, this suggests that it is also a required condition. The results of Table 6 demonstrated that EE, SI, TB, TRB, and BI were significant in terms of usage behaviour. Users would not participate in the proposed outcome if the EE, SI, TB, TRB, and BI were not in a favourable state.