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  2. Torus interconnect - Wikipedia

    en.wikipedia.org/wiki/Torus_interconnect

    3D Torus: three dimensions, the nodes are imagined in a three-dimensional lattice in the shape of a rectangular prism, with each node connected with its six neighbors, with corresponding nodes on opposing faces of the array connected. Each edge consists of n nodes. communication can take place in six directions, +x, −x, +y, −y, +z, −z ...

  3. Recurrent tensor - Wikipedia

    en.wikipedia.org/wiki/Recurrent_tensor

    An example for recurrent tensors are parallel tensors which are defined by = with respect to some connection .. If we take a pseudo-Riemannian manifold (,) then the metric g is a parallel and therefore recurrent tensor with respect to its Levi-Civita connection, which is defined via

  4. The dual tree hypercomplex wavelet transform (HWT) developed in [9] consists of a standard DWT tensor and 2 m -1 wavelets obtained from combining the 1-D Hilbert transform of these wavelets along the n-coordinates. In particular a 2-D HWT consists of the standard 2-D separable DWT tensor and three additional components: H x {ψ(x) h ψ(y) h ...

  5. Cartesian tensor - Wikipedia

    en.wikipedia.org/wiki/Cartesian_tensor

    A dyadic tensor T is an order-2 tensor formed by the tensor product ⊗ of two Cartesian vectors a and b, written T = a ⊗ b.Analogous to vectors, it can be written as a linear combination of the tensor basis e x ⊗ e x ≡ e xx, e x ⊗ e y ≡ e xy, ..., e z ⊗ e z ≡ e zz (the right-hand side of each identity is only an abbreviation, nothing more):

  6. Riemannian connection on a surface - Wikipedia

    en.wikipedia.org/wiki/Riemannian_connection_on_a...

    In more concrete terms this allows parallel transport to be described explicitly using the transport equation. Parallel transport along a curve c(t), with t taking values in [0,1], starting from a tangent from a tangent vector v 0 also amounts to finding a map v(t) from [0,1] to R 3 such that v(t) is a tangent vector to M at c(t) with v(0) = v 0.

  7. List of numerical libraries - Wikipedia

    en.wikipedia.org/wiki/List_of_numerical_libraries

    De facto standard for matrix/tensor operations in Python. Pandas , a library for data manipulation and analysis. SageMath is a large mathematical software application which integrates the work of nearly 100 free software projects and supports linear algebra, combinatorics, numerical mathematics, calculus, and more.

  8. Parallel axis theorem - Wikipedia

    en.wikipedia.org/wiki/Parallel_axis_theorem

    The parallel axis theorem, also known as Huygens–Steiner theorem, or just as Steiner's theorem, [1] named after Christiaan Huygens and Jakob Steiner, can be used to determine the moment of inertia or the second moment of area of a rigid body about any axis, given the body's moment of inertia about a parallel axis through the object's center of gravity and the perpendicular distance between ...

  9. Tensor software - Wikipedia

    en.wikipedia.org/wiki/Tensor_software

    Tensor [4] is a tensor package written for the Mathematica system. It provides many functions relevant for General Relativity calculations in general Riemann–Cartan geometries. Ricci [5] is a system for Mathematica 2.x and later for doing basic tensor analysis, available for free.