The generalized KP hierarchy

We propose one possible generalization of the KP hierarchy, which possesses multi bi--hamiltonian structures, and can be viewed as several KP hierarchies coupled together.Comment: 12

The constrained modified KP hierarchy and the generalized Miura transformations

In this letter, we consider the second Hamiltonian structure of the constrained modified KP hierarchy. After mapping the Lax operator to a pure differential operator the second structure becomes the sum of the second and the third Gelfand-Dickey brackets defined by this differential operator. We simplify this Hamiltonian structure by factorizing the Lax operator into linear terms.Comment: 8 pages, latex, no figure

HRTEM study of a new non-stoichiometric BaTiO(3-δ) structure

BaTiO3-based multilayer ceramic capacitors (MLCCs) with Ni internal electrodes are co-fired in reducing atmospheres to avoid oxidation of the electrode. Although dielectric materials are doped by acceptor, donor and amphoteric dopants to minimize the oxygen vacancy content, there is still a large concentration of oxygen vacancies that are accommodated in the BaTiO3 active layers. In general, ABO3 perovskites demonstrates a strong ability to accommodate the oxygen vacancies and maintain a regular pseudo-cubic structure. Oxygen deficient barium titanate can be transformed to a hexagonal polymorph (h-BT) at high temperatures1,2. In this paper, we report the new modulated and long range ordered structures of non-stoichiometric BaTiO3-δ that are observed in the electrically degraded Ni-BaTiO3 MLCCs at low temperature

Dark Energy as a Born-Infeld Gauge Interaction Violating the Equivalence Principle

We investigate the possibility that dark energy does not couple to gravitation in the same way than ordinary matter, yielding a violation of the weak and strong equivalence principles on cosmological scales. We build a transient mechanism in which gravitation is pushed away from general relativity by a Born-Infeld gauge interaction acting as an "Abnormally Weighting" (dark) Energy. This mechanism accounts for the Hubble diagram of far-away supernovae by cosmic acceleration and time variation of the gravitational constant while accounting naturally for the present tests on general relativity.Comment: 5 pages, 3 figures, sequel of Phys. Rev. D 73 023520 (2006), to appear in Physical Review Letter

On the Treves theorem for the AKNS equation

According to a theorem of Treves, the conserved functionals of the AKNS equation vanish on all pairs of formal Laurent series of a specified form, both of them with a pole of the first order. We propose a new and very simple proof for this statement, based on the theory of B\"acklund transformations; using the same method, we prove that the AKNS conserved functionals vanish on other pairs of Laurent series. The spirit is the same of our previous paper on the Treves theorem for the KdV, with some non trivial technical differences.Comment: LaTeX, 16 page

Urban Observatories in the Midst of COVID-19: Challenges & Responses

In the context of the COVID-19 pandemic, urban observatories have demonstrated their value, but also highlighted the challenges for boundary institutions between knowledge generation and decision-making in a variety of different ways. We aim here to capture some of their voices in a time of crisis. The Connected Cities Lab, in collaboration with University College London and UN-Habitat, and in dialogue with a variety of urban research institutions around the planet, has been working since 2018 to develop a review of the challenges and values of and challenges for ‘urban observatories’. That project aims to present evidence on the boundary-spanning roles of these institutions, capturing the ways in which they bridge information in and about their cities and the potential value they offer to urban governance. As the COVID-19 crisis took hold across cities and continents in early 2020, it became apparent that this study could not prescind from a closer look at how these observatories had both been coping with, but also responding to, the pandemic. This resulted in a series of additional interviews, document reviews and a twopart virtual workshop in August 2020 with observatories, and urban research institutions performing observatory functions, to give further voice to these experiences. As a background to this ‘deep’ dive into the reality of COVID-19 for observatories, the overall study underpinning this working paper has relied on, first, desktop research on publicly available information to identify thirty-two cases of either explicitlynamed ‘urban observatories’ or else urban research institutions performing ‘observatory-like’ functions. This research was then coupled with a series of interviews with experts and senior staff from these observatories to ground truth initial considerations as well as to capture how the processes of boundary-spanning worked beyond the publicly available persona of each observatory. We then referred back to these thirty-two cases and selected a sample of fourteen for specific analysis in relation to COVID-specific interventions, with six of them involved directly into two virtual workshops to capture directly their experience in the context of the pandemic crisis. Capturing initial findings from these engagements (which will ultimately form an integral part of the project’s final report), this working paper offers a preliminary snapshot of some of these lessons drawn from the study. Essential for us has been the chance, amidst the complications of COVID-19 lockdowns and travel bans, to better capture the voice of observatories the world over and their tangible experiences with spanning urban research-practice boundaries in a turbulent historical moment. Whilst the final report for the project will likely include more extensively analysed cases emerging from the current crisis, we have sought to present here much of the raw reflections emerging from our engagement with colleagues in observatories (and ‘observatory-like’ institutions) to both offer useful reflections to other contexts around the world as well as to offer insights on the unique situation urban knowledge institutions find themselves in a reality where cities and urban life has been fundamentally recast by the pandemic. The working paper is organised in a way that follows our broader study’s key themes looking at the structure and activities of observatories, putting our broader findings into dialogue with the voices of observatories during the COVID-19 crisis. Section 1 describes the proposed visions and functions performed by observatories and puts it into dialogue with the COVID-19 crisis. Positionality of urban observatories is also discussed in this section. Section 2 explores outputs produced by, and themes investigated in, observatories and how they have been shaped by and for the crisis. In Sections 1 and 2 we endeavoured to capture vignettes from the participating observatories through the experiences of a set of six more specific interlocutor institutions engaged in the project: the Gauteng City Region Observatory (GCRO) in Johannesburg, the Karachi Urban Lab (KUL) in Karachi, the Indian Institute for Human Settlements (IIHS) in Bangalore, the Metropolis Observatory in Barcelona, and the World Resources Institute Ross Centre in Washington DC. Section 3 concludes with a commentary on the ongoing challenges and opportunities faced by urban observatories in the wake of COVID-19, without underestimating how the crisis might be far from over

