Entire curves avoiding given sets in C^n

Let $F\subset\Bbb C^n$ be a proper closed subset of $\Bbb C^n$ and $A\subset\Bbb C^n\setminus F$ at most countable ($n\geq 2$). We give conditions of $F$ and $A$, under which there exists a holomorphic immersion (or a proper holomorphic embedding) $\phi:\Bbb C\to\Bbb C^n$ with $A\subset\phi(\Bbb C)\subset\Bbb C^n\setminus F$.Comment: 10 page

Ferromagnetism in defect-ridden oxides and related materials

The existence of high-temperature ferromagnetism in thin films and nanoparticles of oxides containing small quantities of magnetic dopants remains controversial. Some regard these materials as dilute magnetic semiconductors, while others think they are ferromagnetic only because the magnetic dopants form secondary ferromagnetic impurity phases such as cobalt metal or magnetite. There are also reports in d0 systems and other defective oxides that contain no magnetic ions. Here, we investigate TiO2 (rutile) containing 1 - 5% of iron cations and find that the room-temperature ferromagnetism of films prepared by pulsed-laser deposition is not due to magnetic ordering of the iron. The films are neither dilute magnetic semiconductors nor hosts to an iron-based ferromagnetic impurity phase. A new model is developed for defect-related ferromagnetism which involves a spin-split defect band populated by charge transfer from a proximate charge reservoir in the present case a mixture Fe2+ and Fe3+ ions in the oxide lattice. The phase diagram for the model shows how inhomogeneous Stoner ferromagnetism depends on the total number of electrons Ntot, the Stoner exchange integral I and the defect bandwidth W; the band occupancy is governed by the d-d Coulomb interaction U. There are regions of ferromagnetic metal, half-metal and insulator as well as nonmagnetic metal and insulator. A characteristic feature of the high-temperature Stoner magnetism is an an anhysteretic magnetization curve which is practically temperature independent below room temperature. This is related to a wandering ferromagnetic axis which is determined by local dipole fields. The magnetization is limited by the defect concentration, not by the 3d doping. Only 1-2 % of the volume of the films is magnetically ordered.Comment: 22 pages, 6 figure

A Search for Non-Perturbative Dualities of Local N=2N=2 Yang--Mills Theories from Calabi--Yau Threefolds

The generalisation of the rigid special geometry of the vector multiplet quantum moduli space to the case of supergravity is discussed through the notion of a dynamical Calabi--Yau threefold. Duality symmetries of this manifold are connected with the analogous dualities associated with the dynamical Riemann surface of the rigid theory. N=2 rigid gauge theories are reviewed in a framework ready for comparison with the local case. As a byproduct we give in general the full duality group (quantum monodromy) for an arbitrary rigid $SU(r+1)$ gauge theory, extending previous explicit constructions for the $r=1,2$ cases. In the coupling to gravity, R--symmetry and monodromy groups of the dynamical Riemann surface, whose structure we discuss in detail, are embedded into the symplectic duality group $\Gamma_D$ associated with the moduli space of the dynamical Calabi--Yau threefold.Comment: Latex. Version of previous paper with enlarged and revised appendix 35 pages, plain LaTe

Science and Film-making

The essay reviews the literature, mostly historical, on the relationship between science and film-making, with a focus on the science documentary. It then discusses the circumstances of the emergence of the wildlife making-of documentary genre. The thesis examined here is that since the early days of cinema, film-making has evolved from being subordinate to science, to being an equal partner in the production of knowledge, controlled by non-scientists

'In the wake of a pandemic': dietary patterns and impact on child health after COVID-19

