Results 221 to 230 of about 208,236 (249)
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Orthogonal and Symplectic Geometries
1990The vector spaces under consideration will generally be of finite dimension over the real number field R or over the complex number field C; we write K for either R or C when reasonings and results are true for both.
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Symplectic and Contact Geometries
1984Many problems in singularity theory (for instance, the classifications of singularities of caustics and of wavefronts and also of determining the singularities in optimization and variational calculus problems) are understandable only in terms of the geometries of symplectic and contact manifolds.
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Symplectic Geometry on Manifolds
1987We understand the symplectic geometry on manifolds not just as the geometry of the symplectic manifolds but as the study of various geometric structures on manifolds where a symplectic vector bundle plays an essential role. In the present chapter, we shall discuss about such structures. Of course, symplectic manifolds are the core of this theory.
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An introduction to symplectic geometry
1994A symplectic form on a vector space V is a skew-symmetric bilinear form α: V × V → R such that \( \tilde \alpha :V \to V^ \star \tilde \alpha (x)(y) = \alpha (x,y) \) is an isomorphism. Here V* denotes the dual of V.
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Programmable interactions and emergent geometry in an array of atom clouds
Nature, 2021Avikar Periwal +2 more
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Study of Virtual Reality Immersive Technology Enhanced Mathematics Geometry Learning
Frontiers in Psychology, 2022Yu-sheng Su, Chin-feng Lai
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Geometry of Symplectic Manifolds
1983Space does not permit a leisurely introduction to the concepts of differential geometry. The reader is assumed to be familiar with the basic ideas. The notation which we have adopted is as follows. For a smooth or \({C^\infty }\) manifold M we let \(A = A\left( M \right)\) denote the ring of \({C^\infty }\) functions on \(M;V = V\left( M \right ...
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The Geometry of Abstraction in the Hippocampus and Prefrontal Cortex
Cell, 2020Silvia Bernardi +2 more
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Geometry-enhanced molecular representation learning for property prediction
Nature Machine Intelligence, 2022Shanzhuo Zhang
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