We show that an infinite-dimensional complete linear space X has: • a dense hereditarily Baire Hamel basis if |X| ≤ c; • a dense non-meager Hamel basis if |X| = κ = 2 for some cardinal κ. According to Corollary 3.4 of [BDHMP] each infinite-dimensional separable Banach space X has a non-meager Hamel basis. This is a special case of Theorem3.3 of [BDHMP], asserting that an infinite-dimensional Ba...

In this article we consider linear isomorphisms over the field of rational numbers between linear spaces R and R. We prove that if f is such an isomorphism, then the image by f of the unit disk is a strictly non-measurable subset of the real line, which is strongly non-similar to any classical nonmeasurable subset of reals. We also show the consistency and independence of the proposition that a...

The purpose of study is to develop numerical techniques for nonlinear magnetohydrodynamics (MHD) JefferyHamel blood flow problem to analyze the behavior of blood flow and its contribution in high blood pressure through artificial neural networks trained with Active Set and Interior Point Algorithm. First we transform three-dimensional flow problem into two-dimensional MHD Jeffery-Hamel flow pro...

In this paper, the Bernstein collocation method (BCM) is used for first time to solve nonlinear magnetohydrodynamics (MHD) Jeffery–Hamel arterial blood flow issue. The model described by partial differential equations transformed a third-order one-dimensional equation. By using method, problem into system of algebraic equations. residual correction procedure estimate error; it simple use and ca...

We investigate various kinds of bases in infinite dimensional Banach spaces. In particular, we consider the complexity of Hamel bases in separable and non-separable Banach spaces and show that in a separable Banach space a Hamel basis cannot be analytic, whereas there are non-separable Hilbert spaces which have a discrete and closed Hamel basis. Further we investigate the existence of certain c...