Hermitian symmetric polynomials and CR complexity

Properties of Hermitian forms are used to investigate several natural questions from CR Geometry. To each Hermitian symmetric polynomial we assign a Hermitian form. We study how the signature pairs of two Hermitian forms behave under the polynomial product. We show, except for three trivial cases, that every signature pair can be obtained from the product of two indefinite forms. We provide several new applications to the complexity theory of rational mappings between hyperquadrics, including a stability result about the existence of non-trivial rational mappings from a sphere to a hyperquadric with a given signature pair.Comment: 19 pages, latex, fixed typos, to appear in Journal of Geometric Analysi

The aspherical explosion of the Type IIP SN 2017gmr

Type IIP supernovae (SNe IIP), which represent the most common class of core-collapse (CC) SNe, show a rapid increase in continuum polarization just after entering the tail phase. This feature can be explained by a highly asymmetric helium core, which is exposed when the hydrogen envelope becomes transparent. Here we report the case of an SN IIP (SN 2017gmr) that shows an unusually early rise of the polarization, 30 d before the start of the tail phase. This implies that SN 2017gmr is an SN IIP that has very extended asphericity. The asymmetries are not confined to the helium core, but reach out to a significant part of the outer hydrogen envelope, hence clearly indicating a marked intrinsic diversity in the aspherical structure of CC explosions. These observations provide new constraints on the explosion mechanism, where viable models must be able to produce such extended deviations from spherical symmetry, and account for the observed geometrical diversity

Magneto-Conductance Anisotropy and Interference Effects in Variable Range Hopping

We investigate the magneto-conductance (MC) anisotropy in the variable range hopping regime, caused by quantum interference effects in three dimensions. When no spin-orbit scattering is included, there is an increase in the localization length (as in two dimensions), producing a large positive MC. By contrast, with spin-orbit scattering present, there is no change in the localization length, and only a small increase in the overall tunneling amplitude. The numerical data for small magnetic fields $B$, and hopping lengths $t$, can be collapsed by using scaling variables $B_\perp t^{3/2}$, and $B_\parallel t$ in the perpendicular and parallel field orientations respectively. This is in agreement with the flux through a `cigar'--shaped region with a diffusive transverse dimension proportional to $\sqrt{t}$. If a single hop dominates the conductivity of the sample, this leads to a characteristic orientational `finger print' for the MC anisotropy. However, we estimate that many hops contribute to conductivity of typical samples, and thus averaging over critical hop orientations renders the bulk sample isotropic, as seen experimentally. Anisotropy appears for thin films, when the length of the hop is comparable to the thickness. The hops are then restricted to align with the sample plane, leading to different MC behaviors parallel and perpendicular to it, even after averaging over many hops. We predict the variations of such anisotropy with both the hop size and the magnetic field strength. An orientational bias produced by strong electric fields will also lead to MC anisotropy.Comment: 24 pages, RevTex, 9 postscript figures uuencoded Submitted to PR

Giant negative magnetoresistance in semiconductors doped by multiply charged deep impurities

A giant negative magnetoresistance has been observed in bulk germanium doped with multiply charged deep impurities. Applying a magnetic field the resistance may decrease exponentially at any orientation of the field. A drop of the resistance as much as about 10000% has been measured at 6 T. The effect is attributed to the spin splitting of impurity ground state with a very large g-factor in the order of several tens depending on impurity.Comment: 4 pages, 4 figure

Unusual echocardiographic evidence of hypercoagulation in usual left atrial appendage as the first and only sign of COVID-19

Coronavirus disease 2019 (COVID-19) is a condition caused by a novel virus, severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2). The disease’s course ranges from entirely asymptomatic to severely ill patients. Hypercoagulation is often a complication of this disease, worsening the prognosis, which is extremely important in patients at higher risk of thromboembolic events, such as atrial fibrillation (AF), where thrombus formation in the left atrial appendage (LAA) is frequent. LAA could be of various sizes, volumes, and shapes, distinguish several morphologies, from which the WindSock LAA is the most frequent. In contrast, thromboembolic complications occur most frequently in patients with AF and the Cactus LAA. We present a clinical case of a 70-year-old woman with an initial negative real-time polymerase chain reaction (RT-PCR) test for SARS-CoV-2, suspicion of device-related infection after dual pacemaker implantation, AF, and LAA without thrombus in the initial transoesophageal echocardiography (TEE). Despite apixaban treatment, spontaneous restoration of sinus rhythm, and WindSock LAA morphology, the sludge in LAA was diagnosed in control TEE. The patient did not present any typical clinical COVID-19 symptoms but re-checked the RT-PCR test for SARS-CoV-2 infection was positive. The described case presents echocardiographic evidence of hypercoagulation as the first and only feature of SARS-CoV-2 condition besides the usual morphological presentation of the WindSock LAA

Random Matrix Theory of Transition Strengths and Universal Magnetoconductance in the Strongly Localized Regime

Random matrix theory of the transition strengths is applied to transport in the strongly localized regime. The crossover distribution function between the different ensembles is derived and used to predict quantitatively the {\sl universal} magnetoconductance curves in the absence and in the presence of spin-orbit scattering. These predictions are confirmed numerically.Comment: 15 pages and two figures in postscript, revte

Tenfold Magnetoconductance in a Non-Magnetic Metal Film

We present magnetoconductance (MC) measurements of homogeneously disordered Be films whose zero field sheet conductance (G) is described by the Efros-Shklovskii hopping law $G(T)=(2e^2/h)\exp{-(T_o/T)^{1/2}}$. The low field MC of the films is negative with G decreasing 200% below 1 T. In contrast the MC above 1 T is strongly positive. At 8 T, G increases 1000% in perpendicular field and 500% in parallel field. In the simpler parallel case, we observe {\em field enhanced} variable range hopping characterized by an attenuation of $T_o$ via the Zeeman interaction.Comment: 9 pages including 5 figure

Evidence for multiple origins of fast declining Type II supernovae from spectropolarimetry of SN 2013ej and SN 2017ahn

The origin of the diverse light-curve shapes of Type II supernovae (SNe), and whether they come from similar or distinct progenitors, has been actively discussed for decades. Here, we report spectropolarimetry of two fast declining Type II (Type IIL) SNe: SN 2013ej and SN 2017ahn. SN 2013ej exhibited high continuum polarization from very soon after the explosion to the radioactive tail phase with time-variable polarization angles. The origin of this polarimetric behaviour can be interpreted as the combination of two different aspherical structures, namely an aspherical interaction of the SN ejecta with circumstellar matter (CSM) and an inherently aspherical explosion. Aspherical explosions are a common feature of slowly declining Type II (Type IIP) SNe. By contrast, SN 2017ahn showed low polarization not only in the photospheric phase but also in the radioactive tail phase. This low polarization in the tail phase, which has never before been observed in other Type IIP/L SNe, suggests that the explosion of SN 2017ahn was nearly spherical. These observations imply that Type IIL SNe have, at least, two different origins: they result from stars that have different explosion properties and/or different mass-loss processes. This fact might indicate that 13ej-like Type IIL SNe originate from a similar progenitor to those of Type IIP SNe accompanied by an aspherical CSM interaction, while 17ahn-like Type IIL SNe come from a more massive progenitor with less hydrogen in its envelope