## What is/are Independent Generalized?

Independent Generalized - To identify unknown parameters of a direct inverse rate-dependent model, an inverse model of the rate-independent Generalized Prandtl-Ishlinskii (GPI) is used.^{[1]}We prove that this so-called Prabhakar process, in the special case β = 1 , can be represented as an α -stable process subordinated by an independent generalized gamma subordinator; thus it can be considered as an extension of the geometric stable process, to which it reduces for γ = 1.

^{[2]}Independent generalized estimation equation models were fitted.

^{[3]}Since the Floquet theory cannot be directly used for stability analysis of periodic responses of DAEs, a new stability analysis procedure is developed, where perturbed, linearized DAEs are reduced to ordinary differential equations with use of independent generalized coordinates.

^{[4]}It is known that the estimating equations for quantile regression (QR) can be solved using an EM algorithm in which the M-step is computed via weighted least squares, with weights computed at the E-step as the expectation of independent generalized inverse-Gaussian variables.

^{[5]}In this paper, we propose LESA, a framework which aims at advancing headfirst into expunging the former issue by assembling a source-independent generalized model that captures syntactic features through part-of-speech and dependency embeddings, as well as contextual features through a fine-tuned language model.

^{[6]}Barth et al originally proposed the term "prepubertal hypertrichosis" to denote a relatively common condition of androgen-independent generalized terminal hair hypertrichosis with prepubertal onset, and absence of endocrinological abnormalities [1].

^{[7]}The Bell nonlocality for initially general W states undergoing independent generalized amplitude damping channels are investigated.

^{[8]}A modeling approach is proposed for analyzing the natural frequencies of parallel manipulators (PMs) using the global independent generalized displacement coordinates (IGDC).

^{[9]}To model the expressed hub oscillation with respect to the link, the assumed modes method and mode shapes of Euler-Bernoulli beam with independent generalized modal coordinate with respect to the link are employed.

^{[10]}All the unknown Fourier coefficients are treated as a set of independent generalized coordinates and solved directly from the Rayleigh-Ritz procedure.

^{[11]}Since the obtained dynamic equations are expressed in terms of independent generalized coordinates which are selected according to active joint variables of the arm, the equations could be best suitable for control law design and implementation.

^{[12]}In this work, motivated by this insightful remark and starting from the consideration of a time-independent generalized quantum search Hamiltonian as originally introduced by Bae and Kwon [Phys.

^{[13]}Then, three stochastic representations are developed based on independent uniform distributions, multivariate Dirichlet distributions, and independent generalized normal (Gaussian) distributions.

^{[14]}

## independent generalized coordinate

Since the Floquet theory cannot be directly used for stability analysis of periodic responses of DAEs, a new stability analysis procedure is developed, where perturbed, linearized DAEs are reduced to ordinary differential equations with use of independent generalized coordinates.^{[1]}All the unknown Fourier coefficients are treated as a set of independent generalized coordinates and solved directly from the Rayleigh-Ritz procedure.

^{[2]}Since the obtained dynamic equations are expressed in terms of independent generalized coordinates which are selected according to active joint variables of the arm, the equations could be best suitable for control law design and implementation.

^{[3]}