On compatibility between isogenies and polarisations of abelian varieties

We discuss the notion of polarised isogenies of abelian varieties, that is, isogenies which are compatible with given principal polarisations. This is motivated by problems of unlikely intersections in Shimura varieties. Our aim is to show that certain questions about polarised isogenies can be reduced to questions about unpolarised isogenies or vice versa. Our main theorem concerns abelian varieties B which are isogenous to a fixed abelian variety A. It establishes the existence of a polarised isogeny A to B whose degree is polynomially bounded in n, if there exist both an unpolarised isogeny A to B of degree n and a polarised isogeny A to B of unknown degree. As a further result, we prove that given any two principally polarised abelian varieties related by an unpolarised isogeny, there exists a polarised isogeny between their fourth powers. The proofs of both theorems involve calculations in the endomorphism algebras of the abelian varieties, using the Albert classification of these endomorphism algebras and the classification of Hermitian forms over division algebras

Clustering and Correlations at the Neutron Dripline

Some recent experimental studies of clustering and correlations within very neutron-rich light nuclei are reviewed. In particular, the development of the novel probes of neutron-neutron interferometry and Dalitz-plot analyses is presented through the example of the dissociation of the two-neutron halo system $^{14}$Be. The utility of high-energy proton radiative capture is illustrated using a study of the $^{6}$He(p,$\gamma$) reaction. A new approach to the production and detection of bound neutron clusters is also described, and the observation of events with the characteristics expected for tetraneutrons ($^{4}$n) liberated in the breakup of $^{14}$Be is discussed. The prospects for future work, including systems beyond the neutron dripline, are briefly outlined.Comment: Invited contribution to a topical issue on Exotic Nuclei of Les Comptes Rendus de l'Academie des Sciences Paris, Serie IV. 29 pages,11 figures (format RevTex preprint

Space and place: writing encounters self

In addition to contributing this editorial article, Susan Orr and Claire Hind guest edited this issue

AXA General Insurance Ltd v Lord Advocate : analysis

Discusses the Supreme Court decision in AXA General Insurance Ltd, Petitioners on whether Scottish legislation which reversed a House of Lords ruling concerning the actionability of certain asbestos-related conditions breached insurers' rights

BeppoSAX observations of low-energy spectral features in AGN

The combination of the broad band coverage and moderate spectral resolution of the LECS and MECS instruments on-board BeppoSAX allow the spectra of AGN to be studied in unprecedented detail down to 0.1 keV. We describe the calibration and the performance of the LECS and report on observations of low-energy absorption features in the spectra of both a low (MCG-6-30-15) and a high luminosity (3C 273) AGN. These features provide important diagnostics on the location and nature of the material surrounding the AGN. A comparison of LECS and ASCA/SIS low energy performance is also presented in the case of 3C 273.Comment: 5 pages. To appear in symposium proceedings: The Active X-Ray Sky, Rome, October 199

Nonmodal energy growth and optimal perturbations in compressible plane Couette flow

Nonmodal transient growth studies and estimation of optimal perturbations have been made for the compressible plane Couette flow with three-dimensional disturbances. The maximum amplification of perturbation energy over time, $G_{\max}$, is found to increase with increasing Reynolds number ${\it Re}$, but decreases with increasing Mach number $M$. More specifically, the optimal energy amplification $G_{\rm opt}$ (the supremum of $G_{\max}$ over both the streamwise and spanwise wavenumbers) is maximum in the incompressible limit and decreases monotonically as $M$ increases. The corresponding optimal streamwise wavenumber, $\alpha_{\rm opt}$, is non-zero at M=0, increases with increasing $M$, reaching a maximum for some value of $M$ and then decreases, eventually becoming zero at high Mach numbers. While the pure streamwise vortices are the optimal patterns at high Mach numbers, the modulated streamwise vortices are the optimal patterns for low-to-moderate values of the Mach number. Unlike in incompressible shear flows, the streamwise-independent modes in the present flow do not follow the scaling law $G(t/{\it Re}) \sim {\it Re}^2$, the reasons for which are shown to be tied to the dominance of some terms in the linear stability operator. Based on a detailed nonmodal energy analysis, we show that the transient energy growth occurs due to the transfer of energy from the mean flow to perturbations via an inviscid {\it algebraic} instability. The decrease of transient growth with increasing Mach number is also shown to be tied to the decrease in the energy transferred from the mean flow ($\dot{\mathcal E}_1$) in the same limit

ties that bind us

when objects converge in a space they start a dialogue of their lives lives that become entangled with your life your memory objects are the narrators of memory a stain, a chip, a tear materials embed meaning and metaphor within the process of creating woven cloth, throwing lines, squeezed and pressed coils all become remnants of the hand as I make, play, and collect materials and objects questions are brought forward How do these components talk to one other? What are they saying? How do I listen? knowledge is generated in the transformation of material through the process of making with my hands. a call and response a conversation an attentive listener / / an intuitive maker I seek to excavate spaces and analyze my findings in hope of contemplation and examination a moment where my art becomes artifact where the unfamiliar appears familiar connecting materials and objects that have anchored our human experience to ask the unanswerable questions of human existence to love to grieve to grasp onto memories to let go to admire fate to mourn to gro