Quintessence Models and the Cosmological Evolution of alpha

The cosmological evolution of a quintessence-like scalar field, phi, coupled to matter and gauge fields leads to effective modifications of the coupling constants and particle masses over time. We analyze a class of models where the scalar field potential V(phi) and the couplings to matter B(phi) admit common extremum in phi, as in the Damour-Polyakov ansatz. We find that even for the simplest choices of potentials and B(phi), the observational constraints on delta alpha/alpha coming from quasar absorption spectra, the Oklo phenomenon and Big Bang nucleosynthesis provide complementary constraints on the parameters of the model. We show the evolutionary history of these models in some detail and describe the effects of a varying mass for dark matter.Comment: 26 pages, 20 eps figure

AGN All the Way Down? AGN-like Line Ratios are Common In the Lowest-Mass Isolated Quiescent Galaxies

We investigate the lowest-mass quiescent galaxies known to exist in isolated environments ($\mathrm{M^* = 10^{9.0-9.5} \ M_\odot}$; 1.5 Mpc from a more massive galaxy). This population may represent the lowest stellar mass galaxies in which internal feedback quenches galaxy-wide star formation. We present Keck/ESI long-slit spectroscopy for 27 isolated galaxies in this regime: 20 quiescent galaxies and 7 star-forming galaxies. We measure emission line strengths as a function of radius and place galaxies on the Baldwin Phillips Terlevich (BPT) diagram. Remarkably, 16 of 20 quiescent galaxies in our sample host central AGN-like line ratios. Only 5 of these quiescent galaxies were identified as AGN-like in SDSS due to lower spatial resolution and signal-to-noise. We find that many of the quiescent galaxies in our sample have spatially-extended emission across the non-SF regions of BPT-space. When considering only the central 1$^{\prime\prime}$, we identify a tight relationship between distance from the BPT star-forming sequence and host galaxy stellar age as traced by $\mathrm{D_n4000}$, such that older stellar ages are associated with larger distances from the star-forming locus. Our results suggest that the presence of hard ionizing radiation (AGN-like line ratios) is intrinsically tied to the quenching of what may be the lowest-mass self-quenched galaxies.Comment: 16 pages, 9 figures, submitted to Ap

Mobilising urban knowledge in an infodemic: Urban observatories, sustainable development and the COVID-19 crisis

Along with disastrous health and economic implications, COVID-19 has also been an epidemic of misinformation and rumours – an ‘infodemic’. The desire for robust, evidence-based policymaking in this time of disruption has been at the heart of the multilateral response to the crisis, not least in terms of supporting a continuing agenda for global sustainable development. The role of boundary-spanning knowledge institutions in this context could be pivotal, not least in cities, where much of the pandemic has struck. ‘Urban observatories’ have emerged as an example of such institutions; harbouring great potential to produce and share knowledge supporting sustainable and equitable processes of recovery. Building on four ‘live’ case studies during the crisis of institutions based in Johannesburg, Karachi, Freetown and Bangalore, our research note aims to capture the role of these institutions, and what it means to span knowledge boundaries in the current crisis. We do so with an eye towards a better understanding of their knowledge mobilisation practices in contributing towards sustainable urban development. We highlight that the crisis offers a key window for urban observatories to play a progressive and effective role for sustainable and inclusive development. However, we also underline continuing challenges in these boundary knowledge dynamics: including issues of institutional trust, inequality of voices, collective memory, and the balance between normative and advisory roles for observatories

Power-law random walks

We present some new results about the distribution of a random walk whose independent steps follow a $q-$Gaussian distribution with exponent $\frac{1}{1-q}; q \in \mathbb{R}$. In the case $q>1$ we show that a stochastic representation of the point reached after $n$ steps of the walk can be expressed explicitly for all $n$. In the case $q<1,$ we show that the random walk can be interpreted as a projection of an isotropic random walk, i.e. a random walk with fixed length steps and uniformly distributed directions.Comment: 5 pages, 4 figure