For a general affine connection with parallel torsion and curvature, we show that a post-Lie algebra structure exists on its space of vector fields, generalizing previous results for flat connections. However, for non-flat connections, the vector fie...
Consider the smooth sections of the tangent bundle of a reductive homogeneous space. This is a vector space over the field of real numbers. The canonical connection acts as a linear binary operator on this vector space, making it an algebra. If we in...
Feb 4, 2023 · In some of these infinite-dimensional vector spaces, when they're normed, there may be Schauder Bases , where we have infinite sums, which require a notion of convergence.
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Vector graphics are a form of computer graphics in which visual images are created directly from geometric shapes defined on a Cartesian plane, such as points, lines, curves and polygons.
Apr 25, 2025 · The storage of the vector is handled automatically, being expanded as needed. Vectors usually occupy more space than static arrays, because more memory is allocated to handle future …
The meaning of VECTOR is a quantity that has magnitude and direction and that is commonly represented by a directed line segment whose length represents the magnitude and whose …
This is a vector: A vector has magnitude (size) and direction: The length of the line shows its magnitude and the arrowhead points in the direction.
We establish Maximum Principles which apply to vectorial approximate minimizers of the general integral functional of Calculus of Variations. Our main result is a version of the Convex Hull Property. The primary advance compared to results already...
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Let M be a globally Riemannian symmetric space. We prove a duality estimate between pairings of vector fields with divergence zero and and in L^1 with vector fields in a critical Sobolev space on M. As a consequence we get a sharp Calderon-Zygmund es...
We consider the relativistic Schrödinger (Gordon-Klein) equation with a time dependent vector and a scalar potential on a bounded cylindrical domain. Using a standard Geometric Optics Ansatz, we establish a logarithmic stability estimate for the rec...
We consider the problem of estimating the mean of a noisy vector. When the mean lies in a convex constraint set, the least squares projection of the random vector onto the set is a natural estimator. Properties of the risk of this estimator, such as...
Let n >1 be an integer, and G a doubly transitive subgroup of the symmetric group on X={1,...,n}. In this paper we find all linear group representations rho of G on an euclidean vector space V which contains a set of equiangular vector lines GG={<...
Dec 22, 2023 · Persist VectorStoreIndex (LlamaIndex) locally Asked 2 years, 2 months ago Modified 1 year, 7 months ago Viewed 2k times
By comparing two different evaluations of a modified (à la Borcherds) higher Siegel theta lift on even lattices of signature $(r,s)$, we prove Eichler--Selberg type relations for a wide class of negative weight vector-valued mock modular forms. In d...
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The study of Cowen-Douglas operators involves not only operator-theoretic tools but also complex geometry on holomorphic vector bundles. By leveraging the properties of holomorphic vector bundles, this paper investigates the cyclicity of Cowen-Dougla...
It is possible to model vector-borne infection using the classical Ross-Macdonald model. This attempt, however fails in several respects. First, using measured (or estimated) parameters, the model predicts a much greater number of cases than what is...