Related papers: Catenary and Mercator projection
The concept of turnaround surface in an accelerating universe is generalized to arbitrarily large deviations from spherical symmetry, to close the gap between the idealized theoretical literature and the real world observed by astronomers.…
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…
In the context of exoplanet detection, the performance of coronagraphs is limited by wavefront errors. To efficiently correct for these aberrations with a deformable mirror, it is mandatory to measure them using the science detector with a…
By quantifying the distance between two collider events, one can triangulate a metric space and reframe collider data analysis as computational geometry. One popular geometric approach is to first represent events as an energy flow on an…
The concept of measurement in classical scattering is interpreted as an overlap of a particle packet with some area in phase space that describes the detector. Considering that usually we record the passage of particles at some point in…
In this paper, we introduce a new method for classifying 3D objects. Our main idea is to project a 3D object onto a spherical domain centered around its barycenter and develop neural network to classify the spherical projection. We…
The signal registered by a plane photodetector placed behind an optically inhomogeneous object irradiated by two coherent Gaussian beams intersecting inside the object at small angle to each other is calculated in the single-scattering…
We construct a special class of Lorentz surfaces in the pseudo-Euclidean 4-space with neutral metric which are one-parameter systems of meridians of rotational hypersurfaces with lightlike axis and call them meridian surfaces. We give the…
In this paper, we consider the feasibility problem, which aims to find a feasible point for the constraint set $\{x \in \mathbb{R}^n: c(x) = 0\}$ over a possibly non-regular subset $\mathcal{X} \subset \mathbb{R}^n$. Under the constraint…
Improvement of the prediction accuracy of the Earth's rotation parameters (ERP) is one of the main problems of applied astrometry. In order to solve this problem, various approaches are used and in order to select the best one, comparison…
Kernel approximation via nonlinear random feature maps is widely used in speeding up kernel machines. There are two main challenges for the conventional kernel approximation methods. First, before performing kernel approximation, a good…
360{\deg} spherical images have advantages of wide view field, and are typically projected on a planar plane for processing, which is known as equirectangular image. The object shape in equirectangular images can be distorted and lack…
Conspiratorial thinking can connect many distinct or distant ills to a central cause. This belief has visual form in the octopus map: a map where a central force (for instance a nation, an ideology, or an ethnicity) is depicted as a literal…
Meanders form a set of combinatorial problems concerned with the enumeration of self-avoiding loops crossing a line through a given number of points, $n$. Meanders are considered distinct up to any smooth deformation leaving the line fixed.…
In this note we are dealing with a particular class of quadratic algebras -- the so-called quantum matrix algebras. The well-known examples are the algebras of quantized functions on classical Lie groups (the RTT algebras). We consider the…
This paper deals with a modifed iterative projection method for approximating a solution of hierarchical fixed point problems for nearly nonexpansive mappings. Some strong convergence theorems for the proposed method are presented under…
Surveillance and surveying are two important applications of empirical research. A major part of terrain modelling is supported by photographic surveys which are used for capturing expansive natural surfaces using a wide range of sensors --…
This paper is devoted to the general problem of projection onto a polyhedral convex cone generated by a finite set of generators.This problem is reformulated into projection onto the polytope obtained by simple truncation of the original…
We revisit the gravitational lensing phenomenon using a new visualization technique. It consists in projecting the observers sky into the source plane, what gives rise to a folded and stretched surface. This provides a clear graphical tool…
Precise and reliable climate projections are required for climate adaptation and mitigation, but Earth system models still exhibit great uncertainties. Several approaches have been developed to reduce the spread of climate projections and…