Euclidean spaces
Qualitative Spatial Logic over 2D Euclidean Spaces Is Not Finitely Axiomatisable
... metric spaces, sound and complete axiomatizations were provided and could be used to detect mistakes in matches (Du et ...2D Euclidean spaces, as shown in the previ- ous sections, these ...
8
Quadratic Hamiltonians on non-Euclidean spaces of arbitrary constant curvature
... Abstract — This paper derives explicit solutions for Rieman- nian and sub-Riemannian curves on non-Euclidean spaces of arbitrary constant cross-sectional curvature. The problem is formulated in the context ...
6
L_1-Biharmonic Hypersurfaces in Euclidean Spaces with Three Distinct Principal Curvatures
... cases. In 1992, I. Dimitri´ c proved that any biharmonic hypersurface in E m (of arbitrary dimension m) with at most two distinct principal curvatures is minimal ([7]). Also, in 1995, T. Hasanis and T. Vlachos have ...
12
From the Lorentz Transformation Group in Pseudo-Euclidean Spaces to Bi-gyrogroups
... pseudo- Euclidean spaces [46], the aim of this article is to study Lorentz transformations in pseudo-Euclidean spaces, where each of the resulting generalized Lorentz transfor- mation group is ...
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Almost Injective Mappings of Totally Bounded Metric Spaces into Finite Dimensional Euclidean Spaces
... It is a classical question in topology, that what kind of topological spaces can be embedded into finite dimensional Euclidean spaces (endowed with the usual Euclidean topology). To motivate ...
12
Spatial reasoning with RCC8 and connectedness constraints in Euclidean spaces
... What, then, would a more conservative approach look like? We have two options. The first is to restrict, by fiat, the domain over which our variables can range to those regular closed sets satisfying certain additional ...
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Quasi-open functions in Euclidean spaces
... Abstract. In this paper we consider the semigroups of quasi-open functions. A function f between topological spaces X and Y is quasi-open if for any non-empty open set U ⊂ X , the interior of f (U ) in Y is ...
5
Compensated convexity methods for approximations and interpolations of sampled functions in Euclidean spaces: theoretical foundations
... Remark 4.2. It is well known that the Euclidean distance function to a nonempty closed set K, i.e., the mapping K 7→ dist(·; K), is Hausdorff–Lipschitz continuous in the sense that |dist(x; K) − dist(x; G)| ≤ dist ...
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Determination of surfaces in three dimensional Minkowski and Euclidean spaces based on solutions of the Sinh Laplace equation
... tial differential equations whose solutions are used to generate surfaces in these types of spaces are known to have soliton solutions and many examples of these have been given [2]. From these types of solutions, ...
12
On the decidability of connectedness constraints in 2D and 3D Euclidean spaces
... This paper investigated topological constraint languages fea- turing connectedness predicates and Boolean operations on regions. Unlike their less expressive cousins, RCC 8 and RCC5, such languages are highly sensitive ...
7
Fine Grained Entity Typing in Hyperbolic Space
... We aim to analyze the effects of hyperbolic and Euclidean spaces when modeling hierarchical in- formation present in the type inventory, for the task of fine-grained entity typing. Since hyper- bolic ...
12
1605.02157.pdf
... Abstract. By assuming a certain localized energy estimate, we prove the existence portion of the Strauss conjecture on asymptotically flat manifolds, possibly exterior to a compact domain, when the spatial dimension is 3 ...
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Limitations of Learning Via Embeddings in Euclidean Half Spaces
... This work addresses the issue of what success guarantees can be proved for SVM like learning, from the assumption that the classification of examples is close to a dichotomy in some concept class of small VC dimension. ...
21
Embedding Text in Hyperbolic Spaces
... Our main contribution is to propose a simpler parametrization of hyperbolic embeddings that al- lows us to train parametric encoders. We avoid the need for a projection step by separately pa- rameterizing the direction ...
11
Cornea_unc_0153D_14968.pdf
... The main part of the research aims at developing a general regression framework for the analysis of a manifold-valued response in a Riemannian symmetric space (RSS) and its association with Euclidean covariates of ...
200
Non Euclidean navigation
... possess Euclidean cognitive maps, constructed on the basis of input from the path integration ...the Euclidean map hypothesis and support the cognitive graph ...Apparently Euclidean behavior, such as ...
10
Improve Adaptive k-Nearest Neighbor Algorithm using Multi-threading
... a ) For each training example, use the Euclidean distance metric to compute the Euclidean distances of it and the rest training examples. b ) Sort the Euclidean dist[r] ...
6
Multiple radial solutions for Dirichlet problem involving two mean curvature equations in Euclidean and Minkowski spaces
... Ma, R., Chen, T.: Multiple positive solutions for Dirichlet problem of prescribed mean curvature equations in Minkowski spaces.. Ma, R., Gao, H., Lu, Y.: Global structure of radial posit[r] ...
10
Registration of Diffusion Tensor Images in Log-Euclidean and Euclidean Space
... To compare or make an atlas from DTI images, it is common to register the sets of diffusion tensors constructed from the diffusion weighted images. When applying geometric transformations to a diffusion tensor, the ...
34
Tangent measure distributions and the geometry of measures
... We have seen in the previous chapter how densities and tangent measures can be used to characterize rectifiabilty of measures. These properties of densities and tangent measures also indicate their limitations as a means ...
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