Search results
Results from the WOW.Com Content Network
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 ...
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
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 ...
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):
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.
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.
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 ...
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.