Related papers: Non-geodesic Spherical Funk Transforms with One an…
The vertical slice transform takes a function on the n-dimensional unit sphere to integrals of that function over spherical slices parallel to the last coordinate axis. This transform arises in thermoacoustic tomography. We obtain new…
We show that on a two-dimensional compact nontrapping manifold with strictly convex boundary, a piecewise constant function is determined by its integrals over geodesics. In higher dimensions, we obtain a similar result if the manifold…
As is well-known, given the complex sphere P^1 minus two points, there exist nonconstant holomorphic maps from the plane into this set, the simplest example of which is given by applying the exponential map and then composing with a…
In this paper the problem of noncommutative elastic scattering in a central field is considered. General formulas for the differential cross-section for two cases are obtained. For the case of high energy of an incident wave it is shown…
We describe the invariant metrics on real flag manifolds and classify those with the following property: every geodesic is the orbit of a one-parameter subgroup. Such a metric is called g.o. (geodesic orbit). In contrast to the complex…
We provide a class of orbits in the curved N-body problem for which no point that could play the role of the centre of mass is fixed or moves uniformly along a geodesic. This proves that the equations of motion lack centre-of-mass and…
In this paper, we analyze the nonlinear single pixel X-ray transform $K$ and study the reconstruction of $f$ from the measurement $Kf$. Different from the well-known X-ray transform, the transform $K$ is a nonlinear operator and uses a…
We discuss if phase diagrams of the two-dimensional XY models in which the interaction of nearest planar spins is a nonmonotonic function of the angle u between them, V(u) = - Jcos(u) - Kcos(qu) can include a phase transition related to the…
In this paper we deal with the problem of recovering functions from their spherical mean transform $\mathcal{R}$, which integrates functions on circles in the plane, in case where the centers of the circles of integration are located on a…
We show the existence of at least two geometrically distinct closed geodesics on an n-dimensional sphere with a bumpy and non-reversible Finsler metric for n>2.
Using large resolution numerical simulations of GK turbulence, spanning an interval ranging from the end of the fluid scales to the electron gyroradius, we study the energy transfers in the perpendicular direction for a proton-electron…
In this paper, orthogonal projection along a geodesic to the chosen k-plane is introduced using edge and Gram matrix of an n-simplex in hyperbolic or spherical n-space. The distance from a point to k-plane is obtained by the orthogonal…
The subject of this thesis is the rigorous construction of QFT models with nontrivial interaction. Two different approaches in the framework of AQFT are discussed. On the one hand, an inverse scattering problem is considered. A given…
I present an exact and explicit solution to the scalar (Stokes flux intensity) radio interferometer imaging equation on a spherical surface which is valid also for non-coplanar interferometer configurations. This imaging equation is…
We define two transforms between non-conformal harmonic maps from a surface into the 3-sphere. With these transforms one can construct, from one such harmonic map, a sequence of harmonic maps. We show that there is a correspondence between…
Volume-fraction expressions are obtained for the systems of an infinite number of parallel planes arranged both regularly and randomly. As a special case of random arrangement, a non-Poissonian point process (the second-order Erlang…
In this paper, we study generalized versions of the k-center problem, which involves finding k circles of the smallest possible equal radius that cover a finite set of points in the plane. By utilizing the Minkowski gauge function, we…
We analyzed the frequency shifts of photons emitted from massive particles that move in stable geodesics around black holes with non-linear electrodynamics. The motion of the photon is modified by an effective metric when the Einstein…
We discuss two topics related to Fourier transforms on Lie groups and on homogeneous spaces: the operational calculus and the Gelfand--Gindikin problem (program) about separation of non-uniform spectra. Our purpose is to indicate some…
We construct and discuss new numerical homotopy invariants of topological spaces that are suitable for the study of functions on loop and sphere spaces. These invariants resemble the Lusternik-Schnirelmann category and provide lower bounds…