Tensor algebra

1967 ◽  
pp. 61-82
Author(s):  
W. H. Greub
Keyword(s):  
Tensor Algebra

scholarly journals A sparse iteration space transformation framework for sparse tensor algebra

2020 ◽  
Vol 4 (OOPSLA) ◽  
pp. 1-30 ◽  
Author(s):  
Ryan Senanayake ◽  
Changwan Hong ◽  
Ziheng Wang ◽  
Amalee Wilson ◽  
Stephen Chou ◽  
...  
Keyword(s):  
Tensor Algebra ◽  
Iteration Space ◽  
Space Transformation

scholarly journals CONSTRUCTIVE NONCOMMMUTATIVE INVARIANT THEORY

2021 ◽  
Author(s):  
MÁTYÁS DOMOKOS ◽  
VESSELIN DRENSKY
Keyword(s):  
Lie Algebra ◽  
Associative Algebra ◽  
Invariant Theory ◽  
Reductive Group ◽  
Symmetric Tensor ◽  
Free Associative Algebra ◽  
Tensor Algebra ◽  
Enveloping Algebra ◽  
Finite Dimensional ◽  
Degree Bounds

AbstractThe problem of finding generators of the subalgebra of invariants under the action of a group of automorphisms of a finite-dimensional Lie algebra on its universal enveloping algebra is reduced to finding homogeneous generators of the same group acting on the symmetric tensor algebra of the Lie algebra. This process is applied to prove a constructive Hilbert–Nagata Theorem (including degree bounds) for the algebra of invariants in a Lie nilpotent relatively free associative algebra endowed with an action induced by a representation of a reductive group.

scholarly journals Analytical Model of Induction Machines with Multiple Cage Faults Using the Winding Tensor Approach

Sensors ◽  
2021 ◽  
Vol 21 (15) ◽  
pp. 5076
Author(s):  
Javier Martinez-Roman ◽  
Ruben Puche-Panadero ◽  
Angel Sapena-Bano ◽  
Carla Terron-Santiago ◽  
Jordi Burriel-Valencia ◽  
...  
Keyword(s):  
Computational Cost ◽  
Induction Machines ◽  
Diagnostic Techniques ◽  
Analytical Models ◽  
Tensor Algebra ◽  
Diagnostic Systems ◽  
Technical Literature ◽  
Twin Model ◽  
Ring Segment ◽  
The One

Induction machines (IMs) are one of the main sources of mechanical power in many industrial processes, especially squirrel cage IMs (SCIMs), due to their robustness and reliability. Their sudden stoppage due to undetected faults may cause costly production breakdowns. One of the most frequent types of faults are cage faults (bar and end ring segment breakages), especially in motors that directly drive high-inertia loads (such as fans), in motors with frequent starts and stops, and in case of poorly manufactured cage windings. A continuous monitoring of IMs is needed to reduce this risk, integrated in plant-wide condition based maintenance (CBM) systems. Diverse diagnostic techniques have been proposed in the technical literature, either data-based, detecting fault-characteristic perturbations in the data collected from the IM, and model-based, observing the differences between the data collected from the actual IM and from its digital twin model. In both cases, fast and accurate IM models are needed to develop and optimize the fault diagnosis techniques. On the one hand, the finite elements approach can provide highly accurate models, but its computational cost and processing requirements are very high to be used in on-line fault diagnostic systems. On the other hand, analytical models can be much faster, but they can be very complex in case of highly asymmetrical machines, such as IMs with multiple cage faults. In this work, a new method is proposed for the analytical modelling of IMs with asymmetrical cage windings using a tensor based approach, which greatly reduces this complexity by applying routine tensor algebra to obtain the parameters of the faulty IM model from the healthy one. This winding tensor approach is explained theoretically and validated with the diagnosis of a commercial IM with multiple cage faults.

scholarly journals HURWITZ THEOREM AND PARALLELIZABLE SPHERES FROM TENSOR ANALYSIS

2001 ◽  
Vol 16 (25) ◽  
pp. 4207-4222 ◽  
Author(s):  
J. A. NIETO ◽  
L. N. ALEJO-ARMENTA
Keyword(s):  
Clifford Algebra ◽  
Point Of View ◽  
Tensor Analysis ◽  
Tensor Algebra ◽  
Normed Algebra ◽  
Curved Spaces ◽  
Hurwitz Theorem ◽  
Analysis Point

By using tensor analysis, we find a connection between normed algebras and the parallelizability of the spheres S 1, S 3 and S 7. In this process, we discovered the analog of Hurwitz theorem for curved spaces and a geometrical unified formalism for the metric and the torsion. In order to achieve these goals we first develop a proof of Hurwitz theorem based on tensor analysis. It turns out that in contrast to the doubling procedure and Clifford algebra mechanism, our proof is entirely based on tensor algebra applied to the normed algebra condition. From the tersor analysis point of view our proof is straightforward and short. We also discuss a possible connection between our formalism and the Cayley–Dickson algebras and Hopf maps.

Symmetric Tensor Algebra

1978 ◽  
pp. 209-226
Author(s):  
Werner Greub
Keyword(s):  
Symmetric Tensor ◽  
Tensor Algebra

scholarly journals Rayleigh Quotient Methods for Estimating Common Roots of Noisy Univariate Polynomials

2019 ◽  
Vol 19 (1) ◽  
pp. 147-163 ◽  
Author(s):  
Alwin Stegeman ◽  
Lieven De Lathauwer
Keyword(s):  
Eigenvalue Problem ◽  
Simulation Study ◽  
Rayleigh Quotient ◽  
Tensor Algebra ◽  
Symbolic Algebra ◽  
Starting Values ◽  
New Methods ◽  
Sylvester Matrix ◽  
Univariate Polynomials ◽  
The Common

AbstractThe problem is considered of approximately solving a system of univariate polynomials with one or more common roots and its coefficients corrupted by noise. The goal is to estimate the underlying common roots from the noisy system. Symbolic algebra methods are not suitable for this. New Rayleigh quotient methods are proposed and evaluated for estimating the common roots. Using tensor algebra, reasonable starting values for the Rayleigh quotient methods can be computed. The new methods are compared to Gauss–Newton, solving an eigenvalue problem obtained from the generalized Sylvester matrix, and finding a cluster among the roots of all polynomials. In a simulation study it is shown that Gauss–Newton and a new Rayleigh quotient method perform best, where the latter is more accurate when other roots than the true common roots are close together.

scholarly journals TensorLib: A Spatial Accelerator Generation Framework for Tensor Algebra

2021 ◽  
Author(s):  
Liancheng Jia ◽  
Zizhang Luo ◽  
Liqiang Lu ◽  
Yun Liang
Keyword(s):  
Tensor Algebra

Tensor Algebra and Young's Symmetry Operators

1941 ◽  
Vol 63 (3) ◽  
pp. 645 ◽  
Author(s):  
T. L. Wade
Keyword(s):  
Tensor Algebra ◽  
Symmetry Operators
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