Dirac Operator on a disk with global boundary conditions

We compute the functional determinant for a Dirac operator in the presence of an Abelian gauge field on a bidimensional disk, under global boundary conditions of the type introduced by Atiyah-Patodi-Singer. We also discuss the connection between our result and the index theorem.Comment: RevTeX, 11 pages. References adde

Determinants of Dirac operators with local boundary conditions

We study functional determinants for Dirac operators on manifolds with boundary. We give, for local boundary conditions, an explicit formula relating these determinants to the corresponding Green functions. We finally apply this result to the case of a bidimensional disk under bag-like conditions.Comment: standard LaTeX, 24 pages. To appear in Jour. Math. Phy

Scattering and self-adjoint extensions of the Aharonov-Bohm hamiltonian

We consider the hamiltonian operator associated with planar sec- tions of infinitely long cylindrical solenoids and with a homogeneous magnetic field in their interior. First, in the Sobolev space $\mathcal H^2$, we characterize all generalized boundary conditions on the solenoid bor- der compatible with quantum mechanics, i.e., the boundary conditions so that the corresponding hamiltonian operators are self-adjoint. Then we study and compare the scattering of the most usual boundary con- ditions, that is, Dirichlet, Neumann and Robin.Comment: 40 pages, 5 figure

Fractional-order operators: Boundary problems, heat equations

The first half of this work gives a survey of the fractional Laplacian (and related operators), its restricted Dirichlet realization on a bounded domain, and its nonhomogeneous local boundary conditions, as treated by pseudodifferential methods. The second half takes up the associated heat equation with homogeneous Dirichlet condition. Here we recall recently shown sharp results on interior regularity and on $L_p$-estimates up to the boundary, as well as recent H\"older estimates. This is supplied with new higher regularity estimates in $L_2$-spaces using a technique of Lions and Magenes, and higher $L_p$-regularity estimates (with arbitrarily high H\"older estimates in the time-parameter) based on a general result of Amann. Moreover, it is shown that an improvement to spatial $C^\infty$-regularity at the boundary is not in general possible.Comment: 29 pages, updated version, to appear in a Springer Proceedings in Mathematics and Statistics: "New Perspectives in Mathematical Analysis - Plenary Lectures, ISAAC 2017, Vaxjo Sweden

A Climate for Change? Critical Reflections on the Durban United Nations Climate Change Conference

Despite more than 15 years of high level efforts led by the United Nations to broker a binding agreement on emissions reduction, negotiations at every annual meeting have failed to establish a global agreement mainly due to significant disagreements between industrialized and developing countries over differentiated responsibilities in reducing emissions. In this paper I describe my experiences as a participant-observer at the 17th United Nations Climate Change summit held in Durban, South Africa during December 2011. I provide a critical analysis of the political economy of climate change and discuss power dynamics between market, state and civil society sectors as well as the shifting geopolitics that marks the emergence of China and India as major players in the climate change arena

Systems Innovation, Inertia and Pliability: A mathematical exploration with implications for climate change abatement

This paper develops a stylised mathematical interpretation of innovation and inertia in economic systems, characteristics which feature in economics literature traceable back at least to Schumpeter and other economic theorists of innovation, as well as economic historians. Such characteristics are particularly important in energy systems and their potential response to climate change, where it is important to distinguish operational/fuel substitution from investment because the latter necessarily embodies both inertia and innovation, in systems as well as technologies. We argue that integrated assessments of climate abatement need to focus on investment, including the associated characteristics of both learning and inertia, and derive in detail the mathematical basis for incorporating these factors through marginal investment cost curves. From this we also introduce the concept of �pliability� as an expression of the ratio between costs which are significant but transitional (including learning investments, infrastructure and overcoming inertia), as compared to the enduring costs implied by purely exogenous technology assumptions. We then incorporate these features in a global model of optimal climate mitigation and show that they can generate a very different profile and pattern of results from traditional �integrated assessment� models, pinpointing the key sensitivities. We conclude that alongside all the attention devoted to evaluating climate change impacts and technology scenarios, far more effort should be devoted to understanding the structural characteristics of how the global energy system may respond to climate change mitigation

RAD54 family translocases counter genotoxic effects of RAD51 in human tumor cells.

The RAD54 family DNA translocases have several biochemical activities. One activity, demonstrated previously for the budding yeast translocases, is ATPase-dependent disruption of RAD51-dsDNA binding. This activity is thought to promote dissociation of RAD51 from heteroduplex DNA following strand exchange during homologous recombination. In addition, previous experiments in budding yeast have shown that the same activity of Rad54 removes Rad51 from undamaged sites on chromosomes; mutants lacking Rad54 accumulate nonrepair-associated complexes that can block growth and lead to chromosome loss. Here, we show that human RAD54 also promotes the dissociation of RAD51 from dsDNA and not ssDNA. We also show that translocase depletion in tumor cell lines leads to the accumulation of RAD51 on chromosomes, forming complexes that are not associated with markers of DNA damage. We further show that combined depletion of RAD54L and RAD54B and/or artificial induction of RAD51 overexpression blocks replication and promotes chromosome segregation defects. These results support a model in which RAD54L and RAD54B counteract genome-destabilizing effects of direct binding of RAD51 to dsDNA in human tumor cells. Thus, in addition to having genome-stabilizing DNA repair activity, human RAD51 has genome-destabilizing activity when expressed at high levels, as is the case in many human tumors

Ellipticity Conditions for the Lax Operator of the KP Equations

The Lax pseudo-differential operator plays a key role in studying the general set of KP equations, although it is normally treated in a formal way, without worrying about a complete characterization of its mathematical properties. The aim of the present paper is therefore to investigate the ellipticity condition. For this purpose, after a careful evaluation of the kernel with the associated symbol, the majorization ensuring ellipticity is studied in detail. This leads to non-trivial restrictions on the admissible set of potentials in the Lax operator. When their time evolution is also considered, the ellipticity conditions turn out to involve derivatives of the logarithm of the tau-function.Comment: 21 pages, plain Te

Klein-Gordon Solutions on Non-Globally Hyperbolic Standard Static Spacetimes

We construct a class of solutions to the Cauchy problem of the Klein-Gordon equation on any standard static spacetime. Specifically, we have constructed solutions to the Cauchy problem based on any self-adjoint extension (satisfying a technical condition: "acceptability") of (some variant of) the Laplace-Beltrami operator defined on test functions in an $L^2$-space of the static hypersurface. The proof of the existence of this construction completes and extends work originally done by Wald. Further results include the uniqueness of these solutions, their support properties, the construction of the space of solutions and the energy and symplectic form on this space, an analysis of certain symmetries on the space of solutions and of various examples of this method, including the construction of a non-bounded below acceptable self-adjoint extension generating the dynamics

Distributing the burdens of climate change

Global climate change raises many questions for environmental political theorists. This article focuses on the question of identifying the agents that should bear the financial burden of preventing dangerous climate change. Identifying in a fair way the agents that should take the lead in climate mitigation and adaptation, as well as the precise burdens that these parties must bear, will be a key aspect of the next generation of global climate policies. After a critical review of a number of rival approaches to burden sharing, the paper argues that only a principled and philosophically robust reconciliation of three approaches to burden sharing (‘contribution to problem’, ‘ability to pay’ and ‘beneficiary pays’) can generate a satisfactory mix of theoretical coherence and practical application