INTRODUCTION Our companion Report: ‘Emerging Dietary Patterns: Impact on Child Health’ discussed ways in which traditional dietary patterns in both the UK and internationally were changing. In concluding we argued that: ‘The interconnected nature of food, climate and health is the biggest challenge we face, but therein also lies its strength and boundless potential should we act with the necessary urgency, creativity and commitment. It is at the local level – supported by national policy – that the largest returns from such pro-activity will accrue.’ We continued: ‘The food that we eat here and now can change the world.’ adding: ‘If we are serious about protecting and restoring natural environments, safeguarding the health and wellbeing of our children today and restoring and protecting that of future generations, then there is only one solution. We must change it.’ Then came Covid-19 and change was imposed – with the arrival and experience of a pandemic. The full outcome of Covid-19; its effects and repercussions not just for the present generations but for the many that will succeed it cannot be estimated now. In the 102 years since Spanish ‘flu devastated an older world order, we are still learning its lessons today. But what has become immediately apparent is that what we eat and how we eat has undergone a revolution in four short months. 6 ‘Coronavirus pandemic will change the food industry and eating habits forever, says CEO of Food and Drink Federation, Ian Wright.’ ([email protected] 7 April 2020) ‘To prevent the next pandemic we must take on factory farming.’ (Jonathan Safran Foer and Aaron Gross, The Guardian, 21 April 2020.) ‘Covid-19 will definitely be an accelerator on the conscious consumer patterns that we see unfolding. As the consumer gets more conscious, we also see more interest in sustainable, locally produced food systems solutions.’ (David Brandes, Food Navigator, 17 April 2020.) ‘The virus is a warning that Britain’s food system must change,’ (‘The Guardian,’ 18th April 2020). It would also be unjust to address the Covid-19 pandemic in isolation without highlighting its interactions with another global force to become manifest in the same era in response to an incident in the US; namely, the police killing of George Floyd and the Black Lives Matter Movement. Pandemics, poor health, systemic inequalities and a lack of environmental protections harm black, ethnic minority and disadvantaged communities in all countries more than any other groups, and the two events have shed a harsh light on those realities and their frightening interconnections – such as the higher death rate in BAME communities including healthcare workers on the frontline (Public Health England, June 2020, ‘Beyond the data: Understanding the impact of COVID-19 on BAME groups’): https://assets.publishing.service.gov.uk/government/uploads/system/uploads/attachment_data/file/892376/COVID_stakeholder_engagement_synthesis_beyond_the_data.pdf Therefore, to address fall-out from the pandemic without considering these marginalised groups would be inappropriate; to address the environmental crisis without considering its impact on such groups would be pointless and the separation of civil rights from health and environmental policy is delusional. The silos in which policy-making still exists in these fields are stubborn obstacles to change. Both within and without the UK’s boundaries, the diverse spectrum of peoples requires a similar diversity and inclusion in the systems that sustain life – and the production of the food that is eaten in order to live. Sometimes change is immediate and imposed rather than incremental and the pandemic has seen an abrupt conclusion to familiar and traditional ways of living. As we offer our thoughts about the many ways in which Covid-19 has changed our dietary patterns, we must remember that the ‘brave new world’ of our future ambition ‘has such people in it’, (‘The Tempest’, William Shakespeare). Those who would construct better dietary patterns in the wake of this pandemic must ensure that people rather than systems prevail…

Genus Two Partition and Correlation Functions for Fermionic Vertex Operator Superalgebras I

We define the partition and $n$-point correlation functions for a vertex operator superalgebra on a genus two Riemann surface formed by sewing two tori together. For the free fermion vertex operator superalgebra we obtain a closed formula for the genus two continuous orbifold partition function in terms of an infinite dimensional determinant with entries arising from torus Szeg\"o kernels. We prove that the partition function is holomorphic in the sewing parameters on a given suitable domain and describe its modular properties. Using the bosonized formalism, a new genus two Jacobi product identity is described for the Riemann theta series. We compute and discuss the modular properties of the generating function for all $n$-point functions in terms of a genus two Szeg\"o kernel determinant. We also show that the Virasoro vector one point function satisfies a genus two Ward identity.Comment: A number of typos have been corrected, 39 pages. To appear in Commun. Math. Phy

Residue currents associated with weakly holomorphic functions

We construct Coleff-Herrera products and Bochner-Martinelli type residue currents associated with a tuple $f$ of weakly holomorphic functions, and show that these currents satisfy basic properties from the (strongly) holomorphic case, as the transformation law, the Poincar\'e-Lelong formula and the equivalence of the Coleff-Herrera product and the Bochner-Martinelli type residue current associated with $f$ when $f$ defines a complete intersection.Comment: 28 pages. Updated with some corrections from the revision process. In particular, corrected and clarified some things in Section 5 and 6 regarding products of weakly holomorphic functions and currents, and the definition of the Bochner-Martinelli type current

The kernel of the edth operators on higher-genus spacelike two-surfaces

The dimension of the kernels of the edth and edth-prime operators on closed, orientable spacelike 2-surfaces with arbitrary genus is calculated, and some of its mathematical and physical consequences are discussed.Comment: 12 page

86-GBaud subcarrier multiplexed 16QAM signal generation using an electrical 90 degree hybrid and IQ mixers

We experimentally demonstrate an aggregate 86-GBaud (over three sub-bands and one polarization) signal generation based on subcarrier multiplexing technique using IQ mixers, an electrical 90 degree hybrid, and diplexers. The electrical hybrid allows transmitter-side digital signal processing to be simplified to pulse shaping and digital pre-emphasis. We verified the configuration by testing the performance of an 86-GBaud Nyquist-shaped 16 quadrature amplitude modulation signal with differential bit encoding. The implementation penalty assuming 7% hard-decision forward error correction is reduced to 2 dB by utilizing a 31-tap decision-directed least mean square based multiple-input multiple-output equalizer for sideband crosstalk mitigation