Related papers: Flat Maps that improve on the Winkel Tripel

Let R be the set of isomorphism classes of ideals in the Weyl algebra $A=A_{1}$, and let C be the set of isomorphism classes of triples (V; X, Y), where V is a finite-dimensional (complex) vector space, and X, Y are endomorphisms of V such…

We consider here 6-regular plane graphs whose faces have size 1, 2 or 3. In Section 2 a practical enumeration method is given that allowed us to enumerate them up to 53 vertices. Subsequently, in Section 3 we enumerate all possible symmetry…

Let $G$ be a semisimple connected Lie group of non-compact type with finite center. Let $K<G$ be a maximal compact subgroup and $P<G$ be a minimal parabolic subgroup. For any pair $(F,x)$, where $F$ is a maximal flat in $G/K$ and $x \in…

We introduce OpenEarthMap, a benchmark dataset, for global high-resolution land cover mapping. OpenEarthMap consists of 2.2 million segments of 5000 aerial and satellite images covering 97 regions from 44 countries across 6 continents, with…

Given an idempotent complete additive category, we show the there is an explicitly constructed topological space such that the lattice of exact substructures is anti-isomorphic to the lattice of closed subsets. In the special case that the…

We describe the internal photometric calibration of the Deep Lens Survey, which consists of five widely separated fields observed by two different observatories. Adopting the global linear least-squares ("ubercal") approach developed for…

Smartphones, tablets and camera systems used, e.g., in cars and UAVs, are typically equipped with IMUs (inertial measurement units) that can measure the gravity vector accurately. Using this additional information, the $y$-axes of the…

Detecting symmetry is crucial for effective object grasping for several reasons. Recognizing symmetrical features or axes within an object helps in developing efficient grasp strategies, as grasping along these axes typically results in a…

Building on the results of Ma, Trudinger and Wang \cite{MTW}, and of the author \cite{L5}, we study two problems of optimal transportation on the sphere: the first corresponds to the cost function $d^2(x,y)$, where $d(\cdot,\cdot)$ is the…

In 2023, 58.0% of the African population experienced moderate to severe food insecurity, with 21.6% facing severe food insecurity. Land-use and land-cover maps provide crucial insights for addressing food insecurity by improving…

Google Earth is the most popular virtual globe in use today. Given its popularity and usefulness, most users do not pay close attention to the positional accuracy of the imagery, and there is limited information on the subject. This study…

We construct non-trivial continuous isospectral deformations of Riemannian metrics on the ball and on the sphere in $\R^n$ for every $n\geq 9$. The metrics on the sphere can be chosen arbitrarily close to the round metric; in particular,…

In this paper, we introduce some known map projections from a model of the Earth to a flat sheet of paper or map and derive the plotting equations for these projections. The first fundamental form and the Gaussian fundamental quantities are…

Joint estimation of surface normals and depth is essential for holistic 3D scene understanding, yet high-resolution prediction remains difficult due to the trade-off between preserving fine local detail and maintaining global consistency.…

The edge-to-edge tilings of the sphere by congruent quadrilaterals of Type $a^2bc$ are classified as $3$ classes: a sequence of two-parameter families of $2$-layer earth map tilings with $2n$ $(n\ge3)$ tiles, a one-parameter family of…

The construction of the COMBINATORIAL data for a surface with n vertices of maximal genus is a classical problem: The maximal genus g=[(n-3)(n-4)/12] was achieved in the famous ``Map Color Theorem'' by Ringel et al. (1968). We present the…

We provide a preliminary estimate of the performance of reflex astrometry on Earth-like planets in the habitable zones of nearby stars. In Monte Carlo experiments, we analyze large samples of astrometric data sets with low to moderate…

With the explosive deployment of non-terrestrial networks (NTNs), the computational complexity of network performance analysis is rapidly escalating. As one of the most suitable mathematical tools for analyzing large-scale network…

This paper studies a specific metric on plane curves that has the property of being isometric to classical manifold (sphere, complex projective, Stiefel, Grassmann) modulo change of parametrization, each of these classical manifolds being…

We show how the Abel-Jacobi map provides all the principal properties of an ample family of integrable mechanical systems associated to hyperelliptic curves. We prove that derivative of the Abel-Jacobi map is just the St\"{a}ckel matrix,…