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Speyer and Sturmfels associated Grobner toric degenerations Gr¨2(Cn)T of Gr2(Cn) witheach trivalent tree T having n leaves. These degenerations induce toric degenerations Mr T of Mr, the space of n or...
The Symplectic Geometry of Polygons in Euclidean Space.
Recently, the Isomap procedure [1] was proposed as a new way to recover a low-dimensional parametrization of data lying on a low-dimensional submanifold in high-dimensional space. The method assumes...
Abstract: For any two configurations of ordered points $p=(p_{1},...,\p_{N})$ and $q=(q_{1},...,q_{N})$ in Euclidean space $E^d$ such that $q$ is an expansion of $p$, there exists a continuous expansi...
To improve the uniform convergence of the classical Lagrange operators of several variables, we construct a new operator with a class of summation factors. It is proved that the new operator converges...
The system of generators of the differential field of all G-invariant differential rational functions of a vector field in the n-dimensional Euclidean space Rn is described for groups G=M(n) and G=SM(...
In a previous work, the authors gave a definition of `front bundles'. Using this, we give a realization theorem for wave fronts in space forms, like as in the fundamental theorem of surface theory. A...
Many sub-Riemannian manifolds like the Heisenberg group do not admit bi- Lipschitz embedding into any Euclidean space. In contrast, the Grushin plane admits a bi-Lipschitz embedding into some Euclidea...
2004Vol.41No.2pp.175-178DOI: Realization of the N(odd)-Dimensional Quantum Euclidean Space by Differential Operators LI Yun and JING Si-Cong Department of Modern Physics...
In this paper, we define a rectifying curve in the Euclidean 4-space as a curve whose position vector always lies in orthogonal complement N\perp of its principal normal vector field N. In particular,...
The Poincar´e superalgebra is introduced from a generalization of the Cartan’s triality principle based on the extension of Chevalley product, between semispinor spaces and even subspaces of the...
We consider some graph type hypersurfaces in a semi-Euclidean space \Bbb Rn+1q and give conditions of the dimension n+1 and the index q when a hypersurface is lightlike, totally geodesic and minimal.
We consider the structure of the surface in the given point, if we vary all its normals in this point.
The purpose of this paper is to obtain a condition for a hypersurface in Euclidean space with belongs to Hessian Tensor and is to give an alternative proof of Otsuki's lemma by applying this condition...

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