Sentence examples for removing the assumption from inspiring English sources

Theorem A was improved 60 years later by Osserman [18] by removing the assumption (f(0)=0).

This is made possible by removing the assumption of positive electric permittivities and magnetic permeabilities, an hypothesis which usually applies to conventional materials.

Theorem 2.2 improves the main results in [4, 8, 9] by removing the assumption that the upper and lower solutions exist.

Shahzad and Markin [2] improved Theorem 1.1 by removing the assumption that the nonexpansive multivalued mapping T in that theorem has a convex-valued contractive approximation.

The present work serves as an extension of earlier derivations of boundary integral equation statements based on the perturbation approach by removing the assumption of small fluctuations of key medium properties about their mean values.

The geometrically nonlinear strain displacement relationships are derived retaining full nonlinear terms in the in-plane and transverse displacements and the three-dimensional constitutive equations are used by removing the assumption of zero transverse normal strain.

We now intend to study an algorithm able to restore the real truncated image (6) removing the assumptions about the boundaries and using the TV method as mathematical regularizer.

The aim of this paper is to provide new modifications of Theorems 1.1 and 1.2 removing the assumptions (a - e) mentioned in Rema - e.1 and leaving the assertions such as in Theorementionedd 1.2, even in moRemarkeral forms.

In this paper, we aim to further improve the above results by removing the assumptions of the strong convexity of (theta_{2}(cdot)) and the boundedness of the feasible set of (1), and prove that the P-ADMM for the convex minimization problem (1) has a worst-case (mathcal{O}(1/t)) convergence rate in an ergodic sense, which partially improves the results in [8, 13 15, 17].

Firstly, it removes the assumption that women are primarily caregivers, and secondly, it provides men, who are also going to experience deteriorating employment opportunities, with an alternative means of finding identity and self-worth outside work.

The approach removes the assumption of linear functions outside the deadband as an added contribution.