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The second order symmetry operators that commute with the Dirac operator with external vector, scalar and pseudo-scalar potentials are computed on a general two-dimensional spin-manifold. It is shown that the operator is defined in terms of…
The space of differential operators acting on skewsymmetric tensor fields or on smooth forms of a smooth manifold are representations of its Lie algebra of vector fields. We compute the first cohomology spaces of these representations and…
We generalise the analysis in [arXiv:0904.1744] to superspace, and explicitly prove that for any embedding of surface operators in a general, twisted N=2 pure abelian theory on an arbitrary four-manifold, the parameters transform naturally…
The notion of spherically symmetric superfunctions as functions invariant under the orthosymplectic group is introduced. This leads to dimensional reduction theorems for differentiation and integration in superspace. These spherically…
Applying convolutional neural networks to spherical images requires particular considerations. We look to the millennia of work on cartographic map projections to provide the tools to define an optimal representation of spherical images for…
In this paper we make an attempt to extend L. Schwartz's classical result on spectral synthesis to several dimensions. Due to counterexamples of D. I. Gurevich this is impossible for translation invariant varieties. Our idea is to replace…
Many applications in science call for the numerical simulation of systems on manifolds with spherical topology. Through use of integer spin weighted spherical harmonics we present a method which allows for the implementation of arbitrary…
We discuss several seemingly assorted objects: the umbral calculus, generalised translations and associated transmutations, symbolic calculus of operators. The common framework for them is representations of the Weyl algebra of the…
We present a new and general framework for convolutional neural network operations on spherical (or omnidirectional) images. Our approach represents the surface as a graph of connected points that doesn't rely on a particular sampling…
The translation equivariance of convolutions can make convolutional neural networks translation equivariant or invariant. Equivariance to other transformations (e.g. rotations, affine transformations, scalings) may also be desirable as soon…
An alternative method is suggested for the description of the velocity and pressure fields in an unbounded incompressible viscous fluid induced by an arbitrary number of spheres moving and rotating in it. Within the framework of this…
Standard practice attempts to remove coordinate influence in physics through the use of invariant equations. Trans-coordinate physics proceeds differently by not introducing space-time coordinates in the first place. Differentials taken…
We present explicit generators of an algebra of commuting difference operators with trigonometric coefficients. The operators are simultaneously diagonalized by recently discovered q-polynomials (viz. Koornwinder's multivariable…
Some concepts, such as non-compactness measure and condensing operators, defined on metric spaces are extended to uniform spaces. Such extensions allow us to locate, in the context of uniform spaces, some classical results existing in…
We study a solenoidal-potential type decomposition of a symmetric $m$-tensor field in $\Rb^2$, and its implications to injectivity questions for the momentum and elastic ray transforms. For symmetric tensor fields, a general decomposition…
Classical spectral theory gives a complete description of a single normal operator, but it fails for noncommuting operators, where no canonical joint spectrum or simultaneous diagonalization exists. Existing approaches provide only partial…
The pull-back, push-forward and multiplication of smooth functions can be extended to distributions if their wave front set satisfies some conditions. Thus, it is natural to investigate the topological properties of these operations between…
We employ multiple-scale analysis to systematically derive analytical approximations describing the cosmological propagation of gravitational waves beyond general relativity, in a framework with two interacting spin-2 fields with…
In the previous paper [arXiv:2210.10435], the nonlinear perturbation theory of cosmological density field is generalized to include the tensor-valued bias of astronomical objects, such as spins and shapes of galaxies and any other tensors…
Convergence of operators acting on a given Hilbert space is an old and well studied topic in operator theory. The idea of introducing a related notion for operators acting on arying spaces is natural. However, it seems that the first…