Sentence examples for improved generalized and from inspiring English sources

The result has been improved, generalized, and extended under various assumptions.

Because of its application in many disciplines such as computer science, chemistry, biology, physics, and many branches of mathematics, a lot of authors have improved, generalized, and extended this classical result in nonlinear analysis; see, e.g., [2 10] and the references therein.

Because of its application in many disciplines such as chemistry, physics, biology, computer science and many branches of mathematics, a lot of authors have improved, generalized and extended this classical result in nonlinear analysis; see, e.g., [2 10] and the references therein.

Several mathematicians improved, generalized and extended the concept of metric spaces to vector-valued metric spaces of Perov [4], G-metric spaces of Mustafa and Sims [5], cone metric spaces of Huang and Zhang [6], modular metric spaces of Chistyakov [7], partial metric spaces of Matthews [8] and others.

Because of its importance in nonlinear analysis, a number of authors have improved, generalized and extended this basic result either by defining a new contractive mapping in the context of a complete metric space or by investigating the existing contractive mappings in various abstract spaces; see, e.g., [2 10] and references therein.

Fang [5] proved some fixed point theorems in fuzzy metric spaces, which improved, generalized, unified and extended some main results of Edelstein [6], Istratescu [7], Sehgal and Bharucha-Reid [8].

First the denominator of the reduced order model is obtained by improved generalized least squares method and the numerator coefficients are determined by minimizing the integral square error between the transient responses of original and reduced order models using DE technique, pertaining to unit step input.

The combined advantages of the improved generalized Least squares method (IGLSM) and error minimization by Differential Evolution technique (DE) is employed for both order reduction and controller design.

The regularization parameter of the Tikhonov method was chosen by the classical L-curve method and the parameter-choice scheme of the TTLS method was the improved generalized cross validation (IGCV).

An improved generalized spectral test for time series models with conditional heteroskedasticity of unknown form, with Y. Lee, Econometric Theory 23, 106-154.

An improved generalized gradient approximation of PBEsol is used in the present first-principles calculations, which is able to well describe both vacancy formation energies and vibrational properties.