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...

I f you make the mistake, as some do, of calling Jeff Dangl a botanist, his embarrassment is palpable. Trained as a mouse immunologist, he admits to a “certain lack” of botanical knowledge. The John N. Couch distinguished professor of biology and adjunct professor of microbiology and immunology at the University of North Carolina, Chapel Hill, will, however, give you an earful about the lack of...

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...

We experimentally demonstrate that nonflagellated Escherichia coli strains follow modified Jeffery orbits in shear flow near a surface. We fully characterize their Jeffery orbits as a function of their aspect ratios and distance from that surface. Thanks to the linearity of Navier-Stokes equations under low-Reynolds-number conditions, the hydrodynamic body-wall interactions described here can b...

This paper seeks to provide clues as to why experimental evidence for the alignment of fibers in semi-dilute suspensions under shear flows does not match theoretical predictions. This paper posits that it is the coupling between Jeffery’s equation and Stokes’ equation that causes the deviation from theory. It is proposed that if the initial data is slightly non-uniform, then there is feedback v...