A hierarchy of parametrizing varieties for representations

The primary purpose is to introduce and explore projective varieties, $\text{GRASS}_{\bf d}(\Lambda)$, parametrizing the full collection of those modules over a finite dimensional algebra $\Lambda$ which have dimension vector $\bf d$. These varieties extend the smaller varieties previously studied by the author; namely, the projective varieties encoding those modules with dimension vector $\bf d$ which, in addition, have a preassigned top or radical layering. Each of the $\text{GRASS}_{\bf d}(\Lambda)$ is again partitioned by the action of a linear algebraic group, and covered by certain representation-theoretically defined affine subvarieties which are stable under the unipotent radical of the acting group. A special case of the pertinent theorem served as a cornerstone in the work on generic representations by Babson, Thomas, and the author. Moreover, applications are given to the study of degenerations

The 2015 Paris Agreement on Climate Change: Significance and Implications for the Future

On December 12, 2015, nearly 200 countries created a major new agreement on climate change, accompanied by national commitments to act. The Paris Agreement has rightly been celebrated as a breakthrough, but was unquestionably constrained by the need for compromise, and its details will continue to be developed at the international, national, and local levels. On January 9, 2016, a panel of expert commentators and delegation members from a variety of national jurisdictions convened at the annual American Association of Law Schools meeting to analyze the Paris Agreement; they considered how the agreement evolved from prior efforts, the structure of its commitments, and its implications for the future. This Dialogue presents a transcript of the discussion, which has been edited for style, clarity, and space considerations

Almost clean rings and arithmetical rings

It is shown that a commutative B\'ezout ring $R$ with compact minimal prime spectrum is an elementary divisor ring if and only if so is $R/L$ for each minimal prime ideal $L$. This result is obtained by using the quotient space $\mathrm{pSpec} R$ of the prime spectrum of the ring $R$ modulo the equivalence generated by the inclusion. When every prime ideal contains only one minimal prime, for instance if $R$ is arithmetical, $\mathrm{pSpec} R$ is Hausdorff and there is a bijection between this quotient space and the minimal prime spectrum $\mathrm{Min} R$, which is a homeomorphism if and only if $\mathrm{Min} R$ is compact. If $x$ is a closed point of $\mathrm{pSpec} R$, there is a pure ideal $A(x)$ such that $x=V(A(x))$. If $R$ is almost clean, i.e. each element is the sum of a regular element with an idempotent, it is shown that $\mathrm{pSpec} R$ is totally disconnected and, $\forall x\in\mathrm{pSpec} R$, $R/A(x)$ is almost clean; the converse holds if every principal ideal is finitely presented. Some questions posed by Facchini and Faith at the second International Fez Conference on Commutative Ring Theory in 1995, are also investigated. If $R$ is a commutative ring for which the ring $Q(R/A)$ of quotients of $R/A$ is an IF-ring for each proper ideal $A$, it is proved that $R_P$ is a strongly discrete valuation ring for each maximal ideal $P$ and $R/A$ is semicoherent for each proper ideal $A$

Parameter-free expression for superconducting Tc in cuprates

A parameter-free expression for the superconducting critical temperature of layered cuprates is derived which allows us to express Tc in terms of experimentally measured parameters. It yields Tc values observed in about 30 lanthanum, yttrium and mercury-based samples for different levels of doping. This remarkable agreement with the experiment as well as the unusual critical behaviour and the normal-state gap indicate that many cuprates are close to the Bose-Einstein condensation regime.Comment: 5 pages, 2 figures. Will be published in Physical Review

Poor screening and nonadiabatic superconductivity in correlated systems

In this paper we investigate the role of the electronic correlation on the hole doping dependence of electron-phonon and superconducting properties of cuprates. We introduce a simple analytical expression for the one-particle Green's function in the presence of electronic correlation and we evaluate the reduction of the screening properties as the electronic correlation increases by approaching half-filling. The poor screening properties play an important role within the context of the nonadiabatic theory of superconductivity. We show that a consistent inclusion of the reduced screening properties in the nonadiabatic theory can account in a natural way for the $T_c$-$\delta$ phase diagram of cuprates. Experimental evidences are also discussed.Comment: 12 Pages, 6 Figures, Accepted on Physical Review

Evaluating the potential for the environmentally sustainable control of foot and mouth disease in Sub-Saharan Africa

Strategies to control transboundary diseases have in the past generated unintended negative consequences for both the environment and local human populations. Integrating perspectives from across disciplines, including livestock, veterinary and conservation sectors, is necessary for identifying disease control strategies that optimise environmental goods and services at the wildlife-livestock interface. Prompted by the recent development of a global strategy for the control and elimination of foot-and-mouth disease (FMD), this paper seeks insight into the consequences of, and rational options for potential FMD control measures in relation to environmental, conservation and human poverty considerations in Africa. We suggest a more environmentally nuanced process of FMD control that safe-guards the integrity of wild populations and the ecosystem dynamics on which human livelihoods depend while simultaneously improving socio-economic conditions of rural people. In particular, we outline five major issues that need to be considered: 1) improved understanding of the different FMD viral strains and how they circulate between domestic and wildlife populations; 2) an appreciation for the economic value of wildlife for many African countries whose presence might preclude the country from ever achieving an FMD-free status; 3) exploring ways in which livestock production can be improved without compromising wildlife such as implementing commodity-based trading schemes; 4) introducing a participatory approach involving local farmers and the national veterinary services in the control of FMD; and 5) finally the possibility that transfrontier conservation might offer new hope of integrating decision-making at the wildlife-livestock interface

Measurements of Spin Polarization of Epitaxial SrRuO3 Thin Films

We have measured the transport spin-polarization of epitaxial thin films of the conductive ferromagnetic oxide, SrRuO3, using Point Contact Andreev Reflection Spectroscopy (PCAR). In spite of the fact that spin-up and spin-down electronic densities of states at the Fermi level for SrRuO3 calculated from band structure theory are practically the same, the experimental transport spin polarization for these films was found to be about 50%. This result is a direct consequence of the Fermi velocity disparity between the majority and minority bands and is in good agreement with our theoretical estimates.Comment: 12 pages pdf onl

Disorder and Quantum Fluctuations in Superconducting Films in Strong Magnetic Fields

We find that the upper critical field in a two-dimensional disordered superconductor can increase essentially at low temperatures. This happens due to the formation of local superconducting islands weakly coupled via the Josephson effect. The distribution of the superconducting islands is derived. It is shown that the value of the critical field is determined by the interplay of the proximity effect and quantum phase fluctuations. We find that the shift of the upper critical field is connected with the pinning properties of a superconductor.Comment: 4 page

Transport spin polarization of Ni_xFe_{1-x}: electronic kinematics and band structure

We present measurements of the transport spin polarization of Ni_xFe_{1-x} (0<x<1) using the recently-developed Point Contact Andreev Reflection technique, and compare them with our first principles calculations of the spin polarization for this system. Surpisingly, the measured spin polarization is almost composition-independent. The results clearly demonstrate that the sign of the transport spin polarization does not coincide with that of the difference of the densities of states at the Fermi level. Calculations indicate that the independence of the spin polarization of the composition is due to compensation of density of states and Fermi velocity in the s- and d- bands