Spaceability in Banach and quasi-Banach sequence spaces

Let $X$ be a Banach space. We prove that, for a large class of Banach or quasi-Banach spaces $E$ of $X$-valued sequences, the sets $E-\bigcup _{q\in\Gamma}\ell_{q}(X)$, where $\Gamma$ is any subset of $(0,\infty]$, and $E-c_{0}(X)$ contain closed infinite-dimensional subspaces of $E$ (if non-empty, of course). This result is applied in several particular cases and it is also shown that the same technique can be used to improve a result on the existence of spaces formed by norm-attaining linear operators.Comment: 9 page

Should Farmers Invest in Financial Assets as a Risk Management Strategy? Some Evidence from New Zealand

Off-farm investment as a risk management strategy is not widespread among New Zealand sheep and beef farmers. This study explores the potential for risk reduction by the diversification of farm asset portfolios to include financial investments such as industrial equities and government bonds of various types. Results show that the negative correlations between long-run rates of return on farm assets and financial investments could result in a significant reduction of risk if equities and bonds were included in farm investment portfolios. However, when combined with information about attitudes to risks, it does not seem likely that farmers would adopt such strategies purely in order to stabilise incomes. Deregulation of the New Zealand economy in the mid 1980's had little impact on farmers' optimal allocation of their assets.Agricultural Finance, Risk and Uncertainty,

Ballistic transport properties across nonuniform strain barriers in graphene

We study the effect of uniaxial strain on the transmission and the conductivity across a strain-induced barrier in graphene. At variance with conventional studies, which consider sharp barriers, we consider a more realistic, smooth barrier, characterized by a nonuniform, continuous strain profile. Our results are instrumental towards a better understanding of the transport properties in corrugated graphene.Comment: High Press. Res., to appea

Theory of integer quantum Hall polaritons in graphene

We present a theory of the cavity quantum electrodynamics of the graphene cyclotron resonance. By employing a canonical transformation, we derive an effective Hamiltonian for the system comprised of two neighboring Landau levels dressed by the cavity electromagnetic field (integer quantum Hall polaritons). This generalized Dicke Hamiltonian, which contains terms that are quadratic in the electromagnetic field and respects gauge invariance, is then used to calculate thermodynamic properties of the quantum Hall polariton system. Finally, we demonstrate that the generalized Dicke description fails when the graphene sheet is heavily doped, i.e. when the Landau level spectrum of 2D massless Dirac fermions is approximately harmonic. In this case we `integrate out' the Landau levels in valence band and obtain an effective Hamiltonian for the entire stack of Landau levels in conduction band, as dressed by strong light-matter interactions.Comment: 20 pages, 7 figure