Related papers: Sphere paths in outer space
By considering a spatial curve in a Euclidean space, we use its components, together with attaining a cyclic matrix, to show that this matrix is homothetic too and is in correspondence with a homothetic motion. Furthermore, if the curve…
For sampling values along spherical Lissajous curves we establish a spectral interpolation and quadrature scheme on the sphere. We provide a mathematical analysis of spherical Lissajous curves and study the characteristic properties of…
The ongoing quest to identify molecules in the interstellar medium by their electronic spectra in the visible region is reviewed. Identification of molecular absorption is described in the context of the elucidation of the carriers of the…
In spacetime physics, we frequently need to consider a set of all spaces (`universes') as a whole. In particular, the concept of `closeness' between spaces is essential. However, there has been no established mathematical theory so far…
Every spacetime is defined by its metric, the mathematical object which further defines the spacetime curvature. From the relativity principle, we have the freedom to choose which coordinate system to write our metric in. Some coordinate…
The paper is devoted to geometrical investigation of the Gromov-Hausdorff distance on the classes of all metric spaces and of all bounded metric spaces. The main attention is paid to pass connectivity questions. The pass connected…
We consider an extremal problem for subsets of high-dimensional spheres that can be thought of as an extension of the classical isoperimetric problem on the sphere. Let $A$ be a subset of the $(m-1)$-dimensional sphere $\mathbb{S}^{m-1}$,…
The spherometer used for measuring radius of curvature of spherical surfaces is explicitly based on a geometric relation unique to circles and spheres. We present an alternate approach using coordinate geometry, which reproduces the…
We provide an estimate of the distance (in the dual flat seminorm) of the normal cycles of convex bodies with given Hausdorff distance. We also give an estimate (in the bounded Lipschitz metric) of the support measures of convex bodies.
We discuss a path integral formalism to introduce noncommutative generalizations of spacetime manifold in even dimensions, which have been suggested to be reasonable effective pictures at very small length scales, of the order of Planck…
I present a brief review of some of the most recent and active topics of star formation process in the Milky Way using mid and far infrared observations, and motivated by the research being carried out by our science group using data…
We have developed a method for deriving the distribution of the Milky Way's interstellar medium as a function of longitude, latitude, distance and line-of-sight velocity. This method takes as input maps of reddening as a function of…
The motion of a mechanical system can be defined as a path through its configuration space. Computing such a path has a computational complexity scaling exponentially with the dimensionality of the configuration space. We propose to reduce…
For a given metric measure space $(X,d,\mu)$ we consider finite samples of points, calculate the matrix of distances between them and then reconstruct the points in some finite-dimensional space using the multidimensional scaling (MDS)…
We note that in large space shell model calculaiotns and experiment one sometimes get results, the form of which also appear in smaller space calculations. On the other hand there are some results which demand the large space approach.
We use global bifurcation techniques to establish the existence of arbitrarily many geometrically distinct nonplanar embedded smooth minimal 2-spheres in sufficiently elongated 3-dimensional ellipsoids of revolution. More precisely, we…
Transiting exoplanets provide access to data to study the mass-radius relation and internal structure of extrasolar planets. Long-period transiting planets allow insight into planetary environments similar to the Solar System where, in…
Projected in the sky, galaxies are spatially-resolved objects. To understand how they formed and evolve it is necessary to study the spatial distribution of their observables. In this review talk, we briefly describe some scaling relations…
Some features of a parametrized space of orbits in the Schwarzschild geometry are described.
The new approach of the regular spacing of planetary orbits and planet mass distribution in the Solar system is considered. The relative planetary distances will be represented as the inverse composite probabilities of two discrete…