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Parabolic-type pseudodifferential equations with elliptic symbols in dimension 3 over $p$-adics

In this paper we deal with the operator defined as 𝑓(∂,𝛼)𝜙:=−1𝜉→𝑥(|𝑓(𝜉)|𝛼𝑝𝑥→𝜉𝜙), where f(ξ) is an elliptic quadratic form of dimension 3 over ℚ p . We study the Cauchy problem associated that operator, and find the fundamental solution and some …

MegaMorph – multiwavelength measurement of galaxy structure: physically meaningful bulge–disc decomposition of galaxies near and far

Bulge–disc decomposition is a valuable tool for understanding galaxies. However, achieving robust measurements of component properties is difficult, even with high-quality imaging, and it becomes even more so with the imaging typical of large …

Galaxy And Mass Assembly: the wavelength-dependent sizes and profiles of galaxies revealed by MegaMorph

We investigate the relationship between colour and structure within galaxies using a large, volume-limited sample of bright, low-redshift galaxies with optical–near-infrared imaging from the Galaxy And Mass Assembly survey. We fit single-component, …

$p$-Adic elliptic quadratic forms, parabolic-type pseudodifferential equations with variable coefficients and Markov processes

In this article we study the Cauchy problem for a new class of parabolic-type pseudodifferential equations with variable coefficients for which the fundamental solutions are transition density functions of Markov processes in the four dimensional …

The problem of the first return attached to a pseudodifferential operator in dimension 3

In this article we study the problem of first return associated to an elliptic pseudodifferential operator with non-radial symbol of dimension 3 over the p-adics.

MegaMorph – multiwavelength measurement of galaxy structure: Sérsic profile fits to galaxies near and far

We demonstrate a new multiwavelength technique for two-dimensional parametric modelling of galaxy surface-brightness profiles, which we have incorporated into the widely used software GALFIT. Our new method, named GALFITM, extends GALFIT3's current …

Riesz Kernels and Pseudodifferential Operators Attached to Quadratic Forms over $p$-Adic Fields

We study pseudodifferential equations and Riesz kernels attached to certain quadratic forms over p-adic fields. We attach to an elliptic quadratic form of dimension two or four a family of distributions depending on a complex parameter, the Riesz …

MegaMorph – multiwavelength measurement of galaxy structure: complete Sérsic profile information from modern surveys

In this paper, we demonstrate a new method for fitting galaxy profiles which makes use of the full multiwavelength data provided by modern large optical–near-infrared imaging surveys. We present a new version of GALAPAGOS, which utilizes a recently …

Revealing components of the galaxy population through non-parametric techniques

The distributions of galaxy properties vary with environment, and are often multimodal, suggesting that the galaxy population may be a combination of multiple components. The behaviour of these components versus environment holds details about the …

Differentiating Major Depressive Disorder in Youths with Attention Deficit Hyperactivity Disorder

**Background:** Youths with attention deficit hyperactivity disorders (ADHD) frequently have comorbid major depressive disorders (MDD) sharing overlapping symptoms. Our objective was to examine which depressive symptoms best discriminate MDD among …