Related papers: Gaussian-convolution-invariant shell approximation…

Spherical Bessel functions appear commonly in many areas of physics wherein there is both translation and rotation invariance, and often integrals over products of several arise. Thus, analytic evaluation of such integrals with different…

In this paper we consider a semitetrad covariant decomposition of spherically symmetric spacetimes and find a governing hyperbolic equation of the Gaussian curvature of two dimensional spherical shells, that emerges due to the…

We use nonstandard analysis to study the problem of expressing a Gaussian integral in terms of the limiting behavior of a sequence of spherical integrals. Peterson and Sengupta proved that if a Gaussian measure $\mu$ has full support on a…

Multiplicative convolution $\mu \ast \nu$ of two finite signed measures $\mu$ and $\nu$ on $\mathbb{R}^n$ and a related product $\mu \circledast \nu$ on the sphere $S^{n-1}$ are studied. For fixed $\mu$ the injectivity in $\nu$ of both…

The reconstruction of 3D objects from calibrated photographs represents a fundamental yet intricate challenge in the domains of computer graphics and vision. Although neural reconstruction approaches based on Neural Radiance Fields (NeRF)…

The tau function corresponding to the affine ring of a certain plane algebraic curve, called (n,s)-curve, embedded in the universal Grassmann manifold is studied. It is neatly expressed by the multivariate sigma function. This expression is…

Gaussian particles provide a flexible framework for modelling and simulating three-dimensional star-shaped random sets. In our framework, the radial function of the particle arises from a kernel smoothing, and is associated with an…

The Mat{\'e}rn family of isotropic covariance functions has been central to the theoretical development and application of statistical models for geospatial data. For global data defined over the whole sphere representing planet Earth, the…

Spherical symmetry is ubiquitous in nature. It's therefore unfortunate that spherical system simulations are so hard, and require complete spheres with millions of interacting particles. Here we introduce an approach to model spherical…

We provide a method for fast and exact simulation of Gaussian random fields on spheres having isotropic covariance functions. The method proposed is then extended to Gaussian random fields defined over spheres cross time and having…

We discuss symmetries of the spherical shell model that make contact with the geometric collective model of Bohr and Mottelson. The most celebrated symmetry of this kind is SU(3), which is the basis of Elliott's model of rotation. It…

We discuss infinitesimal isometries of the middle surfaces and present some characteristic conditions for a function to be the normal component of an infinitesimal isometry. Our results show that those characteristic conditions depend on…

We develop a general framework for isotropic functional Gaussian fields on the $d$-dimensional sphere $\mathbb{S}^{d}$, where the field takes values in a separable Hilbert space $\mathcal{H}$. We establish an operator-valued extension of…

We study N=2 supersymmetric four dimensional gauge theories, in a certain N=2 supergravity background, called Omega-background. The partition function of the theory in the Omega-background can be calculated explicitly. We investigate…

In this paper, we compare two optimization algorithms using full Hessian and approximation Hessian to obtain numerical spherical designs through their variational characterization. Based on the obtained spherical design point sets, we…

Spherical representations and functions are the building blocks for harmonic analysis on riemannian symmetric spaces. In this paper we consider spherical functions and spherical representations related to certain infinite dimensional…

Let $\Omega$ be a measurable Euclidean set in $\mathbb{R}^{n}$ that is symmetric, i.e. $\Omega=-\Omega$, such that $\Omega\times\mathbb{R}$ has the smallest Gaussian surface area among all measurable symmetric sets of fixed Gaussian volume.…

We continue the study, initiated in arXiv:1404.1094, of the $O(N)$ symmetric theory of $N+1$ massless scalar fields in $6-\epsilon$ dimensions. This theory has cubic interaction terms $\frac{1}{2}g_1 \sigma (\phi^i)^2 + \frac{1}{6}g_2…

This work addresses the problem of simulating Gaussian random fields that are continuously indexed over a class of metric graphs, termed graphs with Euclidean edges, being more general and flexible than linear networks. We introduce three…

We define the two-dimensional $O(n)$ conformal field theory as a theory that includes the critical dilute and dense $O(n)$ models as special cases, and depends analytically on the central charge. For generic values of $n\in\mathbb{C}$, we…