We study spectral properties of the Laplace-Beltrami operator on two relevant almost-Riemannian manifolds, namely the Grushin structures on the cylinder and on the sphere. This operator contains first order diverging terms caused by the divergence of...
The possible existence of black holes has fascinated scientists at least since Michell and Laplace's proposal that a gravitating object could exist from which light could not escape. In the 20th century, in light of the general theory of relativity...
We prove existence and asymptotic behavior of the transition density for a large class of subordinators whose Laplace exponents satisfy lower scaling condition at infinity. Furthermore, we present lower and upper bounds for the density. Sharp estimat...
Eigenvalue transformations, which include solving time-dependent differential equations as a special case, have a wide range of applications in scientific and engineering computation. While quantum algorithms for singular value transformations are we...
We study Dirac-type operators on incomplete cusp edge spaces with invertible boundary families. In particular, we construct the heat kernel for the associated Laplace-type operator and prove that the Dirac operators are essentially self-adjoint and F...
We provide a necessary and sufficient condition for the representability of a function as the classical multidimensional Laplace transform, when the support of the representing measure is contained in some generalized semi-algebraic set. This is done...
Since the pioneering work of Kelvin on Laplace tidal equations, a zoology of trapped waves have been found in the context of coastal dynamics. Among them, the one originally computed by Kelvin plays a particular role, as it is an unidirectional mode...
We prove that the lowest eigenvalue of the Laplace operator with a magnetic field having a self-intersecting zero set is a monotone function of the parameter defining the strength of the magnetic field, in a neighborhood of infinity. We apply this mo...
The Laplace equation on Euclidean flat space admits a discrete radial inversion symmetry. In 1983, Couch and Torrence (CT) found -- surprisingly -- that the massless wave equation continues to display this symmetry on the background of an extremal (a...
In mathematics, and specifically in potential theory, the Poisson kernel is an integral kernel, used for solving the two-dimensional Laplace equation
The complex transverse water proton magnetization subject to diffusion-encoding magnetic field gradient pulses in a heterogeneous medium such as brain tissue can be modeled by the Bloch-Torrey partial differential equation. The spatial integral of th...
Generalized Gaussian processes (GGPs) are highly flexible models that combine latent GPs with potentially non-Gaussian likelihoods from the exponential family. GGPs can be used in a variety of settings, including GP classification, nonparametric coun...
I honestly dont know where people fall on this. I get that politics isn't for everyone, but The appeal of Gundam (for me) has always been how in depth they go with certain issues, then contrast th...
In the most recent Xtreme Talent, it was stated by Robo-X that he would need 10 billion USD to create this proposed research rocket which was 1 million times X’s salary. That means that X’s sala...
Pytorch implementations of Bayes By Backprop, MC Dropout, SGLD, the Local Reparametrization Trick, KF-Laplace, SG-HMC and more (⭐ 1957)
Like seriously, did anything change? I watched UC:0096 and narrative and I don’t think anything changed. Please tell me I’m wrong because I don’t want to bell that marida died for nothing....
∇ ⋅ ∇ {\displaystyle \nabla \cdot \nabla } , ∇ 2 {\displaystyle \nabla ^{2}} (where ∇ {\displaystyle \nabla } is the nabla operator), or Δ {\displaystyle
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They're so fun, I love the dynamics between them. Ulrich & Enigma's 'can't stand each other but also can't really go without each other' never disappoints. Here's to hoping we see them playable so...
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