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Micromachined Contactless Suspensions
Published in Kevin Yallup, Krzysztof Iniewski, Technologies for Smart Sensors and Sensor Fusion, 2017
Kirill V. Poletkin, Christopher Shearwood, Alexandr I. Chernomorsky, Ulrike Wallrabe
Hence, the second h-derivative of the function F(h) must have a negative sign and, accounting for (13.58), can be written as () ddt(mg+dM12(h)dhM12(h)L2i2)>0.
Mathematical Review
Published in Simant Ranjan Upreti, Optimal Control for Chemical Engineers, 2016
The definition of the derivative follows from the differential. We multiply and divide d f(x0; h) by h in the last equation to obtain f(x0+h)=f(x0)+df(x0;h)h︸derivativeh+∈(h) where the derivative is the coefficient of h and is defined as limh→0df(x0;h)h≡dfdx|x0=limh→0f(x0+h)−f(x0)h
Uncertain parameter based dynamical model among the interaction of immature prey, mature prey and predator
Published in International Journal of Modelling and Simulation, 2023
Prabir Panja, Sailen Gayen, Dipak Kumar Jana
There have been numerous reports on fuzzy approaches, stochastic approaches, fuzzy stochastic approaches, and interval approaches based on inaccurate ecological models [5]. When processing ambiguous or imprecise environmental data, fuzzy ways of handling ambiguity are quite beneficial. Fuzzy set theory is a potent tool for representing uncertainty and interpreting hazy or subjective data in mathematical models. FDE is a very important topic, both theoretically and in terms of practical applications, such as in population models that several academics have examined [6–8]. Initially, the derivative for fuzzy-valued mappings was developed by Puri and Ralescu [9], who generalized and extended the concept of Hukuhara differentiability (H-derivative) for set-valued mappings to the class of fuzzy mappings. Kaleva [10] then began to create a hypothesis for FDE using the H-derivative. This method occasionally has drawbacks since the solution’s diameter diam () becomes unbounded as time rises [11,12]. This problem demonstrates that this interpretation fails to sufficiently extend the associated crisp scenario, and we assume that it is a consequence of the quantification of the derivative used in the FDE’s formulation.
Moderate deviations for stochastic variational inequalities
Published in Optimization, 2023
Mingjie Gao, Ka-Fai Cedric Yiu
Hadamard differentiability. Let us recall some conceptions of Hadamard differentiability (see Shapiro [17], van der Vaar and Wellner [18]). Let and be two Banach spaces. A map g defined on a subset of with values in is called Hadamard (directional) differentiable at x if there exists a continuous mapping such that holds for all sequences converging to and converging to h in such that for every n. Such a function G is called the H-derivative of g at x and is also denoted as .
Two temperature generalized thermoelasticity involving memory-dependent derivative under fuzzy environment
Published in Waves in Random and Complex Media, 2021
Saroj Mandal, Monalisa Middya, Smita Pal (Sarkar)
The concept of the fuzzy set was first introduced by Zadeh [36] in 1965. Dubois and Parade [37] introduced the idea of differentiation of an ordinary function at a fuzzy point and differentiation of a fuzzy valued function at a non-fuzzy point. They defined the membership function by using the supremum of a set and used the extension principle in their approach. The concept of H-derivative of a fuzzy valued function has been introduced by Hukuhara [38]. J. Buckley and T. Feuring [39] introduced the solution to the fuzzy differential equations. In this paper, we have used triangular fuzzy number such that and are the endpoints of the r-level sets for . H-difference and Hakuhara differentiability of a fuzzy function have been used. If we consider and as two fuzzy numbers, then the difference is defined as [38].